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NCERT MCQ ON TRIANGLES

Question 1.

In given figure, the measure of ∠BAC is

(a) 60°
(b) 50°
(c) 70°
(d) 80°

Answer: (b) 50°

Question 2.

In figure if AE || DC and AB = AC, find the value of ∠ABD.

(a) 130°
(b) 110°
(c) 120°
(d) 70°

Answer: (a) 130°

Question 3.

In figure X is a point in the interior of square ABCD, AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then find BY.

(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm

Answer: (c) 7 cm

Question 4.

In figure AB ⊥ AE, BC ⊥ AB, CE = DE and ∠AED = 120°, then find ∠ECD.

(a) 80°
(b) 70°
(c) 85°
(d) 60°

Answer: (d) 60°

Question 5.

In ΔABC, ∠C = ∠A and BC = 4 cm and AC = 5 cm, then find length of AB.
(a) 5 cm
(b) 3 cm
(c) 4 cm
(d) 2.5 cm

Answer: (c) 4 cm

Question 6.
In ΔABC, AB = AC and ∠B = 50°, then find ∠C.
(a) 50°
(b) 40°
(c) 80°
(d) 120°

Answer: (a) 50°

Question 7.

In figure, D is the mid-point of side BC of a ΔABC and ∠ABD = 50°. If AD = BD = CD, then find the measure of ∠ACD.

(a) 30°
(b) 70°
(c) 80°
(d) 40°

Answer: (d) 40°

Question 8.

In figure, ABC is an isosceles triangle whose side AC is produce to E and through C, CD is drawn parallel to BA. Find the value of x.

(a) 52°
(b) 156°
(c) 76°
(d) 104°

Answer: (d) 104°

Question 9.

In figure AB ⊥ BE and EF ⊥ BE. If BC = DE and AB = EF, then ΔABD is congruent to

(a) ΔEFC
(b) ΔECF
(c) ΔDEF
(d) ΔFEC

Answer: (d) ΔFEC

Question 10.

D is a point on the side BC of a ΔABC such that AD bisects ∠BAC. Then
(a) BD = CD
(b) BA > BD
(c) BD > BA
(d) CD > CA

Answer: (b) BA > BD

Question 11.

It is given that ΔABC = ΔFDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
(а) DF = 5 cm, ∠F = 60°
(b) DF = 5 cm, ∠E = 60°
(c) DE = 5 cm, ∠E = 60°
(d) DE = 5 cm, ∠D = 40°

Answer: (b) DF = 5 cm, ∠E = 60°

Question 12.

Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be
(a) 3.6 cm
(b) 4.1 cm
(c) 3.8 cm
(d) 3.4 cm

Answer: (d) 3.4 cm

Question 13.

In ΔPQR, if ∠R > ∠Q, then
(a) QR > PR
(b) PQ > PR
(c) PQ < PR
(d) QR < PR

Answer: (b) PQ > PR

Question 14.

In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are
(a) isosceles but not congruent
(b) isosceles and congruent
(c) congruent but not isosceles
(d) neither congruent nor isosceles

Answer: (a) isosceles but not congruent

Question 15.

In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom if
(a) BC = EF
(b) AC = DE
(c) AC = EF
(d) BC = DE

Answer: (b) AC = DE

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NCERT MCQ FOR LINES AND ANGLES

Question 1.

In ΔABC, ∠A = 50° and the external bisectors of ∠B and ∠C meet at O as shown in figure. The measure of ∠BOC is

(a) 40°
(b) 65°
(c) 115°
(d) 140°

Answer: (b) 65°

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Question 2.

In figure the value of x is

(a) 120°
(b) 130°
(c) 110°
(d) 100°

Answer: (b) 130°

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Question 3.

An exterior angle of a triangle is 80° and the interior opposite angles are in the ratio 1 : 3, measure of interior opposite angles are
(a) 30°, 90°
(b) 40°, 120°
(c) 20°, 60°
(d) 30°, 60°

Answer: (c) 20°, 60°

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Question 4.

