Author Archives: school

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

1.) Assertion: The probability of an event that cannot happen or which is impossible, is equal to zero.

Reason: The probability lies between 0 and 1. Hence, it cannot be negative

a)Both Assertion and Reason are correct and reason is correct explanation for the.

b)Both Assertion and Reason are false but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and reason are false.

Ans: b) both assertion and  reason are correct but  reason is  not correct explanation for assertion.

2.) Assertion: If P(E) = 0.07, then  its  probability of ‘not E’ is 0.93

Reason : P(E) + P(not E) = 1

Since, P(E) = 0.05

 P(not E) = 1 – P(E)

P(not E) = 1 – 0.07P = 0.93

a)Both Assertion and Reason are correct and reason is correct explanation for the.

b)Both Assertion and Reason are false but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

3.) Assertion: . A bag has 3 red balls and 5 green balls. If we take a ball from the bag, then probability of getting red balls only 3/8.

Reason: Probability of getting red balls = number of red balls/total number of balls

a)Both Assertion and Reason are correct and reason is correct explanation for the.

b)Both Assertion and Reason are false but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

4.) Assertion: The sum of the probabilities of all the elementary events of an experiment is 1.

Reason: If an event cannot occur, then its probability is 0.

a)Both Assertion and Reason are correct and reason is correct explanation for the.

b)Both Assertion and Reason are false but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion.

5.) Assertion: The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is 14.

Reason: . If the probability of an event is p, the probability of its complementary event will be 1-p.

a)Both Assertion and Reason are correct and reason is correct explanation for the.

b)Both Assertion and Reason are false but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion.

6.) Assertion: The probability of getting exactly one head in tossing a pair of coins is 1/2.

Reason: The sample space of two coin tossed is ={HH,TT,HT,TH}=4

a)Both Assertion and Reason are correct and reason is correct explanation for the.

b)Both Assertion and Reason are false but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.7

7.) Assertion: The probability of getting a spade card from a well shuffled deck of 52 cards is 13.

Reason: The probability of getting less than 3 in a single throw of a die is 1/3.

a)Both Assertion and Reason are correct and reason is correct explanation for the.

b)Both Assertion and Reason are false but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion.

8.) Assertion: -0.4 can not be the probability of an event.

Reason: The probability of an event can neither be a negative value, nor it can exceed unity.

a)Both Assertion and Reason are correct and reason is correct explanation for the.

b)Both Assertion and Reason are false but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

9.) Assertion: Three coins are tossed simultaneously. The probability of getting all heads is 1/8.

Reason: The chance of throwing 5 with an ordinary die is 1/6.

a)Both Assertion and Reason are correct and reason is correct explanation for the.

b)Both Assertion and Reason are false but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion.

10) Assertion: The probability of getting a prime number when a die is thrown once is 2/3.
Reason: Prime numbers on a die are 2, 3, 5.

Answer: (d)

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

1.) Assertion: The runs scored by a batsman in 5 ODIs are 31,97,112, 63, and 12. The standard deviation is 25.79.

Reason: mean = total sum of number in data sets./ total number in data sets.

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: a) both assertion and  reason are correct but  reason is  not correct explanation for assertion.

 2.) Assertion: the mode of the call received on 7 consecutive day 11,13,13,17,19,23,25 is 13.

Reason: Mode is the value that appears most frequent;

a)Both Assertion and Reason are correct and reason is correct explanation for the.

b)Both Assertion and Reason are false but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and reason are false.

Ans: a) both assertion and  reason are correct but  reason is  not correct explanation for assertion.

3.) Assertion: Frequency is the number of times a particular observation occurs in data.

Reason: Data can be grouped into class intervals such that all observations in that range belong to that class.

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion.

4.) Assertion: Class width = upper class limit – lower class limit

Reason: Class mark =(Upper Class Limit+ Lower Class Limit)/2

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion.

5) Assertion: If the value of mode and mean is 60 and 66 respectively, then the value of median is 64.

Reason: Median = (mode + 2 mean)/2

Answer: (c)

6) Assertion: The arithmetic mean of the following given frequency distribution table is 13.81.

