24740 + Interview Questions in Mathematics

1.	In fig., if <OAB=40∘, the < ACB is equal to:
Answer» In fig., if $< O A B = 40^{\circ}$ , the < ACB is equal to:

Discussion

2.	Factors of x6−y6 is:
Answer» Factors of $x^{6} - y^{6}$ is:

Discussion

3.	Question 4 ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.
Answer» Question 4 ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.

Discussion

4.	Let x, y, z be three observations. The mean of these observations is
Answer» Let x, y, z be three observations. The mean of these observations is

Discussion

5.	The point whose abscissa is -3 and lies on x-axis is.
Answer» The point whose abscissa is -3 and lies on x-axis is.

Discussion

6.	If x = √1+√1+√1+....to infinity, then x =
Answer» If x = $\sqrt{1 + \sqrt{1 + \sqrt{1 + . . . . t o i n f i n i t y}}}$ , then x =

Discussion

7.	1500 families with 2 children were selected randomly, and the following data were recorded Number of girls in a family210Number of families300500700 Compute the probability of a family chosen at random having 2 girls.
Answer» 1500 families with 2 children were selected randomly, and the following data were recorded $\begin{matrix} N u m b e r o f g i r l s i n a f a m i l y & 2 & 1 & 0 N u m b e r o f f a m i l i e s & 300 & 500 & 700 \end{matrix}$ Compute the probability of a family chosen at random having 2 girls.

7.

1500 families with 2 children were selected randomly, and the following data were recorded Number of girls in a family210Number of families300500700 Compute the probability of a family chosen at random having 2 girls.

Answer»

1500 families with 2 children were selected randomly, and the following data were recorded

$\begin{matrix} N u m b e r o f g i r l s i n a f a m i l y & 2 & 1 & 0 N u m b e r o f f a m i l i e s & 300 & 500 & 700 \end{matrix}$

Compute the probability of a family chosen at random having 2 girls.

Discussion

8.	The area of one face of a cube is 100 m2. Find the volume of the cube.
Answer» The area of one face of a cube is $100 m^{2}$ . Find the volume of the cube.

Discussion

9.	Which of the following statements are incorrect?
Answer» Which of the following statements are incorrect?

Discussion

10.	If A=∫sinθ1t dt1+t2dt,B=∫cosecθ11t(1+t2)dt then ∣∣∣∣∣AA2BeA+BB2−11A2+B2−1∣∣∣∣∣=?
Answer» If $A = \int_{1}^{s i n θ} \frac{t d t}{1 + t^{2}} d t, B = \int_{1}^{c o s e c θ} \frac{1}{t (1 + t^{2})} d t$ then $∣ ∣∣∣ ∣ \begin{matrix} A & A^{2} & B e^{A + B} & B^{2} & - 1 1 & A^{2} + B^{2} & - 1 \end{matrix} ∣ ∣∣∣ ∣ = ?$

Discussion

11.	Question 6 Ordinate of all points on the x-axis is A) 0 B) 1 C) -1 D) Any number
Answer» Question 6 Ordinate of all points on the x-axis is A) 0 B) 1 C) -1 D) Any number

Discussion

12.	The number which exceeds its positive square root by 12 is
Answer» The number which exceeds its positive square root by $12$ is

Discussion

13.	The value of ∑ni=1xi is
Answer» The value of $\sum_{i = 1}^{n} x_{i}$ is

Discussion

14.	The class - mark of class interval 10-15 is _____________
Answer» The class - mark of class interval 10-15 is _____________

Discussion

15.	Question 4 (iv) State whether the following are true or false. Justify your answer. (iv) sinθ=cosθ for all values of θ.
Answer» Question 4 (iv) State whether the following are true or false. Justify your answer. (iv) $s i n θ = c o s θ$ for all values of $θ$ .

Discussion

16.	The base radii of two cylinders are in the ratio 3:4 and their heights in the ratio 5:2. The volume of the first cylinder is 300 cm3. What is the volume of the second?
Answer» The base radii of two cylinders are in the ratio 3:4 and their heights in the ratio 5:2. The volume of the first cylinder is 300 $c m^{3}$ . What is the volume of the second?

