24740 + Interview Questions in Mathematics

1.	Question 4 Write True or False and justify your answer : Through three collinear points, a circle can be drawn.
Answer» Question 4 Write True or False and justify your answer : Through three collinear points, a circle can be drawn.

Discussion

2.	If 3x+1=9x−2,find the value of 21+x.
Answer» If $3^{x + 1} = 9^{x - 2}, f i n d t h e v a l u e o f 2^{1 + x}$ .

Discussion

3.	Medians of △ABC, intersect at G. If ar(△ABC)=27cm2 then ar(△BGC)=
Answer» Medians of $△ A B C,$ intersect at G. If $a r (△ A B C) = 27 c m^{2}$ then $a r (△ B G C) =$

Discussion

4.	From the choices given below, choose the equation whose graph is given in Fig. 7.13. (i) y=x (ii) x+y=0 (iii) y=2x (iv) 2+3y=7x
Answer» From the choices given below, choose the equation whose graph is given in Fig. 7.13. $(i) y = x$ $(i i) x + y = 0$ $(i i i) y = 2 x$ $(i v) 2 + 3 y = 7 x$

4.

From the choices given below, choose the equation whose graph is given in Fig. 7.13. (i) y=x (ii) x+y=0 (iii) y=2x (iv) 2+3y=7x

Answer»

From the choices given below, choose the equation whose graph is given in Fig. 7.13.

$(i) y = x$ $(i i) x + y = 0$ $(i i i) y = 2 x$ $(i v) 2 + 3 y = 7 x$

Discussion

5.	In the figure, ABCD and PQRC are rectangles and Q is the mid-point of AC. Prove that (i) DP = PC (ii) PR=12AC.
Answer» In the figure, ABCD and PQRC are rectangles and Q is the mid-point of AC. Prove that (i) DP = PC (ii) $P R = \frac{1}{2} A C$ .

5.

In the figure, ABCD and PQRC are rectangles and Q is the mid-point of AC. Prove that (i) DP = PC (ii) PR=12AC.

Answer»

In the figure, ABCD and PQRC are rectangles and Q is the mid-point of AC.

Prove that (i) DP = PC (ii) $P R = \frac{1}{2} A C$ .

Discussion

6.	(i) Give an example of a monomial of degree 5. (ii) Give an example of a binomial of degree 8. (iii) Given an example of a binomial of degree 4. (iv) Give an example of a monomial of degree 0.
Answer» (i) Give an example of a monomial of degree 5. (ii) Give an example of a binomial of degree 8. (iii) Given an example of a binomial of degree 4. (iv) Give an example of a monomial of degree 0.

Discussion

7.	In two right triangles, one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.
Answer» In two right triangles, one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

Discussion

8.	A rectangular sheet of paper, 44 cm × 20 cm, is rolled along its lenght of form a cylinder. Find the volume of the cylinder so formed.
Answer» A rectangular sheet of paper, 44 cm $\times$ 20 cm, is rolled along its lenght of form a cylinder. Find the volume of the cylinder so formed.

Discussion

9.	Question 59 Solve the following: 10x-5-7x=5x+15-8
Answer» Question 59 Solve the following: 10x-5-7x=5x+15-8

9.

Question 59 Solve the following: 10x-5-7x=5x+15-8

Answer»

Question 59

Solve the following:

10x-5-7x=5x+15-8

Discussion

10.	Question 165 In a quadrilateral PQRS, ∠P=50∘,∠Q=50∘,∠R=60∘. Find ∠S. Is this quadrilateral convex or concave?
Answer» Question 165 In a quadrilateral PQRS, $∠ P = 50^{\circ}, ∠ Q = 50^{\circ}, ∠ R = 60^{\circ}$ . Find $∠ S$ . Is this quadrilateral convex or concave?

Discussion

11.	Construct a triangle ABC, in which ∠B = 60∘ , ∠ C = 45∘ and AB + BC + CA = 22 cm. [4 MARKS]
Answer» Construct a triangle ABC, in which $∠$ B = $60^{\circ}$ , $∠$ C = $45^{\circ}$ and AB + BC + CA = 22 cm. [4 MARKS]

Discussion

12.	Prove that a quadrilateral with both pairs of opposite sides equal, is a parallelogram. [4 MARKS]
Answer» Prove that a quadrilateral with both pairs of opposite sides equal, is a parallelogram. [4 MARKS]

Discussion

13.	Two supplementary angles are in the ratio of 3 : 7. Find the angles.
Answer» Two supplementary angles are in the ratio of 3 : 7. Find the angles.

