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: Sum of natural number from 1 to 100 is 5050

 reason: Sum of n natural number is n(n+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

2.) Assertion: Sum of fist n terms in an A.P. is given by the formula: Sn = 2n×[2a+(n−1)d]

reason: Sum of first 15 terms of 2+5+8——- is 345.

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 constant difference between any two terms of an AP is commonly known as common difference

Reason: the common difference of 2,4,6,8 this A.P. sequence is 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: Arithmetic progression is a sequence of numbers in which the difference of any two adjacent terms is constant.

Reason :4,8,12,16 this sequence is an A.P.

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

6.) Assertion: If numbers a,b,c are in A.P then b-a=c-b

reason: given three numbers are in AP, then the common difference will be same.

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

7.) Assertion: The sum of series with the nth term tn= (9-5n) is 220 when no. of terms n=6

reason : Sum of first n terms in an A.P. is given by the formula: Sn = 2n×[2a+(n−1)d]

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

 8.)Assertion: An AP containing a finite number of terms is called finite AP

Reason: 3,5,7,9,11,13,15,17,19,21 is an finite AP

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 n, if a = 10, d = 5, an = 95.

Reason: the  formula of general term an is an= a+(n-1)d.

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: arithmatic between 5 and 90 is 47.5

Reason: arithmatic between two given number a,b is (a+b)/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

11.) Assertion: The 11 th term of an AP is 7,9,11,13_________is 67

Reason: if sn is the sum of first n terms of an AP then its nth term an is given by an=sn+sn-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 false.

12.Assertion : Let the positive numbers a, b, c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.
Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.

Answer: (a)

13.Assertion : If S_n is the sum of the first n terms of an A.P., then its nth term an is given by a_n = S_n – S_{n – 1} .
Reason : The 10th term of the A.P. 5, 8, 11, 14, ………………. is 35.

Answer: (c)

14. Assertion : The sum of the series with the nth term, t_n = (9 – 5n) is (465), when no. of terms n = 15.
Reason : Given series is in A.P. and sum of n terms of an A.P. is

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

Q.1. Assertion: If one root of the quadratic equation 6x² – x – k = 0 is 2/3, then the value of k is 2.
Reason: The quadratic equation ax² + bx + c = 0, a ≠ 0 has almost two roots.

Q.2. Assertion: (2x – 1)² – 4x² + 5 = 0 is not a quadratic equation.
Reason: An equation of the form ax² + bx + c = 0, a ≠ 0, where a, b, c ∈ R is called a quadratic equation.

Answer:

Q.3. Assertion: The roots of the quadratic equation x² + 2x + 2 = 0 are imaginary
Reason: If discriminant D = b² – 4ac < 0 then the roots of quadratic equation ax² + bx + c = 0 are imaginary.

Answer:

Q.4. Assertion: 3x² – 6x + 3 = 0 has repeated roots.
Reason: The quadratic equation ax² + bx + c = 0 have repeated roots if discriminant D > 0.

Answer:

Q5. Assertion: x²+x³+2 has no quadratic equation.

     Reason: it has degree 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

Q6. Assertion: If one root of the quadratic equation 2x² + kx – 6 = 0 is 2, the value of k is -1

Reason: x = 2 is a root of the equation 2x² + kx -6 = 0

∴ 2(2)² +k(2) – 6 = 0

⇒ 8 + 2k – 6 = 0

⇒ 2k = -2

∴ k = -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

Q7. Assertion: The roots of the equation 7x² + x – 1 = 0 are real and distinct

     Reason : if b²-4ac >0 then roots are real and distinct.

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

Q8.Assertion: Every quadratic equation has at most two root

Reason: Every quadratic equation has atleast one real root.

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.

Q9. Assertion: 4x² – 12x+ 9= 0 has repeated roots.