Discussion

17.	In the class interval 22-26, the lower limit is _____ .
Answer» In the class interval 22-26, the lower limit is _____ .

Discussion

18.	A student while doing a math problem , misplaced the decimal point. Due to this the digit at thousandths place became the digit at hundredths place. Identify the number which the child had written incorrectly if the actual number was 45.6547.
Answer» A student while doing a math problem , misplaced the decimal point. Due to this the digit at thousandths place became the digit at hundredths place. Identify the number which the child had written incorrectly if the actual number was 45.6547.

Discussion

19.	A mixture of paint is prepared by mixing 1 part of red pigment with 8 parts of base. In the following table, find the parts of base that need to be added. If 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base? Parts of red pigment1471220Parts of base8 [3 MARKS]
Answer» A mixture of paint is prepared by mixing 1 part of red pigment with 8 parts of base. In the following table, find the parts of base that need to be added. If 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base? $\begin{matrix} P a r t s o f r e d p i g m e n t & 1 & 4 & 7 & 12 & 20 P a r t s o f b a s e & 8 \end{matrix}$ [3 MARKS]

Discussion

20.	If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, show that CA=2 OD.
Answer» If $B C$ is a diameter of a circle with centre $O$ and $O D$ is perpendicular to the chord $A B$ of a circle, show that $C A = 2 O D$ .

20.

If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, show that CA=2 OD.

Answer»

If $B C$ is a diameter of a circle with centre $O$ and $O D$ is perpendicular to the chord $A B$ of a circle, show that $C A = 2 O D$ .

Discussion

21.	Find the point (a,a) which is on 4x+5y=27. [1 MARK]
Answer» Find the point (a,a) which is on $4 x + 5 y = 27$ . [1 MARK]

Discussion

22.	What is the Ratio between KQ and KM? PQRS is a square and K and M are midpoints of PQ and QR respectively.
Answer» What is the Ratio between KQ and KM? PQRS is a square and K and M are midpoints of PQ and QR respectively.

22.

What is the Ratio between KQ and KM? PQRS is a square and K and M are midpoints of PQ and QR respectively.

Answer»

What is the Ratio between KQ and KM? PQRS is a square and K and M are midpoints of PQ and QR respectively.

Discussion

23.	ABC is a triangle in which D is the mid point of BC and E is the mid point of AD. Then area (∆BED) is equal to
Answer» ABC is a triangle in which D is the mid point of BC and E is the mid point of AD. Then area (∆BED) is equal to

23.

ABC is a triangle in which D is the mid point of BC and E is the mid point of AD. Then area (∆BED) is equal to

Answer»

ABC is a triangle in which D is the mid point of BC and E is the mid point of AD. Then area (∆BED) is equal to

Discussion

24.	Find the ratio of the areas of two similar triangles ΔABC and ΔPQR shown in the figure.
Answer» Find the ratio of the areas of two similar triangles $Δ A B C$ and $Δ P Q R$ shown in the figure.

Discussion

25.	In the given figure, AB is the diameter of the circle. Find the value of x.
Answer» In the given figure, AB is the diameter of the circle. Find the value of $x$ .

25.

In the given figure, AB is the diameter of the circle. Find the value of x.

Answer»

In the given figure, AB is the diameter of the circle. Find the value of $x$ .

Discussion

26.	The largest sphere is carved out of a cube of side 7 cm. Then, the volume of the sphere is
Answer» The largest sphere is carved out of a cube of side 7 cm. Then, the volume of the sphere is

Discussion

27.	An isosceles triangle ABC has AC = BC. CD bisects AB at D and ∠ CAB = 55o. Find ∠ ACB.70
Answer» An isosceles triangle ABC has AC = BC. CD bisects AB at D and $∠$ CAB = 55^o. Find $∠ A C B$ . 70

Discussion

28.	The value of (√3+√2)2 is equal to ____.
Answer» The value of $(\sqrt{3} + \sqrt{2})^{2}$ is equal to ____.

Discussion

29.	Question 39 Fill in the blanks to make the statement true. If a wire in the shape of a square is rebent into a rectangle, then the ___ of both shapes remain same, but ___ may vary.
Answer» Question 39 Fill in the blanks to make the statement true. If a wire in the shape of a square is rebent into a rectangle, then the ___ of both shapes remain same, but ___ may vary.