Discussion

14.	Ted has a geometry box. Out of several equipments that are there, there are 2 set squares. He was thinking about the angles that could be constructed using those 2 set squares. He took 4 examples to work on which are given in the options below. Which of the following is impossible to draw using the given set squares?
Answer» Ted has a geometry box. Out of several equipments that are there, there are 2 set squares. He was thinking about the angles that could be constructed using those 2 set squares. He took 4 examples to work on which are given in the options below. Which of the following is impossible to draw using the given set squares?

Discussion

15.	Question 3 The median BE and CF of a triangle ABC intersect at G. Prove that the area of ΔGBC = area of the quadrilateral AFGE.
Answer» Question 3 The median BE and CF of a triangle ABC intersect at G. Prove that the area of $Δ$ GBC = area of the quadrilateral AFGE.

Discussion

16.	Question 4 Plot the following points and check whether they are collinear or not. (i) (1, 3), (-1, -1), (-2, -3) (ii) (1, 1), (2, -3), (-1, -2) (iii) (0, 0), (2, 2), (5, 5)
Answer» Question 4 Plot the following points and check whether they are collinear or not. (i) (1, 3), (-1, -1), (-2, -3) (ii) (1, 1), (2, -3), (-1, -2) (iii) (0, 0), (2, 2), (5, 5)

Discussion

17.	In the adjoining figure A, D, B, C are four points on the circumference of a circle with centre O. Arc AB = 2 Arc BC and ∠AOB = 1080. FInd: i. ∠ACB ii. ∠CAB III. ∠ADB
Answer» In the adjoining figure A, D, B, C are four points on the circumference of a circle with centre O. Arc AB = 2 Arc BC and $∠$ AOB = $108^{0}$ . FInd: i. $∠$ ACB ii. $∠$ CAB III. $∠$ ADB

17.

In the adjoining figure A, D, B, C are four points on the circumference of a circle with centre O. Arc AB = 2 Arc BC and ∠AOB = 1080. FInd: i. ∠ACB ii. ∠CAB III. ∠ADB

Answer»

In the adjoining figure A, D, B, C are four points on the circumference of a circle with centre O. Arc AB = 2 Arc BC and $∠$ AOB = $108^{0}$ . FInd:

i. $∠$ ACB

ii. $∠$ CAB

III. $∠$ ADB

Discussion

18.	If the line represented by the equation 3x+4y+c=0 passes through the origin, then the value of c is equal to:\N
Answer» If the line represented by the equation $3 x + 4 y + c = 0$ passes through the origin, then the value of $c$ is equal to: \N

Discussion

19.	The sum and product of two numbers is 10 and 20 respectively. Find the sum of their squares.
Answer» The sum and product of two numbers is 10 and 20 respectively. Find the sum of their squares.

Discussion

20.	How is {(x + 1) / 2}2. - {(x - 1) / 2}2 = x
Answer» How is {(x + 1) / 2}^2.- {(x - 1) / 2}²= x

Discussion

21.	X=√2 Then does that mean X= +_ √2
Answer» X=√2 Then does that mean X= +_ √2

21.

X=√2 Then does that mean X= +_ √2

Answer»

X=√2

Then does that mean

X= +_ √2

Discussion

22.	How do you find out the mirror image of a point?
Answer» How do you find out the mirror image of a point?

Discussion

23.	Simplify: 25×t−45−3×10×t−8 where,(t≠0)
Answer» Simplify: $\frac{25 \times t^{- 4}}{5^{- 3} \times 10 \times t^{- 8}} w h e r e, (t \neq 0)$

Discussion

24.	Which of the following should be the FIRST sentence after rearrangement?
Answer» Which of the following should be the FIRST sentence after rearrangement?

Discussion

25.	ABCD is a parallelogram with ∠ABC = 90∘, then number of right angles in the parallelogram excluding ∠ABC is/are ____?
Answer» ABCD is a parallelogram with $∠$ ABC = $90^{\circ}$ , then number of right angles in the parallelogram excluding $∠$ ABC is/are ____?

Discussion

26.	ABC is an equilateral triangle of side 8 cm. A, B and C are the centres of circular arcs of radius 4 cm. Find the area of the shaded region correct upto 2 decimal places.(Take π=3.142 and √3=1.732)
Answer» ABC is an equilateral triangle of side 8 cm. A, B and C are the centres of circular arcs of radius 4 cm. Find the area of the shaded region correct upto 2 decimal places.(Take $π = 3.142$ and $\sqrt{3} = 1.732$ )

26.