Reason : The quadratic equation ax²+ bx² + c = 0 have repeated roots if discriminant D > 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: c) Assertion  is  correct but reason is false

Q10. Assertion: Any equation of the form ax²+ bx+c = 0 where a not equal to  0, is called a quadratic equation

Reason: The equation x² +3x+1=(x-2)² is a quadratic equation .

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.

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 pairs of equations x+2y-5 = 0 and -4x-8y+20=0 have infinitely many solution.

Reason: if a1/a2 = b1/b2 = c1/c2 then  the pair of equations has infinitely many solutions.

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

b) both assertion and reason are correct but reason is 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 a pair of linear equations is consistent, then the lines are intersecting or coincident

Reason: Because the two lines definitely have a solution.

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

b) both assertion and reason are correct but reason is 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: The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have no solution.

Reason: a1/a2 = b1/b2 ≠ c1/c2 So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.

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

b) both assertion and reason are correct but reason is 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: If the lines 3x+2ky – 2 = 0 and 2x+5y+1 = 0 are parallel, then  the value of k is 15/4

Reason: The condition for parallel lines is a1/a2 = b1/b2 ≠ c1/c2

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

b) both assertion and reason are correct but reason is 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

5) Assertion: If one equation of a pair of dependent linear equations is -3x+5y-2=0. The second equation will be -6x+10y-4=0

Reason: The condition for dependent linear equations is a1/a2 = b1/b2 = c1/c2

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

b) both assertion and reason are correct but reason is 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

6) Assertion: The angles of cyclic quadrilaterals ABCD are: A = (6x+10), B=(5x)°, C = (x+y)° and D=(3y-10)°. The value of x and y is 20° and 30°

Reason: in cyclic quadrilaterals, the sum of the opposite angles are 180°.

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

b) both assertion and reason are correct but reason is 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) Assertion: The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has infinitely many solution.

Reason: a1/a2 = b1/b2 ≠ c1/c2 it satisfy the condition of infinitely many solution .

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

b) both assertion and reason are correct but reason is 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: The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have unique solution

Reason: an equations a1/a2= b1 /b2 = c1/c2 Hence, the given pair of equations have no solution

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

b) both assertion and reason are correct but reason is 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

9) Assertion: The graphical representation of a pair of equations 4x + 3y – 1 = 5 and 12x + 9y = 15 will be parallel lines.

Reason: if the the given pair of equations has no solution.That means, the lines representing the given pair of equations are parallel to each other.

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

b) both assertion and reason are correct but reason is 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: a1x+b1y+c1=0; a2x+b2y+c2=0 represent parallel line if  a1/a2 = b1/b2 ≠ c1/c2

Reason: 3x+4y+5=0 and 6x+ky+9=0 represent parallel line if K= 5

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

b) both assertion and reason are correct but reason is 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.

11) Assertion: The given pair of linear  equations are inconsistent

−3x−4y−12=0 and 3x+4y−12=0

Reason:  if a1/a2 = b1/b2 ≠ c1/c2  the the pair of linear equation is inconsistant

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

b) both assertion and reason are correct but reason is 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: A straight line is just a line with no curves.

Reason: a line that extends to both sides till infinity and has no curves is called a straight 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 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

13) Assertion: a pair of line given by ax^2+2hxy+by^2+2gx+2fy+c=0 are perpendicular if a-b=0

Reason: the equation 2x^2+3xy-2y^2+5x-5y+3=0 is not represent a pair of perpendicular straight 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 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.

13) Assertion:  lines are x+2y−4=0 and 2x+4y−12=0 the graphical representation of line is parallel line.

Reason: if pair of given lines are parallel then a1/a2=b1/b2≠ c1/c2

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

b) both assertion and reason are correct but reason is 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 two linear equations in the same two variables X and Y are called pair of linear equation in two variable

Reason: The equation of the form ax + by + c= 0 where a and b both are not zero is called linear equation in two variable

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

b) both assertion and reason are correct but reason is 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

15) Assertion: The two lines intersect each other in a single point

Reason: The two lines are not intersecting that means these lines are parallel to each other

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

b) both assertion and reason are correct but reason is 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

16) Assertion: The slope of the line 2x-y= 0 is 2

Reason: The slope of the line which lies in first and third quadrant is positive

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

b) both assertion and reason are correct but reason is 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 slope of the line which lies in the second and fourth quadrant is negative.