Discussion

30.	A set of numbers which include both positive and negative numbers and do not have a fractional component and are denoted by letter Z are known as __
Answer» A set of numbers which include both positive and negative numbers and do not have a fractional component and are denoted by letter Z are known as __

Discussion

31.	A square is inscribed in a circle with radius 'r'. What is the probability that a randomly selected point within the circle is not within the square?
Answer» A square is inscribed in a circle with radius 'r'. What is the probability that a randomly selected point within the circle is not within the square?

Discussion

32.	In the below figure find the value of ∠QOR. Given that ∠QSR=40∘ and O is the centre of the circle.
Answer» In the below figure find the value of $∠ Q O R$ . Given that $∠ Q S R = 40^{\circ}$ and O is the centre of the circle.

32.

In the below figure find the value of ∠QOR. Given that ∠QSR=40∘ and O is the centre of the circle.

Answer»

In the below figure find the value of $∠ Q O R$ . Given that $∠ Q S R = 40^{\circ}$ and O is the centre of the circle.

Discussion

33.	If I join 2 equilateral triangles along a side, what quadrilteral do I get?
Answer» If I join 2 equilateral triangles along a side, what quadrilteral do I get?

Discussion

34.	How do you represent 0.3125 in the form of pq, where p and q are integers and q is not zero?
Answer» How do you represent $0.3125$ in the form of $\frac{p}{q}$ , where $p$ and $q$ are integers and $q$ is not zero?

Discussion

35.	Find a quadratic polynomial with 18 as the sum and 2 as product of its zeroes.
Answer» Find a quadratic polynomial with $\frac{1}{8}$ as the sum and 2 as product of its zeroes.

Discussion

36.	What is (x−y)3?
Answer» What is $(x - y)^{3}$ ?

Discussion

37.	List-II gives distance between pair of points given in List-I. Match them correctly. List−I List II(P)(−5,7),(−1,3)(1)5(Q)(5,6),(1,3)(2)√8(R)(√3+1,1),(0,√3)(3)√6(S)(0,0),(−√3,√3)(4)4√2
Answer» List-II gives distance between pair of points given in List-I. Match them correctly. $\begin{matrix} L i s t - I & L i s t I I (P) & (- 5, 7), (- 1, 3) & (1) & 5 (Q) & (5, 6), (1, 3) & (2) & \sqrt{8} (R) & (\sqrt{3} + 1, 1), (0, \sqrt{3}) & (3) & \sqrt{6} (S) & (0, 0), (- \sqrt{3}, \sqrt{3}) & (4) & 4 \sqrt{2} \end{matrix}$

Discussion

38.	Factorise: 5x2−16x−21
Answer» Factorise: $5 x^{2} - 16 x - 21$

Discussion

39.	if sin 10A∘=cos(2A−30)∘, then the value of A in degrees is ____ .
Answer» if $s i n 10 A^{\circ} = c o s (2 A - 30)^{\circ}$ , then the value of A in degrees is ____ .

Discussion

40.	What is the degree of the 0 polynomial
Answer» What is the degree of the 0 polynomial

Discussion

41.	P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meets BC at Q, prove that ΔBPQ is an isosceles triangle.
Answer» $P is a point on the bisector of ∠ A B C . If the line through P, parallel to BA meets BC at Q, prove that Δ B P Q is an isosceles triangle.$

Discussion

42.	Draw the graph of the modulus function, defined by f:R→R:f(x)=\|x\|={x, when x≥0−x, when x<0
Answer» Draw the graph of the modulus function, defined by $f : R \to R : f (x) = \| x \| = {\begin{matrix} x, when x \geq 0 - x, when x < 0 \end{matrix}$

42.

