32581 + Interview Questions in Mathematics

1.	11.Cot 15/2 is equal to 1)1+2+3+4 (2)2+3+45 3)2+3+4+6 (4)3+4+5+7
Answer» 11.Cot 15/2 is equal to 1)1+2+3+4 (2)2+3+45 3)2+3+4+6 (4)3+4+5+7

Discussion

2.	Question 9 (vii)Solve the following pairs of equation2xyx+y=32, xy2x−y=−310, x+y≠0,2x−y≠0
Answer» Question 9 (vii) Solve the following pairs of equation $\frac{2 x y}{x + y} = \frac{3}{2}, \frac{x y}{2 x - y} = \frac{- 3}{10}, x + y \neq 0, 2 x - y \neq 0$

Discussion

3.	5. How to find equation of a line
Answer» 5. How to find equation of a line

Discussion

4.	If A, B and C are interior angles of a triangle ABC, andsin(B+C2)=cos(x),then what is the value of x?
Answer» If A, B and C are interior angles of a triangle ABC, and $sin (\frac{B + C}{2}) = cos (x),$ then what is the value of x?

Discussion

5.	Identify the correct construction of the division of ¯¯¯¯¯¯¯¯PQ into three parts.
Answer» Identify the correct construction of the division of $¯ ¯¯¯¯¯¯ ¯ P Q$ into three parts.

Discussion

6.	If A = {2, 3, 4} and n represents any element of A, then write the following sets containing all numbers represented by a) 4n – 1 b) 3(n – 1)
Answer» If A = {2, 3, 4} and n represents any element of A, then write the following sets containing all numbers represented by a) 4n – 1 b) 3(n – 1)

Discussion

7.	Write the value of k for which the system of equations x + ky = 0, 2x − y = 0 has unique solution.
Answer» Write the value of k for which the system of equations x + ky = 0, 2x − y = 0 has unique solution.

Discussion

8.	The length of a chord which is at a distance of 5 cm from the centre a circle of radius 13 cm is
Answer» The length of a chord which is at a distance of 5 cm from the centre a circle of radius 13 cm is

Discussion

9.	In the given figure, ∠ACB=90o and CD⊥AB.Prove that BC2AC2=BDAD.
Answer» In the given figure, $∠ A C B = 90^{o} a n d C D ⊥ A B$ . Prove that $\frac{B C^{2}}{A C^{2}} = \frac{B D}{A D}$ .

9.

In the given figure, ∠ACB=90o and CD⊥AB.Prove that BC2AC2=BDAD.

Answer»

In the given figure, $∠ A C B = 90^{o} a n d C D ⊥ A B$ .

Prove that $\frac{B C^{2}}{A C^{2}} = \frac{B D}{A D}$ .

Discussion

10.	Question 06. A game consists of spinning an arrow which comes to rest pointing at one of the regions (1, 2 or 3)(see figure). Are the outcomes 1, 2 and 3 equally likely to occur ? Give reasons.
Answer» Question 06. A game consists of spinning an arrow which comes to rest pointing at one of the regions (1, 2 or 3)(see figure). Are the outcomes 1, 2 and 3 equally likely to occur ? Give reasons.

Discussion

11.	30. A cone of maximum volume is inscribed in a given sphere. Then show that the ratio of the height of the cone to the diameter of the sphere is ⅔.
Answer» 30. A cone of maximum volume is inscribed in a given sphere. Then show that the ratio of the height of the cone to the diameter of the sphere is ⅔.

Discussion

12.	If tan 2A = cot (A-18∘), then find the value of A.
Answer» If tan 2A = cot (A- $18^{\circ}$ ), then find the value of A.

Discussion

13.	If two zeros of the polynomial f(x)=x4−6x3−26x2+138x−35 are 2±√3, find ohter zeros. [4 MARKS]
Answer» If two zeros of the polynomial $f (x) = x^{4} - 6 x^{3} - 26 x^{2} + 138 x - 35$ are $2 \pm \sqrt{3}$ , find ohter zeros. [4 MARKS]

Discussion

14.	Question 33 A letter of English alphabets is chosen at random. Determine the probability that the letter is a constant.
Answer» Question 33 A letter of English alphabets is chosen at random. Determine the probability that the letter is a constant.

Discussion

15.	For what values of x, equation \|tan x + sec x\| = \|tan x\| + \|sec x\| is true?
Answer» For what values of x, equation \|tan x + sec x\| = \|tan x\| + \|sec x\| is true?