Reason: x̅ = ∑ f_i x_i / ∑f_i 

Answer: (a)

7) Assertion: If the number of runs scored by 11 players of a cricket team of India are 5, 19, 42, 11, 50, 30, 21, 0, 52, 36, 27 then median is 30.

Reason: Median = (n+1)/2, if n is odd.

Answer: (d)

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

1.) Assertion: The radius of the top and bottom of a bucket of slant height 35 cm are 25 cm and 8 cm. The curved surface of the bucket is 3630 sq.cm.

Reason: Curved surface of bucket = π(R1 + R2) x slant height (l)

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d)Both Assertion and reason are false.

Ans: a) both assertion and  reason are correct and reason is correct explanation for assertion.

2.) Assertion: If we join two hemispheres of same radius along their bases, then we get a sphere.

Reason: A tank is made of the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and radius is 30 cm. The total surface area of the tank is 3.3 m

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: b) both assertion  and reason  are  correct  but  reason is  not  correct  explanation  for  assertion

3.) Assertion: Two identical solid cubes of side a are joined end to end. Then the total surface area of the resulting cuboid is 10a^2

reason: The total surface area of a cube having side a = 6a2

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

4.) Assertion: Number of spherical ball that can be made out of a solid cube lead whose edge is 44cm each ball being 4 cm in diameter is 2541

Reason: Number of balls = ( volume of one ball )/( volume of lead)

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: c) assertion  is  true  but  reason  is  false.

5.) Assertion: The volume of two sphere are in the ratio 27: 8 then yes surface area in the ratio 3:2 .

Reason: Volume of sphere=4/3 pie r^3 and it’s surface area 4 pie r^4

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: d) both assertion and reason are false.

6.) Assertion: The number of solid sphere of diameter  6 cm can be made by a melting a solid metallic  cylinder of height 45 cm and diameter 4 cm is 5 .

Reason: if three solid metallic spherical  balls of radius 3,4,5 cm are melted into single spherical ball then its radius is 6 cm.

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is correct explanation for assertion.

7.) Assertion: if three cubes of Iron whose edges are 3cm,4cm, and 5cm are melted and formed into a single cube then the edge of single cube is 6 cm.

Reason:  12 solid spheres of same size  are made by melting  a solid metallic cone of base radius 1 cm and height of 48cm then the radius of each sphere is 2 cm.

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: c) assertion is correct but reason is false.

8.) Assertion: If a solid sphere of radius r is melted snd recast into the shape of right circular cylinder  of radius 0.5 cm then the height of cylinder is 8 cm.

Reason: if a metallic sphere of total volume n is melted and recast into the shape of right circular cylinder of radius 0.5 cm then the height of cylinder is 8 cm .

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: c) assertion is correct but reason is false.

9.) Assertion: Savitri had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope. 550cm^2 would be the area of chart paper required by her, if she wantedto make a kaleidoscope of length 25 cm with a 3.5 cm radius.

Reason: Area of chart paper required = curved surface area of the kaleidoscope= 2πrh

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

10.) Assertion: if we have a cuboid whose length, breadth and height are 15 cm,10 cm and 20 cm respectively, then its surface area would be 1300 cm^2.

Reason: surface area of cuboid = 2(lb+bh+lh)

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

11.) Assertion: The curved surface area of a right circular cone whose slant height

is 10 cm and base radius is 7 cm.

Reason: Curved surface area = pie *r*l

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

12.)Assertion: The height of a cone is 16 cm and its base radius is 12 cm.  The

curved surface area and the total surface area of the cone is 753.6cm^2,1205.76cm^2

Reason: Curved surface area of cone = 2*pie*r*l and total surface area of cone = pie*r*l+pie *r^3

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: c) assertion is correct but reason is false.

13.) Assertion: : A shot-putt is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g per cm3 the mass of the shot-put 3.85 kg.

Reason:  volume of the sphere = (4/3)πr^3

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

14.) Assertion: The lateral surface area of a right circular cone of height 28 cm and base radius 21 cm(in sq. cm) is2310 cm^2.