ABC is an equilateral triangle of side 8 cm. A, B and C are the centres of circular arcs of radius 4 cm. Find the area of the shaded region correct upto 2 decimal places.(Take π=3.142 and √3=1.732)

Answer»

ABC is an equilateral triangle of side 8 cm. A, B and C are the centres of circular arcs of radius 4 cm. Find the area of the shaded region correct upto 2 decimal places.(Take $π = 3.142$ and $\sqrt{3} = 1.732$ )

Discussion

27.	The areas of three adjacent faces of a cuboid are a, b and c. If its volume is V, then V=
Answer» The areas of three adjacent faces of a cuboid are a, b and c. If its volume is V, then V=

Discussion

28.	Find the value of the polynomial 6 – 4x + 3x2 at x = 3
Answer» Find the value of the polynomial 6 – 4x + 3x² at x = 3

Discussion

29.	Question 24 (i) A die is thrown twice. What is the probability that 5 will not come up either time?
Answer» Question 24 (i) A die is thrown twice. What is the probability that 5 will not come up either time?

Discussion

30.	The volume of a right circular cone of height 12 cm and radius 7 cm is
Answer» The volume of a right circular cone of height 12 cm and radius 7 cm is

Discussion

31.	A sum of money at simple interest amounts to ₹815 in 3 years and to ₹854 in 4 years. What is the sum invested?
Answer» A sum of money at simple interest amounts to ₹815 in 3 years and to ₹854 in 4 years. What is the sum invested?

Discussion

32.	Question 1 (i) A survey conducted by an organization for the cause of illness and death among the women between the ages 15-44 (in years) worldwide, found the following figures (in %): S.No.CausesFemale fatality rate(%)1.Reproductive health conditions31.82.Neuropsychiatric conditions25.43.Injuries12.44.Cardiovascular conditions4.35.Respiratory conditions4.16.Other causes22.0 (i) Represent the information given above graphically.
Answer» Question 1 (i) A survey conducted by an organization for the cause of illness and death among the women between the ages 15-44 (in years) worldwide, found the following figures (in %): $\begin{matrix} S . N o . & C a u s e s & F e m a l e f a t a l i t y r a t e (%) 1. & R e p r o d u c t i v e h e a l t h c o n d i t i o n s & 31.8 2. & N e u r o p s y c h i a t r i c c o n d i t i o n s & 25.4 3. & I n j u r i e s & 12.4 4. & C a r d i o v a s c u l a r c o n d i t i o n s & 4.3 5. & R e s p i r a t o r y c o n d i t i o n s & 4.1 6. & O t h e r c a u s e s & 22.0 \end{matrix}$ (i) Represent the information given above graphically.

Discussion

33.	Find the Length of all sides of the given right angled triangle if the area is 36 cm2
Answer» Find the Length of all sides of the given right angled triangle if the area is 36 $c m^{2}$

33.

Find the Length of all sides of the given right angled triangle if the area is 36 cm2

Answer»

Find the Length of all sides of the given right angled triangle if the area is 36 $c m^{2}$

Discussion

34.	Question 97 Find the area enclosed by the following figure:
Answer» Question 97 Find the area enclosed by the following figure:

34.

Question 97 Find the area enclosed by the following figure:

Answer»

Question 97

Find the area enclosed by the following figure:

Discussion

35.	Which of the following is not a simple closed figure?
Answer» Which of the following is not a simple closed figure?

Discussion

36.	The sum of two angles of a triangle is 80∘ and their difference is 20∘. Find all the angles. [4 MARKS]
Answer» The sum of two angles of a triangle is $80^{\circ}$ and their difference is $20^{\circ}$ . Find all the angles. [4 MARKS]

Discussion

37.	The figure whose vertices are the points O(0, 0), A(5, 0), B(5, 5) and C(0, 5) is ___
Answer» The figure whose vertices are the points O(0, 0), A(5, 0), B(5, 5) and C(0, 5) is ___

Discussion

38.	Question 11 The value of the expression (sin222∘+sin268∘cos222∘+cos268∘+sin263∘+cos63∘27∘) is (A) 3 (B) 2 (C) 1 (D) 0
Answer» Question 11 The value of the expression $(\frac{s i n^{2} 22^{\circ} + s i n^{2} 68^{\circ}}{c o s^{2} 22^{\circ} + c o s^{2} 68^{\circ}} + s i n^{2} 63^{\circ} + c o s 63^{\circ} 27^{\circ})$ is (A) 3 (B) 2 (C) 1 (D) 0