Discussion

16.	Question 2(i)Represent the following situations in the form of quadratic equations.(i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Answer» Question 2(i) Represent the following situations in the form of quadratic equations. (i) The area of a rectangular plot is $528 m^{2}$ . The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Discussion

17.	At any point on a circle, there can be ___ tangent/tangents
Answer» At any point on a circle, there can be ___ tangent/tangents

Discussion

18.	if x^2-6x+5 is a factor of x^4+ax^2-b then the value of a and b are?
Answer» if x^2-6x+5 is a factor of x^4+ax^2-b then the value of a and b are?

Discussion

19.	IF (2p-1), 7, 3p are in AP, find hte value of p.
Answer» IF (2p-1), 7, 3p are in AP, find hte value of p.

Discussion

20.	If x=-12, is a solution of the quadratic equation 3x2+2kx-3=0, find the value of k.
Answer» If $x = - \frac{1}{2}$ , is a solution of the quadratic equation $3 x^{2} + 2 k x - 3 = 0$ , find the value of k.

Discussion

21.	In order to paint a solid frustum, which area would be taken into consideration?
Answer» In order to paint a solid frustum, which area would be taken into consideration?

Discussion

22.	If the surface area of a sphere is 2826 cm2 then find its volume. (π=3.14)
Answer» If the surface area of a sphere is $2826 c m^{2}$ then find its volume. $(π = 3.14)$

Discussion

23.	Solve the following quadratic equation by factorization. 2x2+ax−a2=0
Answer» Solve the following quadratic equation by factorization. $2 x^{2} + a x - a^{2} = 0$

Discussion

24.	In the given figure, O is the centre of the circle. Find x.
Answer» In the given figure, O is the centre of the circle. Find $x$ .

24.

In the given figure, O is the centre of the circle. Find x.

Answer»

In the given figure, O is the centre of the circle. Find $x$ .

Discussion

25.	Question 7If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
Answer» Question 7 If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

Discussion

26.	Question 10A pair of linear equations which has a unique solution x = 2 and y = - 3 is(A) x + y = 1 and 2x – 3y = -5(B) 2x + 5y = - 11 and 4x + 10y = - 22(C) 2x – y = 1 and 3x + 2y = 0(D) x – 4y + 14 = 0 and 5x – y – 13 = 0
Answer» Question 10 A pair of linear equations which has a unique solution x = 2 and y = - 3 is (A) x + y = 1 and 2x – 3y = -5 (B) 2x + 5y = - 11 and 4x + 10y = - 22 (C) 2x – y = 1 and 3x + 2y = 0 (D) x – 4y + 14 = 0 and 5x – y – 13 = 0

Discussion

27.	If the ratio of volume to total surface area of a solid sphere is 8 : 1, then find the radius of the sphere.
Answer» If the ratio of volume to total surface area of a solid sphere is 8 : 1, then find the radius of the sphere.

Discussion

28.	Find the centre of a circle passing through points (6, -6), (3, -7) and (3, 3).
Answer» Find the centre of a circle passing through points (6, -6), (3, -7) and (3, 3).

Discussion

29.

Find the mean of each of the following frequency distributions : Class interval: 0−10 10−20 20−30 30−40 40−50 Frequency: 9 12 15 10 14

Answer» Find the mean of each of the following frequency distributions :

Class interval:	0−10	10−20	20−30	30−40	40−50
Frequency:	9	12	15	10	14

Discussion

30.	In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Find the (i) perimeter, (ii) area of the shaded region. [CBSE 2011]
Answer» In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Find the (i) perimeter, (ii) area of the shaded region. [CBSE 2011]

Discussion

31.	78.A man observes that at a point due south os a certain tower its angle of elevation is 60 degree .he then walks 100 metres due west on a horizontal plane and finds that the angle of elevation is 30 degree .find the height of the tower and his original distance from it.
Answer» 78.A man observes that at a point due south os a certain tower its angle of elevation is 60 degree .he then walks 100 metres due west on a horizontal plane and finds that the angle of elevation is 30 degree .find the height of the tower and his original distance from it.

Discussion

32.	The logarithmic form of 100=5x is .
Answer» The logarithmic form of $100 = 5^{x}$ is .

Discussion

33.	14. Prove Euclid's division lemma
Answer» 14. Prove Euclid's division lemma

Discussion

34.	A bag contains 8 red, 2 black and 7 white balls. One ball is drawn at random. The probability that the ball drawn is not white is__.
Answer» A bag contains 8 red, 2 black and 7 white balls. One ball is drawn at random. The probability that the ball drawn is not white is__.