Reason: Lateral surface area = πrl^2.

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false.

Ans: c) assertion is correct but reason is false.

15.) Assertion:  A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is 1 m, 463.39cm^2 is the area of cloth required.

Reason: Surface area of hemisphere = 2πr^2

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

16.) Assertion: Radius 6cm, height 7cm then the volume of right circular cone is 264cm^3.

Reason: Volume of a right circular cone = 1/3 πr^2h

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

17.) Assertion: The height of a cone is 15 cm. If its volume is 500π cm3, then 10 cm the radius of its base.

Reason: volume of hemisphere = 2/3*pier^3

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion.

18.) Assertion: Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the
cone.

Reason: Top is obtained by fixing the plane surfaces of the hemisphere and cone together.

a) Both Assertion and Reason are correct and reason is correct explanation for the.

b) Both Assertion and Reason are false but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and reason are false

Ans. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

Q.1. Assertion (A): In a circle of radius 6 cm, the angle of a sector is 60°. Then the area of the sector is 132/7 cm².
Reason (R): Area of the circle with radius r is πr².

Answer: (b)

Q.2. Assertion (A): If the circumference of a circle is 176 cm, then its radius is 28 cm.
Reason (R): Circumference = 2π × radius.

Answer: (a)

Q.3. Assertion (A): If the outer and inner diameter of a circular path is 10 m and 6 m respectively, then area of the path is 16πm².
Reason (R): If R and r be the radius of outer and inner circular path respectively, then area of circular path = π(R² – r²).

Answer: (a)

Q.4. Assertion (A): The length of the minute hand of a clock is 7 cm. Then the area swept by the minute hand in 5 minute is 77/6 cm².
Reason (R): The length of an arc of a sector of angle q and radius r is given by

Answer: (b)

5) Assertion (A): In the figure, C1 and C2are two circles with radii 7 cm and 5 cm respectively, then area of shaded portion is 24πcm2 .              

Reason (R): When two circles touch internally, the distance between their centres is equal to sum of their radii.

A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)

B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)

C) Assertion (A) is true but Reason (R) is false

D) Assertion (A) is false but Reason (R) is true

Correct Answer: C

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Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

1.) Assertion: a, b and c are the lengths of three sides of a triangle, then a+b > c

Reason: The sum of two sides of a triangle is always greater than the third side.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

2) Assertion: The side lengths 4cm, 4cm and 4cm can be sides of equilateral triangle

Reason: : Equilateral triangle has all its three sides equal

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

3) Assertion: To construct an angle of 60 degrees, we need to draw first a ray

Reason: To construct an angle of 60 degrees we need to start at the initial point of a ray.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

4) Assertion: The construction of a triangle ABC in which AB = 4 cm, ∠A = 60° is not possible when the difference of BC and AC is equal to 4.5

Reason: the difference of any two sides of a triangle cannot be greater than the third side.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

5) Assertion: The side length of 2 cm, 3 cm, and 4 cm can be the sides of Scalene triangle

Reason: the sides of a scalene triangle, as all the sides have different measurements.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d both Assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

6) Assertion: The internal and external bisectors of an angle forms a right angle

Reason: the bisector always divides an angle in two equal parts.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d both Assertion and reason are false

Ans: c) Assertion is true but reason is false

7) Assertion: bisector of angle divide the angle in two equal parts.

Reason: Every angle has an angle bisector.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d both Assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for the Assertion

8) Assertion: All the points of angle bisector are equidistant from both the arms of the angle

Reason: An angle bisector can be drawn to any angle, such as acute, obtuse, or right angle

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d both Assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for the Assertion

9) Assertion: The perpendicular bisector of the line is Perpendicular to the line

Reason: Perpendicular bisector passes through the midpoint of a line segment.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d both Assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for the Assertion

10) Assertion: The starting point of the ray is called vertex

Reason: A ray does not have a height or width

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d both Assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for the Assertion

11) Assertion: When two lines crosses each other at a common point then this lines are called intersecting line.