In ΔABC, the bisectors of ∠ABC and ∠BCA intersect each other at O. The measure of ∠BOC is
(a) 90° + ∠A
(b) 90° + ∠A2
(c) 180 – ∠A
(d) 90° – ∠A2

Answer: (b) 90° + ∠A2

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Question 5.

In figure if ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = k right angles, then find value of k.

(а) 2
(b) 3
(c) 4
(d) 5

Answer: (c) 4

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Question 6.

In the given figure, the measure of ∠ABC is

(a) 80°
(b) 20°
(c) 100°
(d) 60°

Answer: (a) 80°

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Question 7.

The angle of a triangle are in the ratio 5 : 3 : 7, the triangle is
(а) an acute-angled triangle
(b) an obtuse angled triangle
(c) an right angled triangle
(d) an isosceles triangle.

Answer: (а) an acute-angled triangle

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Question 8.

In figure l₁ || l₂, the value of x is

(a) 80°
(b) 100°
(c) 110°
(d) 70°

Answer: (a) 80°

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Question 9.

If one angle of triangle is equal to the sum of the other two, then the triangle is
(a) an isosceles triangle
(b) an obtuse-angled triangle
(c) an equilateral triangle
(d) a right triangle

Answer: (d) a right triangle

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Question 10.

One of the angles of a triangle is 75°. If the difference of other two is 35°, then the largest angle of other two angles has a measure
(a) 80°
(b) 75°
(c) 70°
(d) 135°

Answer: (c) 70°

Question 11 .

 If AB = x + 3, BC = 2x and AC = 4x – 5, then for what value of ‘x’, B lies on AC?

a) 2

b) 3

c) 5

d) 8

Answer: (d) 8

Question 12 .

 In the given figure, if AOB is a line then the measure of ∠BOC, ∠COD and ∠DOA respectively are:

a) 36^o, 54^o, 90^o

b) 36^o, 90^o, 54^o

c) 90^o, 36^o, 54^o

d) 90^o, 54^o, 36^o

 Answer: (a) 36^o, 54^o, 90^o

Question 13 .

In the figure, if x, y and z are exterior angles of ΔABC then x + y + z is:

a) 90^o

b) 180^o

c) 270^o

d) 360^o

Answer: (d) 360^o

Question 14 .

In the given figure, PQ || RS and ∠ACS = 127°, ∠BAC is:

a) 50^o
b) 53^o
c) 77^o
d) 107^o

Answer c) 77^o

Question 15.

In figure, AB || ED, the value of x is:

a) 26^o
b) 36^o
c) 54^o
d) 62^o

Answer a) 26^o

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NCERT MCQ FOR INTRODUCTION TO ELUCID’S GEOMETRY

Question 1.

The number of dimensions, a solid has:
(a) 1
(b) 2
(c) 3
(d) 0

Answer: (c) 3

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Question 2.

The total number of propositions in the elements are:
(a) 465
(b) 460
(c) 13
(d) 55

Answer: (a) 465

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Question 3.

In Indus valley civilisation (about 3000 BC), the bricks used for construction work were having dimensions in the ratio
(a) 1 : 3 : 4
(b) 4 : 2 : 1
(c) 4 : 4 : 1
(d) 4 : 3 : 2

Answer: (b) 4 : 2 : 1

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Question 4.

The things which are double of same thing are
(a) equal
(b) halves of same thing
(c) unequal
(d) double of the same thing

Answer: (a) equal

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Question 5.

Which of the following statements is incorrect?
(а) A line segment has definite length.
(b) Three lines are concurrent if and only if they have a common point.
(c) Two lines drawn in a plane always intersect at a point.
(d) One and only one line can be drawn passing through a given point and parallel to a given line.

Answer: (c) Two lines drawn in a plane always intersect at a point.

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Question 6.

Select the wrong statement:
(а) Only one line can pass through a single point.
(b) Only one line can pass through two distinct points.
(c) A terminated line can be produced indefinitely on both the sides.
(d) If two circles are equal, then their radii are equal.

Answer: (а) Only one line can pass through a single point.

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Question 7.