Discussion

35.	The volume of hemisphere with total surface area 115.62 cm2 is approximately (Take π= 22/7)
Answer» The volume of hemisphere with total surface area 115.62 cm² is approximately (Take π= 22/7)

Discussion

36.	A point C on the level ground is at some distance from a 15 m pole AB. If the angle of elevation of the top of the pole from point C is 30°, then how far is point C from the foot of the pole?
Answer» A point C on the level ground is at some distance from a 15 m pole AB. If the angle of elevation of the top of the pole from point C is 30°, then how far is point C from the foot of the pole?

Discussion

37.	Let Sn denotes the sum of the first n terms of an AP and S2n = 3 Sn . Then find the ratio S3n : Sn
Answer» Let S_ndenotes the sum of the first n terms of an AP and S_2n= 3 S_n. Then find the ratio S_3n: S_n

37.

Let Sn denotes the sum of the first n terms of an AP and S2n = 3 Sn . Then find the ratio S3n : Sn

Answer»

Let S_ndenotes the sum of the first n terms of an AP and

S_2n= 3 S_n. Then find the ratio S_3n: S_n

Discussion

38.	If chords AB and PQ are equal, ∠AOB=55∘, and ∠ POQ=x, then x = ___.
Answer» If chords AB and PQ are equal, $∠ A O B = 55^{\circ}$ , and $∠ P O Q = x,$ then $x$ = ___.

38.

If chords AB and PQ are equal, ∠AOB=55∘, and ∠ POQ=x, then x = ___.

Answer»

If chords AB and PQ are equal, $∠ A O B = 55^{\circ}$ , and $∠ P O Q = x,$ then $x$ = ___.

Discussion

39.	If the sum to n terms of an AP is given by Sn = (11 - a + b)n + (a - b) n2 , then the first term is _______ .
Answer» If the sum to n terms of an AP is given by $S_{n}$ = (11 - a + b)n + (a - b) $n^{2}$ , then the first term is _______ .

Discussion

40.	Check graphically whether the pair of linear equation 4x − y − 8 = 0 and 2x − 3y + 6 = 0 is consistent. Also, find the vertices of the triangle formed by these lines with the x-axis.
Answer» Check graphically whether the pair of linear equation 4x − y − 8 = 0 and 2x − 3y + 6 = 0 is consistent. Also, find the vertices of the triangle formed by these lines with the x-axis.

Discussion

41.	Question 5A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs. 16 per 100 cm2.[Assume π=227]
Answer» Question 5 A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of $R s . 16 p e r 100 c m^{2} . [A s s u m e π = \frac{22}{7}]$

Discussion

42.	The two equal sides of an isosceles triangle with fixed base 2√3 cm are decreasing at the rate of 0.3 cm/sec. The rate (in sq.cm/sec) of decrease in its area, when the two equal sides are equal to base, is equal to
Answer» The two equal sides of an isosceles triangle with fixed base $2 \sqrt{3} cm$ are decreasing at the rate of $0.3 cm/sec .$ The rate (in $sq.cm/sec$ ) of decrease in its area, when the two equal sides are equal to base, is equal to

Discussion

43.	In the given below figure, from an external point P, a tangent PT and a secant PAB is drawn to a circle with centre O. ON is perpendicular on the chord AB. Prove that PA. PB = PT2.
Answer» In the given below figure, from an external point P, a tangent PT and a secant PAB is drawn to a circle with centre O. ON is perpendicular on the chord AB. Prove that PA. PB = PT2.

Discussion

44.	86.Three concentric spherical shell have radii a b c ( (a
Answer» 86.Three concentric spherical shell have radii a b c ( (a

Discussion

45.	Yash scored 55 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. If 4 marks had been awarded for each correct answer and 2 marks had been deducted for each incorrect answer, then Yash would have scored 70 marks. How many questions were there in the test?
Answer» Yash scored 55 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. If 4 marks had been awarded for each correct answer and 2 marks had been deducted for each incorrect answer, then Yash would have scored 70 marks. How many questions were there in the test?

Discussion

46.	A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 cm3 and its diameter is 7 cm, then find the height of the toy. [CBSE 2012]
Answer» A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 cm³ and its diameter is 7 cm, then find the height of the toy. [CBSE 2012]

Discussion

47.	Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:(i) (ii) (iii)
Answer» Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: (i) (ii) (iii)

47.