Reason: Intersecting lines meet at a single point, they can meet at more than one point.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d both Assertion and reason are false

Ans: c) Assertion is true but reason is false

12) Assertion: Intersecting lines meet at a single point, they cannot meet at more than one point.

Reason: When two lines crosses each other at a common point then this lines are called intersecting line

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d) both Assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

13) Assertion: When two straight lines intersect each other at a right angle in a common point then that lines are called as perpendicular line

Reason: The angle between any two perpendicular lines is always equal to 90. °

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d) both Assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

14) Assertion: The lines which do not intersect each other and can be extended to infinity in a plane then this lines are called as parallel lines.

Reason: The parallel lines meet at the point of infinity.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d) both Assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

15) Assertion: The lines which are not parallel and also does not intersect are called as skew line.

Reason: Lines that are non-intersecting, non-parallel, and non-coplanar are skew lines.

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is true but reason is false

d) both Assertion and reason are false

Ans: b)

    

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

1) Assertion: AB and CD are two parallel chords of a circle whose diameter is AC. Then AB ≠ CD.

Reason : Perpendicular from the centre of a circle does not bisects the chord.

a)both Assertion and Reason are correct  and Reason is the correct explanation of Assertion.

(b) Assertion and Reason both are correct  but Reason is not the correct explanation of Assertion.

(c) Assertion is correct  but Reason is false

(d)  both assertion and reason are wrong.

Ans: d) both assertion and reason are false

2.) Assertion: Angles in the same segment of a circle are equal.

Reason: In cyclic quadrilateral, opposite angles are supplementary.

a)both Assertion and Reason are correct  and Reason is the correct explanation of Assertion.

(b) Assertion and Reason both are correct  but Reason is not the correct explanation of Assertion.

(c) Assertion is correct  but Reason is false

(d)  both assertion and reason are wrong.

Ans: b)both assertion and reason are correct and reason is correct explanation for assertion.

3 ) Assertion: Perpendicular bisectors of two chords of a circle intersect at its centre.

Reason: : A line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

a)both Assertion and Reason are correct  and Reason is the correct explanation of Assertion.

(b) Assertion and Reason both are correct  but Reason is not the correct explanation of Assertion.

(c) Assertion is correct  but Reason is false

(d)  both assertion and reason are wrong.

Ans: b) both assertion and reason are correct and reason is correct explanation for assertion.

4) Assertion: If a sector of a circle of diameter 21 cm subtends an angle of 120° at the centre, then its area is 85.5cm^2

Reason:. In a circle of radius 21 cm, an arc substends an angle

of 60° the centre the length of the arc is 22 cm.

a)both Assertion and Reason are correct  and Reason is the correct explanation of Assertion.

(b) Assertion and Reason both are correct  but Reason is not the correct explanation of Assertion.

(c) Assertion is correct  but Reason is false

(d)  both assertion and reason are wrong.

Ans: b) both assertion and reason are correct and reason is correct explanation for assertion.

5) Assertion: Area of a segment of a circle is less than the area of its corresponding sector.

Reason: The area of the circle inscribed in a square of side a cm, πa^2 cm^2.

a)both Assertion and Reason are correct  and Reason is the correct explanation of Assertion.

(b) Assertion and Reason both are correct  but Reason is not the correct explanation of Assertion.

(c) Assertion is correct  but Reason is false

(d)  both assertion and reason are wrong.

Ans: d) both assertion and reason are false.

6) Assertion: Perimeter of a semi circle , (πr+d) units.

Reason: Area of circle is πr^2

a)both Assertion and Reason are correct  and Reason is the correct explanation of Assertion.

(b) Assertion and Reason both are correct  but Reason is not the correct explanation of Assertion.

(c) Assertion is correct  but Reason is false

(d)  both assertion and reason are wrong.

Ans: b) both assertion and reason are correct and reason is correct explanation for assertion.

7) Assertion: If the circumference of a circle is 88 cm, then its radius is 14 cm.

Reason: 2π r is circumference of a circle.

a)both Assertion and Reason are correct  and Reason is the correct explanation of Assertion.