Draw the graph of the modulus function, defined by f:R→R:f(x)=|x|={x, when x≥0−x, when x<0

Answer»

Draw the graph of the modulus function, defined by

$f : R \to R : f (x) = | x | = {\begin{matrix} x, when x \geq 0 - x, when x < 0 \end{matrix}$

Discussion

43.	Find the product (2x+7)(2x–7) using identities.
Answer» Find the product $(2 x + 7) (2 x - 7)$ using identities.

Discussion

44.	John covers a part of the journey at 20kmhr and the remaining at 70kmhr, taking total of 8 hours to cover the distance of 400 km. How many hours he has been driving at 70kmhr?
Answer» John covers a part of the journey at $20 \frac{k m}{h r}$ and the remaining at $70 \frac{k m}{h r}$ , taking total of 8 hours to cover the distance of 400 km. How many hours he has been driving at $70 \frac{k m}{h r}$ ?

Discussion

45.	sin 36∘ sin 72∘ sin 108∘ sin 144∘=516
Answer» $s i n 36^{\circ} s i n 72^{\circ} s i n 108^{\circ} s i n 144^{\circ} = \frac{5}{16}$

Discussion

46.	12(x2+7)2-8(x2+7)2(2x-1)-15(2x-1)2
Answer» 12(x²+7)²-8(x²+7)²(2x-1)-15(2x-1)²

Discussion

47.	The quotient when 4x3+x2+5x+8 is divided by (x+1) is .
Answer» The quotient when $4 x^{3} + x^{2} + 5 x + 8$ is divided by $(x + 1)$ is .

Discussion

48.	The value of x that satisfies \|x−1\|=\|x+3\| is
Answer» The value of x that satisfies $\| x - 1 \| = \| x + 3 \|$ is

Discussion

49.	Simplify : (a2−b2)3+(b2−c2)3+(c2−a2)3÷[(a−b)3+(b−c)3+(c−a)3]
Answer» Simplify : $(a^{2} - b^{2})^{3} + (b^{2} - c^{2})^{3} + (c^{2} - a^{2})^{3} \div [(a - b)^{3} + (b - c)^{3} + (c - a)^{3}]$

49.

Simplify : (a2−b2)3+(b2−c2)3+(c2−a2)3÷[(a−b)3+(b−c)3+(c−a)3]

Answer»

Simplify : $(a^{2} - b^{2})^{3} + (b^{2} - c^{2})^{3} + (c^{2} - a^{2})^{3} \div [(a - b)^{3} + (b - c)^{3} + (c - a)^{3}]$

Discussion

50.	In the given figure, if ∠ACB = 30∘, the value of ∠ACD is ___∘.
Answer» In the given figure, if $∠$ ACB = $30^{\circ}$ , the value of $∠$ ACD is ___ $^{\circ}$ .

50.

In the given figure, if ∠ACB = 30∘, the value of ∠ACD is ___∘.

Answer»

In the given figure, if $∠$ ACB = $30^{\circ}$ , the value of $∠$ ACD is

___

^{\circ}

.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In fig., if &lt;OAB=40∘, the &lt; ACB is equal to:

Factors of x6−y6 is:

Question 4 ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.

Let x, y, z be three observations. The mean of these observations is

The point whose abscissa is -3 and lies on x-axis is.

If x = √1+√1+√1+....to infinity, then x =

1500 families with 2 children were selected randomly, and the following data were recorded Number of girls in a family210Number of families300500700 Compute the probability of a family chosen at random having 2 girls.

The area of one face of a cube is 100 m2. Find the volume of the cube.

Which of the following statements are incorrect?

If A=∫sinθ1t dt1+t2dt,B=∫cosecθ11t(1+t2)dt then ∣∣∣∣∣AA2BeA+BB2−11A2+B2−1∣∣∣∣∣=?

Question 6 Ordinate of all points on the x-axis is A) 0 B) 1 C) -1 D)​​​​​​​ Any number

The number which exceeds its positive square root by 12 is

The value of ∑ni=1xi is

The class - mark of class interval 10-15 is _____________

Question 4 (iv) State whether the following are true or false. Justify your answer. (iv) sinθ=cosθ for all values of θ.