Reason: The slope of the line y= -x +6 is-1

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

b) both assertion and reason are correct but reason is 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

18) Assertion: only one line passes through two points

Reason: the line will connect the two points as one as the initial and another point as the ending 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 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

19) Assertion: If the lines given by3x + 2ky = 22x + 5y + 1 = 0 are parallel, then the value of k is 15/4

Reason: For parallel lines a1/a2=b1/b2≠ c1/c2

3/2= 2k/5

K=15/4

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

b) both assertion and reason are correct but reason is 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

20)Assertion: If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is inconsistent

Reason:  pair of linear equation is given by a₁x+ b₁y+ c₁=0 and a₂x +b₂y +c₂=0 a1/a2=b1/b2≠ c1/c2  In this case,the pair of linear equations is consistent

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

b) both assertion and reason are correct but reason is 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

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: x²+7x+12 has no real zeroes.
Reason: A quadratic polynomial can have at the most two zeroes.

Answer: (d)

2.) Assertion: If the sum of the zeroes of the quadratic polynomial x^2-2kx+8 is 2 then value of k is 1.

Reason: Sum of zeroes of a quadratic polynomial ax^2+bx+c is-b/a

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

3.)Assertion: If the sum of the zeroes of the quadratic polynomial x²-2kx+8 is 2 then value of k is 1.
Reason: Sum of zeroes of a quadratic polynomial ax²+bx+c is -b/a

Answer: (a)

4.)Assertion: P(x) = 4x³-x²+5x⁴+3x-2 is a polynomial of degree 3.
Reason: The highest power of x in the polynomial P(x) is the degree of the polynomial.

Answer: (d)

5.) Assertion: x³+x has only one real zero.
Reason: A polynomial of nth degree must have n real zeroes.

Answer: (c)

6.)Assertion: If one zero of polynomial p(x) = (k²+4)x²+13x+4k is reciprocal of the other, then k=2.
Reason: If (x-a) is a factor of p(x), then p(a) = 0 i.e., a is a zero of p(x).

Answer: (b)

7)Assertion: Degree of aa zero polynomial is not defined.

Reason: Degree of a non-zero constant polynomial is 0.

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

8) Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3.

Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes

Ans: c) Assertion is correct but reason is false

9) Assertion: 3-2√5 is one zero of the quadratic polynomial then other zero will be 3+2√5.

Reason: Irrational zeros (roots) always occurs in pairs.           

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

10) Assertion: If the product of the zeroes of the quadratic polynomial x²+3x+5k is -10 then value of k is -2.
Reason: Sum of zeroes of a quadratic polynomial ax²+bx+c is -b/a

Answer: (b)

11)Assertion: (2 − √3) is one zero of the quadratic polynomial then other zero will be (2 + √3) .
Reason: Irrational zeroes (roots) always occurs in pairs.

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

12) Assertion: The polynomial p(x) = 5x – 1/2 is a linear polynomial.
Reason: The general form of linear polynomial is ax+b.

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

13) Assertion: The graph of a polynomial intersect x-axis at 3 points and y-axis at 1 points, the polynomial has 3 zeroes.
Reason: The number of zeroes that a polynomial p(x) can have is the number of times polynomial intersect x and y axis.

Answer: (c) Assertion is correct but reason is wrong.

14) Assertion:x+1is a Linear Polynomial

Reason (R): The polynomials of degree 1 are called linear polynomials.

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

15) Assertion: The graph of a polynomial p(x) is a straight line parallel to x axis. The polynomial has no zeros.

Reason (R): If a polynomial P(x) does not intersect the x-axis at any point, it does not have any zero.

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