Discussion

39.	If a rectangular sheet is folded along its length to cover the curved surface of the cylinder with radius R and height H, then find the length and breadth of the rectangular sheet. [2 MARKS]
Answer» If a rectangular sheet is folded along its length to cover the curved surface of the cylinder with radius R and height H, then find the length and breadth of the rectangular sheet. [2 MARKS]

Discussion

40.	If α,β and γ are the zeros of the polynomial f(x)= ax3+bx2+cx+d, then 1α+1β+1γ is:
Answer» If $α, β$ and $γ$ are the zeros of the polynomial f(x)= $a x^{3} + b x^{2} + c x + d$ , then $\frac{1}{α} + \frac{1}{β} + \frac{1}{γ}$ is:

Discussion

41.	Let AB and CD be two equal chords of a circle which intersect within the circle centered at O, as shown below. Then which of the following is/are true?
Answer» Let AB and CD be two equal chords of a circle which intersect within the circle centered at O, as shown below. Then which of the following is/are true?

41.

Let AB and CD be two equal chords of a circle which intersect within the circle centered at O, as shown below. Then which of the following is/are true?

Answer»

Let AB and CD be two equal chords of a circle which intersect within the circle centered at O, as shown below.

Then which of the following is/are true?

Discussion

42.	In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?
Answer» In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

42.

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

Answer»

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

Discussion

43.	The sketches drawn on a sheet which is divided into small equilateral triangles are called:
Answer» The sketches drawn on a sheet which is divided into small equilateral triangles are called:

Discussion

44.	Solve {5(813+2713)3}14
Answer» Solve ${5 (8^{\frac{1}{3}} + 27^{\frac{1}{3}})^{3}}^{\frac{1}{4}}$

Discussion

45.	Statement 1: Diagonals of a rhombus intersect at right angles. Statement 2: All sides of a rhombus are equal. Choose the correct statement.
Answer» Statement 1: Diagonals of a rhombus intersect at right angles. Statement 2: All sides of a rhombus are equal. Choose the correct statement.

45.

Statement 1: Diagonals of a rhombus intersect at right angles. Statement 2: All sides of a rhombus are equal. Choose the correct statement.

Answer»

Statement 1: Diagonals of a rhombus intersect at right angles.

Statement 2: All sides of a rhombus are equal.

Choose the correct statement.

Discussion

46.	Question 50 Fill in the blanks to make the statement true. 3×(−1)×(−15)=___ .
Answer» Question 50 Fill in the blanks to make the statement true. $3 \times (- 1) \times (- 15) =$ ___ .

46.

Question 50 Fill in the blanks to make the statement true. 3×(−1)×(−15)=___ .

Answer»

Question 50

Fill in the blanks to make the statement true.

$3 \times (- 1) \times (- 15) =$ ___ .

Discussion

47.	Based on the construction below, which of the following must be true?
Answer» Based on the construction below, which of the following must be true?

47.

Based on the construction below, which of the following must be true?

Answer»

Based on the construction below, which of the following must be true?

Discussion

48.	Question 34 State whether the given statements are true (T) or false (F). The two terms of a ratio can be in two different units.
Answer» Question 34 State whether the given statements are true (T) or false (F). The two terms of a ratio can be in two different units.

48.

Question 34 State whether the given statements are true (T) or false (F). The two terms of a ratio can be in two different units.

Answer»

Question 34

State whether the given statements are true (T) or false (F).

The two terms of a ratio can be in two different units.

Discussion

49.	If the area of a rhombus-shaped box is 6√7cm2 and its one diagonal is 6cm. Find the side of the rhombus.
Answer» If the area of a rhombus-shaped box is $6 \sqrt{7} {c m}^{2}$ and its one diagonal is $6 c m$ . Find the side of the rhombus.

Discussion

50.	Question 8 If in two right triangles, one of the acute angles of one triangle is equal to an acute of the other triangle. Can you say that two triangles will be similar? Why?
Answer» Question 8 If in two right triangles, one of the acute angles of one triangle is equal to an acute of the other triangle. Can you say that two triangles will be similar? Why?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 4 Write True or False and justify your answer :​​​​​​​ Through three collinear points, a circle can be drawn.

If 3x+1=9x−2,find the value of 21+x.

Medians of △ABC, intersect at G. If ar(△ABC)=27cm2 then ar(△BGC)=

From the choices given below, choose the equation whose graph is given in Fig. 7.13. (i) y=x (ii) x+y=0 (iii) y=2x (iv) 2+3y=7x

In the figure, ABCD and PQRC are rectangles and Q is the mid-point of AC. Prove that (i) DP = PC (ii) PR=12AC.