(b) Assertion and Reason both are correct  but Reason is not the correct explanation of Assertion.

(c) Assertion is correct  but Reason is false

(d)  both assertion and reason are wrong.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

8) Assertion: measure of an semicircle of an angle is 90°

Reason: Concentric circles are circles having same centre.

a)both Assertion and Reason are correct  and Reason is the correct explanation of Assertion.

(b) Assertion and Reason both are correct  but Reason is not the correct explanation of Assertion.

(c) Assertion is correct  but Reason is false

(d)  both assertion and reason are wrong.

Ans: b) both assertion and reason are correct but  reason is not correct explanation for assertion.

9) Assertion: If length of a tangent from an external point to a circle is 8 cm, then length of the other tangent from
the same point is 8 cm.
Reason: length of the tangents drawn from an external point to a circle are equal.

Answer: (a)

10) Assertion: If in a cyclic quadrilateral, one angle is 40°, then the opposite angle is 140°
Reason: Sum of opposite angles in a cyclic quadrilateral is equal to 360°

Answer: (c)

    

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

1) Assertion: The angle of elevation of an object viewed, is the angle formed by the line of sight with the horizontal when it is above the horizontal level.

reason: The angle of depression. of an object viewed, is the angle formed by the line of sight with the horizontal when it is below the horizontal level.

a) Both assertion and reason are correct and reason is correct explanation for assertion.

b) Both Assertion and Reason are correct but reason is not correct explanation for assertion.

c) Assertion is correct but reason is false.

d) Both Assertion and Reason are false.

Ans: b) both assertion and reason are correct and reason is correct explanation for assertion.

2) Assertion: The line of sight  is the line drawn from the eye of an observer to the point in the object viewed by the observer.

 reason: trigonometric ratios are used to find height or length of an object or distance between two distant

a) Both assertion and reason are correct and reason is correct explanation for assertion.

b)Both Assertion and Reason are correct but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and Reason are false.

Ans: b) both assertion and reason are correct and reason is correct explanation for assertion.

3) Assertion: If the length of shadow of a vertical pole is  equal to its height, then the angle of elevation of the  sun is 45°

Reason : According to pythagoras theorem, h^2=l^2+b^2 , where h = hypotenuse, l = length and b = base

a)Both assertion  and  reason are correct and reason is correct explanation for assertion.

b)Both Assertion and Reason are correct but reason is not correct explanation for assertion.

c)Assertion is correct but reason is false.

d)Both Assertion and Reason are false.

Ans: b) both assertion and reason are correct and reason is correct explanation for assertion.

4)Assertion: If the length of shadow of a vertical pole is equal to its height, then the angle of elevation of the sun is 45°.
Reason: According to Pythagoras theorem, h² = l² + b², where h = hypotenuse, l = length and b = base

Answer: (b)

5) Assertion: In the figure, if BC = 20 m, then height AB is 11.56 m.

Reason: tanθ = AB/BC = perpendicular/base, where θ is the angle ∠ACB

Answer: (a)

6)

7)

    

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

1.) Assertion: The value of cosec 30°+cot45°is 3.

Reason: cosec 30°=2, cot 45°=1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

2.) Assertion: If    =45° then the value of cosec^2     is 2.

Reason: cosec ^2 45°=( 2 ^1/2) 2 =2

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

3.) Assertion: if tanθ=cotθ then the value of secθ is 2^1/2.

Reason: tanθ=cotθ

tan^2θ=1 =tanθ=1

θ=45°

∴sec45°= 2^1/2

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

5.) Assertion: The value of sinA is always less than 1

Reason: SinA is the product of sin and A

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason  are  false.

Ans: c) assertion  is true but reason  is  false.

6.) Assertion: 2 tan^245° + cos^230° – sin^260° is 2

Reason: The value of sin60°cos30° + sin30° cos60° is 1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) Both Assertion and Reason are correct but Reason is not  the correct explanation for Assertion.

7.) Assertion: cosecA is the abbreviation used for cosecant of angle A.

Reason: cotA is the product of cot and A.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason  are  false.