Which one of the following statements is true?
(a) Only one line can pass through a single point.
(b) There are an infinite number lines which pass through two distinct points.
(c) Two distinct lines cannot have more than one point in common.
(d) If two circles are equal, then their radii are not equal.

Answer: (c) Two distinct lines cannot have more than one point in common.

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Question 8.

If the point P lies in between M and N and C is mid point of MP, then:
(a) MC + PN = MN
(b) MP + CP – MN
(c) MC + CN = MN
(d) CP + CN = MN

Answer: (c) MC + CN = MN

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Question 9.

‘Lines are parallel if they do not intersect’ is stated in the form of:
(a) an axiom
(b) a definition
(c) a postulate
(d) a proof

Answer: (b) a definition

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Question 10.

Two planes intersect each other to form a:
(a) plane
(b) point
(c) straight line
(d) angle

Answer: (c) straight line

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Question 11.

The number of lines that can pass through a given point is
(a) two
(b) none
(c) only one
(d) infinitely many

Answer: (d) infinitely many

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Question 12.

How many lines do pass through two distinct points?
(a) 1
(b) 2
(c) 3
(d) 4

Answer: (a) 1

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Question 13.

The number of line segments determined by three collinear points is:
(a) two
(b) three
(c) only one
(d) four

Answer: (b) three

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Question 14.

Number of dimension(s) a surface has:
(a) 0
(b) 1
(c) 2
(d) 3

Answer: (c) 2

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Question 15.

Euclid stated that things which are equal to the same thing are equal to one another in the form of:
(a) an axiom
(b) a definition
(c) a postulate
(d) a proof

Answer: (a) an axiom

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NCERT MCQ ON NUMBER SYSTEM

Question 1.

A rational number lying between √2 and √3 is
(a) √2+√32/2
(b) √6
(c) 1.6
(d) 1.9

Answer: (c) 1.6

Question 2.

Find the value of 54250√3
(a) 925
(b) 35
(c) 27125
(d) 2√35

Answer: (b) 35

Question 3.

Simplified value of (16)^–14 × 16√4 is
(a) 16
(b) 4
(c) 1
(d) 0

Answer: (c) 1

Question 4.

Find the value of 64−2√4.
(a) 18
(b) 12
(c) 8
(d) 164

Answer: (a) 18

Question 5.

Find the value of 216√3 – 125√3
(a) 1
(b) -1
(c) 91√3
(d) 6/5

Answer: (a) 1

Question 6.

When 1515√ is divided by 3√3 find the quotient.
(a) 5√3
(b) 3√5
(c) 5√5
(d) 3√3

Answer: (c) 5√5

Question 7.

If √3 = 1.732 and √2 = 1.414, find the value of 1√3−√2
(a) 0.318
(b) 3.146
(c) 13.146
(d) √1.732 – √  1.414

Answer: (b) 3.146

Question 8.

Which of the following numbers is an irrational number?
(a) 16√ 4
(b) (3 – √3) (3 + √3)
(c) √5 + 3
(d) – √ 25

Answer: (c) √5 + 3

Question 9.

The decimal expansion of √2 is
(а) finite decimal
(b) 1.4121
(c) non-terminating recurring
(d) non-terminating non-recurring

Answer: (d) non-terminating non-recurring

Question 10.

If x = √75 and 5x = p√7, then the value of p is
(а) 5√7
(b) 257
(c) 725
(d) √75

Answer: (b) 257

Question 11.

If x = 2+√3, then x + 1/x =
(a) 5
(b) 4
(c) -4
(d) -5

Answer: (b) 4

Question 12.

Every rational number is:
(a) Whole number
(b) Natural number
(c) Integer
(d) Real number

Answer: (d) Real number

Question 13.

3√6 + 4√6 is equal to:
(a) 6√6
(b) 7√6
(c) 4√12
(d) 7√12

Answer: (b) 7√6

Question 14.

Expression of 2.2323… in the form of a/ b is ________.
(a) 221/99
(b) 75/31
(c) 7/99
(d) 223/99

Answer: (a) 221/99

Question 15.

Which of the following lies between 0 and -1?
(a) 0
(b) -3
(c) -2/3
(d) 4/3

Answer: (c) -2/3

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