(i) Give an example of a monomial of degree 5. (ii) Give an example of a binomial of degree 8. (iii) Given an example of a binomial of degree 4. (iv) Give an example of a monomial of degree 0.

In two right triangles, one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

A rectangular sheet of paper, 44 cm × 20 cm, is rolled along its lenght of form a cylinder. Find the volume of the cylinder so formed.

Question 59 Solve the following: 10x-5-7x=5x+15-8

Question 165 In a quadrilateral PQRS, ∠P=50∘,∠Q=50∘,∠R=60∘. Find ∠S. Is this quadrilateral convex or concave?

Construct a triangle ABC, in which ∠B = 60∘ , ∠ C = 45∘ and AB + BC + CA = 22 cm. [4 MARKS]

Prove that a quadrilateral with both pairs of opposite sides equal, is a parallelogram. [4 MARKS]

Two supplementary angles are in the ratio of 3 : 7. Find the angles.

Question 3 The median BE and CF of a triangle ABC intersect at G. Prove that the area of ΔGBC = area of the quadrilateral AFGE.

Question 4 Plot the following points and check whether they are collinear or not. (i) (1, 3), (-1, -1), (-2, -3) (ii) (1, 1), (2, -3), (-1, -2) (iii) (0, 0), (2, 2), (5, 5)

In the adjoining figure A, D, B, C are four points on the circumference of a circle with centre O. Arc AB = 2 Arc BC and ∠AOB = 1080. FInd: i. ∠ACB ii. ∠CAB III. ∠ADB

If the line represented by the equation 3x+4y+c=0 passes through the origin, then the value of c is equal to:\N

The sum and product of two numbers is 10 and 20 respectively. Find the sum of their squares.

How is {(x + 1) / 2}2. - {(x - 1) / 2}2 = x

X=√2 Then does that mean X= +_ √2

How do you find out the mirror image of a point?

Simplify: 25×t−45−3×10×t−8 where,(t≠0)

Which of the following should be the FIRST sentence after rearrangement?

ABCD is a parallelogram with ∠ABC = 90∘, then number of right angles in the parallelogram excluding ∠ABC is/are ____?

ABC is an equilateral triangle of side 8 cm. A, B and C are the centres of circular arcs of radius 4 cm. Find the area of the shaded region correct upto 2 decimal places.(Take π=3.142 and √3=1.732)

The areas of three adjacent faces of a cuboid are a, b and c. If its volume is V, then V=

Find the value of the polynomial 6 – 4x + 3x2 at x = 3

Question 24 (i) A die is thrown twice. What is the probability that 5 will not come up either time?

The volume of a right circular cone of height 12 cm and radius 7 cm is

A sum of money at simple interest amounts to ₹815 in 3 years and to ₹854 in 4 years. What is the sum invested?

Find the Length of all sides of the given right angled triangle if the area is 36 cm2

Question 97 Find the area enclosed by the following figure:

Which of the following is not a simple closed figure?

The sum of two angles of a triangle is 80∘ and their difference is 20∘. Find all the angles. [4 MARKS]

The figure whose vertices are the points O(0, 0), A(5, 0), B(5, 5) and C(0, 5) is ___

Question 11 The value of the expression (sin222∘+sin268∘cos222∘+cos268∘+sin263∘+cos63∘27∘) is (A) 3 (B) 2 (C) 1 (D) 0

If a rectangular sheet is folded along its length to cover the curved surface of the cylinder with radius R and height H, then find the length and breadth of the rectangular sheet. [2 MARKS]

If α,β and γ are the zeros of the polynomial f(x)= ax3+bx2+cx+d, then 1α+1β+1γ is:

Let AB and CD be two equal chords of a circle which intersect within the circle centered at O, as shown below. Then which of the following is/are true?

In the figure; P and Q are the points of intersection of two circles with centres O &amp; O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

The sketches drawn on a sheet which is divided into small equilateral triangles are called:

Solve {5(813+2713)3}14

Statement 1: Diagonals of a rhombus intersect at right angles. Statement 2: All sides of a rhombus are equal. Choose the correct statement.

Question 50 Fill in the blanks to make the statement true. 3×(−1)×(−15)=___ .

Based on the construction below, which of the following must be true?

Question 34 State whether the given statements are true (T) or false (F). The two terms of a ratio can be in two different units.

If the area of a rhombus-shaped box is 6√7cm2 and its one diagonal is 6cm. Find the side of the rhombus.

Question 8 If in two right triangles, one of the acute angles of one triangle is equal to an acute of the other triangle. Can you say that two triangles will be similar? Why?

Question 4 Write True or False and justify your answer : Through three collinear points, a circle can be drawn.

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?