Ans: c) assertion  is true but reason  is  false.

8.) Assertion: ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of tan C is 24/7

Reason: tan C = Opposite side/Adjacent side

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

9) Assertion:The value of tan 60°/cot 30° is equal to1.

Reason: tan 60° = √3 and cot 30° = √3

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

10.) Assertion: 1 – cos^2A is equal to sin^2A.

Reason: sin^2A + cos^2A = 1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

11.) Assertion: 2 tan 30°/(1 + tan^230°) =sin60°

Reason : tan 30° = 1/√3

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

12.) Assertion: sin 2A = 2 sin A is true when A =0°

Reason: sin 2A = sin 0° = 0

2 sin A = 2 sin 0° = 0

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

13.) Assertion: The maximum value of 1/cosecα is 1.

Reason: If cosec θ – cot θ = 13, the value of (cosec θ + cot θ) is 3.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

14.) Assertion: Reciprocal of sinθ is cosecθ

Reason: The value of sin θ  increases as θ  increases.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

15.) Assertion: cotA is not defined for A = 0°

Reason: sin θ=cos θ for all values of θ.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason  are  false.

Ans: c) assertion  is true but reason  is  false.

16.) Assertion: If sin30° = 1/2 ,cos30°=(3^1/2)/2 then the value of tan30°is 1/(3)^1/2.

Reason: tan30°=sin30°/cos30°

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

17.) Assertion: In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals= 1

Reason: cosec A (sin B cos C + cos B sin C)

= cosec A × sin(B+C) = cosec A × sin(180 – A)

= cosec A × sin A = cosec A × 1/cosec A

= 1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

18.) Assertion: If tan A = 1/2 and tan B = 1/3, then the value of A + B is π/4

Reason: tan(A + B) = (tan A + tan B)/(1 – tan A tan B)

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

19.) Assertion: The value of sin 50° – sin 70° + sin 10° is equal to 0.

Reason: sin(A – B) = sin A cos B – cos A sin B

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

20.) Assertion: The value of 4 × sin x × sin(x + π/3) × sin(x + 2π/3) is sin3x.

Reason: cos a + 2cos b + cos c = 2 then a, b, c are in 2b=a+c

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

21.) Assertion: The value of cos² 48° – sin²12° is √5 + 1/8.

Reason: If tan x = (cos 9 + sin 9)/(cos 9 – sin 9), then x =45

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

22.) Assertion: In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals 1.

Reason: If sin A = 3/4, then  cos A= √7/4and tan A= 3/√7

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b.) Both Assertion and Reason are correct but Reason is not  the correct explanation for Assertion.

22) Assertion: The value of sin60⁰ cos30⁰ + sin30⁰ cos60⁰ is 1
Reason: sin90⁰=1 and cos90⁰=0

Answer: (b)

23) Assertion: The value of 2tan²45⁰+cos²30⁰-sin²60⁰ is 2.
Reason: value of tan45⁰=1, cos30⁰=√3/2 and sin60⁰=√3/2.

Answer: (a)

    

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

1.) Assertion :The distance point P(2,3) from the x-axis is 3.

Reason: The distance from x-axis is equal to its ordinary.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion

2.) Assertion: The points (-5, 1), (1, p) and (4, -2) are collinear if the value of p is-1.

Reason: The points are collinear if area of Δ = 0

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

3.) Assertion: The area of triangle having vertices are A(3,1) B(12,2) C(0,2) is 6 units.

Reason: Area of triangle = 1/2{x1(y2-y3)+x2(y3-y1)+x3(y1-y2)}

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

4.) Assertion: The point (4, 0) lies on y-axis.

Reason : The x-coordinate on the point on y-axis is not zero.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: d) both assertion  and  reason  are  false.

5.) Assertion: The point (3,0) lies on x-axis.

Reason (R): The y-coordinate on the point on x-axis is zero.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

6.) Assertion: The point(6,0) lies on x-axis.

Reason: the point (0,7) lies on y-axis.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.         

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.     