The base radii of two cylinders are in the ratio 3:4 and their heights in the ratio 5:2. The volume of the first cylinder is 300 cm3. What is the volume of the second?

In the class interval 22-26, the lower limit is _____ .

A student while doing a math problem , misplaced the decimal point. Due to this the digit at thousandths place became the digit at hundredths place. Identify the number which the child had written incorrectly if the actual number was 45.6547.

If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, show that CA=2 OD.

Find the point (a,a) which is on 4x+5y=27. [1 MARK]

What is the Ratio between KQ and KM? PQRS is a square and K and M are midpoints of PQ and QR respectively.

ABC is a triangle in which D is the mid point of BC and E is the mid point of AD. Then area (∆BED) is equal to

Find the ratio of the areas of two similar triangles ΔABC and ΔPQR shown in the figure.

In the given figure, AB is the diameter of the circle. Find the value of x.

The largest sphere is carved out of a cube of side 7 cm. Then, the volume of the sphere is

An isosceles triangle ABC has AC = BC. CD bisects AB at D and ∠ CAB = 55o. Find ∠ ACB.70

The value of (√3+√2)2 is equal to ____.

Question 39 Fill in the blanks to make the statement true. If a wire in the shape of a square is rebent into a rectangle, then the ___ of both shapes remain same, but ___ may vary.

A set of numbers which include both positive and negative numbers and do not have a fractional component and are denoted by letter Z are known as __

A square is inscribed in a circle with radius 'r'. What is the probability that a randomly selected point within the circle is not within the square?

In the below figure find the value of ∠QOR. Given that ∠QSR=40∘ and O is the centre of the circle.

If I join 2 equilateral triangles along a side, what quadrilteral do I get?

How do you represent 0.3125 in the form of pq, where p and q are integers and q is not zero?

Find a quadratic polynomial with 18 as the sum and 2 as product of its zeroes.

What is (x−y)3?

List-II gives distance between pair of points given in List-I. Match them correctly. List−I List II(P)(−5,7),(−1,3)(1)5(Q)(5,6),(1,3)(2)√8(R)(√3+1,1),(0,√3)(3)√6(S)(0,0),(−√3,√3)(4)4√2

Factorise: 5x2−16x−21

if sin 10A∘=cos(2A−30)∘, then the value of A in degrees is ____ .

What is the degree of the 0 polynomial

P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meets BC at Q, prove that ΔBPQ is an isosceles triangle.

Draw the graph of the modulus function, defined by f:R→R:f(x)=|x|={x, when x≥0−x, when x&lt;0

Find the product (2x+7)(2x–7) using identities.

John covers a part of the journey at 20kmhr and the remaining at 70kmhr, taking total of 8 hours to cover the distance of 400 km. How many hours he has been driving at 70kmhr?

sin 36∘ sin 72∘ sin 108∘ sin 144∘=516

12(x​​​​​​2​​​+7)2-8(x​​​​​​2​​​​​+7)2(2x-1)-15(2x-1)2

The quotient when 4x3+x2+5x+8 is divided by (x+1) is .

The value of x that satisfies |x−1|=|x+3| is

Simplify : (a2−b2)3+(b2−c2)3+(c2−a2)3÷[(a−b)3+(b−c)3+(c−a)3]

In the given figure, if ∠ACB = 30∘, the value of ∠ACD is ___∘.

In fig., if <OAB=40∘, the < ACB is equal to:

Question 6 Ordinate of all points on the x-axis is A) 0 B) 1 C) -1 D) Any number

Question 39 Fill in the blanks to make the statement true. If a wire in the shape of a square is rebent into a rectangle, then the _ of both shapes remain same, but _ may vary.

Draw the graph of the modulus function, defined by f:R→R:f(x)=|x|={x, when x≥0−x, when x<0

12(x2+7)2-8(x2+7)2(2x-1)-15(2x-1)2