12.) Assertion:  The points A (–1, 0), B (3, 1), C (2, 2) and D (–2, 1) are the vertices of a parallelogram.

Reason: The coordinates of the mid-points of both the diagonals AC and BD are 1/2,1

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.     

13.) Assertion:  the mid-point of the line segment joining the points A (3, 4) and B (k, 6) is P (x, y) and x + y – 10 = 0, the value of k is 7

Reason: mid point of line segment is( (x1+x2)/2,(y1+y2)/2)

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for assertion.     

14.) Assertion: The distance of a point from the x -axis is its ordinate.

Reason: The distance of a point from the y-axis is called its x-coordinate,

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is  not correct explanation for assertion.     

15.) Assertion:  The abscissa of point in the third quadrant is always negative.

Reason: The x coordinate of point in 2nd quadrant is always negative.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) assertion is correct but reason is false.

16.) Assertion: The abscissa and ordinate of a point in IV quadrant have different sign.

Reason: The abscissa and ordinate of a point in IV quadrant

have same sign.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) assertion is correct but reason is false.

17.) Assertion:  The point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio2 :7 externally.

Reason : Three points A B and C are collinear if area of  triangle ABC is not equal to  0.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: d) both assertion and reason are false.

18.) Assertion. If area of triangle is non zero that means points are non collinear.

Reason : : Mid-point of a line segment divides line in the ratio 1 : 1

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is  not correct explanation for assertion.    

19.) Assertion:  Centroid of a triangle ABC with vertices A(x1,y1),B(x2,y2),C(x3,y3) is given by ((x1+x2+x3)/3,(y1+y2+y3)/3)

Reason: Centroid of a triangle formed by the point(a,b),(b,c),(c,a) is at origin then a+b+c=0

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and  reason is   correct explanation for assertion.  

20.) Assertion: The points (1,5) lies on the perpendicular bisectors of line segment joining the points p(6,5) Q(1,10)

Reason : the ordinate of points A  on y axis  is 5 and B has coordinates(-3,1) then the length of AB is 5 units.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is  not correct explanation for assertion.    

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

1.) Assertion : a right triangle, means  the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Reason: if one side of right angle is 8 cm and other is 6cm then the remaining side will be 10 cm.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

3.) Assertion: Scalene Triangle is the triangle whose All the sides and angles are unequal.

Reason: Triangle ABC is a scalene  triangle whose side are AB=5,BC=8,AC=4.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

4.) Assertion: All congruent triangles are similar but the similar triangles need not congruent

Reason: : If ∆ABC and ∆PQR are congruent triangles, then they are also  different triangles.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: d) both assertion  and reason are false.

5.) Assertion: The ratio of the areas of two similar triangles is equal to the square root of the ratio of their sides.

Reason : The sides of two similar triangles are in the ratio 4 : 25, then the areas of these triangles are in the 2: 5.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: d) both assertion  and reason are false.

6.) Assertion (A): If two sides of a right angle are 7 cm and 8 cm, then its third side will be 9 cm.
Reason (R): In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Answer: (d)

7) Assertion (A): If ∆ABC and ∆PQR are congruent triangles, then they are also similar triangles.
Reason (R): All congruent triangles are similar but the similar triangles need not be congruent.

Answer: (a)

8) Assertion (A): In the given figures, ΔABC ~ ΔGHI.
Reason (R): If the corresponding sides of two triangles are proportional, then they are similar.

Answer: (a)

9) Assertion (A): The sides of two similar triangles are in the ratio 2 : 5, then the areas of these triangles are in the
ratio 4 : 25.
Reason (R): The ratio of the areas of two similar triangles is equal to the square of the ratio of their sides.

Answer: (a)

10)

Assertion (A): In the given figure, PA || QB || RC || SD.
Reason (R): If three or more line segments are perpendiculars to one line, then they are parallel to each other.

Answer: (a)

11) Assertion (A): In the ∆ABC, AB = 24 cm, BC = 10 cm and AC = 26 cm, then ∆ABC is a right angle triangle.
Reason (R): If in two triangles, their corresponding angles are equal, then the triangles are similar.

Answer: (b)