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:(i) (ii) (iii)

Answer»

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

(i)

(ii)

(iii)

Discussion

48.	Question 5 In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Answer» Question 5 In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

Discussion

49.	Find the area of ∆ABC with A(1, −4) and midpoints of sides through A being (2, −1) and (0, −1). [CBSE 2015]
Answer» Find the area of $∆ A B C$ with A(1, −4) and midpoints of sides through A being (2, −1) and (0, −1). [CBSE 2015]

Discussion

50.	Question 2 (iii) Write whether the given statement is true or false. Justify your answer. Every quadratic equation has at least two roots.
Answer» Question 2 (iii) Write whether the given statement is true or false. Justify your answer. Every quadratic equation has at least two roots.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

11.Cot 15/2 is equal to 1)1+2+3+4 (2)2+3+45 3)2+3+4+6 (4)3+4+5+7

Question 9 (vii)Solve the following pairs of equation2xyx+y=32, xy2x−y=−310, x+y≠0,2x−y≠0

5. How to find equation of a line

If A, B and C are interior angles of a triangle ABC, andsin(B+C2)=cos(x),then what is the value of x?

Identify the correct construction of the division of ¯¯¯¯¯¯¯¯PQ into three parts.

If A = {2, 3, 4} and n represents any element of A, then write the following sets containing all numbers represented by a) 4n – 1 b) 3(n – 1)

Write the value of k for which the system of equations x + ky = 0, 2x − y = 0 has unique solution.

The length of a chord which is at a distance of 5 cm from the centre a circle of radius 13 cm is

In the given figure, ∠ACB=90o and CD⊥AB.Prove that BC2AC2=BDAD.

Question 06. A game consists of spinning an arrow which comes to rest pointing at one of the regions (1, 2 or 3)(see figure). Are the outcomes 1, 2 and 3 equally likely to occur ? Give reasons.

30. A cone of maximum volume is inscribed in a given sphere. Then show that the ratio of the height of the cone to the diameter of the sphere is ⅔.

If tan 2A = cot (A-18∘), then find the value of A.

If two zeros of the polynomial f(x)=x4−6x3−26x2+138x−35 are 2±√3, find ohter zeros. [4 MARKS]

Question 33 A letter of English alphabets is chosen at random. Determine the probability that the letter is a constant.

For what values of x, equation |tan x + sec x| = |tan x| + |sec x| is true?

Question 2(i)Represent the following situations in the form of quadratic equations.(i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

At any point on a circle, there can be ___ tangent/tangents

if x^2-6x+5 is a factor of x^4+ax^2-b then the value of a and b are?

IF (2p-1), 7, 3p are in AP, find hte value of p.

If x=-12, is a solution of the quadratic equation 3x2+2kx-3=0, find the value of k.

In order to paint a solid frustum, which area would be taken into consideration?

If the surface area of a sphere is 2826 cm2 then find its volume. (π=3.14)

Solve the following quadratic equation by factorization. 2x2+ax−a2=0

In the given figure, O is the centre of the circle. Find x.

Question 7If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

Question 10A pair of linear equations which has a unique solution x = 2 and y = - 3 is(A) x + y = 1 and 2x – 3y = -5(B) 2x + 5y = - 11 and 4x + 10y = - 22(C) 2x – y = 1 and 3x + 2y = 0(D) x – 4y + 14 = 0 and 5x – y – 13 = 0

If the ratio of volume to total surface area of a solid sphere is 8 : 1, then find the radius of the sphere.

Find the centre of a circle passing through points (6, -6), (3, -7) and (3, 3).

Find the mean of each of the following frequency distributions : Class interval: 0−10 10−20 20−30 30−40 40−50 Frequency: 9 12 15 10 14

In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Find the (i) perimeter, (ii) area of the shaded region. [CBSE 2011]

78.A man observes that at a point due south os a certain tower its angle of elevation is 60 degree .he then walks 100 metres due west on a horizontal plane and finds that the angle of elevation is 30 degree .find the height of the tower and his original distance from it.

The logarithmic form of 100=5x is .

14. Prove Euclid's division lemma

A bag contains 8 red, 2 black and 7 white balls. One ball is drawn at random. The probability that the ball drawn is not white is__.

The volume of hemisphere with total surface area 115.62 cm2 is approximately (Take π= 22/7)

A point C on the level ground is at some distance from a 15 m pole AB. If the angle of elevation of the top of the pole from point C is 30°, then how far is point C from the foot of the pole?

Let Sn denotes the sum of the first n terms of an AP and S2n = 3 Sn . Then find the ratio S3n : Sn

If chords AB and PQ are equal, ∠AOB=55∘, and ∠ POQ=x, then x = ___.

If the sum to n terms of an AP is given by Sn = (11 - a + b)n + (a - b) n2 , then the first term is _______ .

Check graphically whether the pair of linear equation 4x − y − 8 = 0 and 2x − 3y + 6 = 0 is consistent. Also, find the vertices of the triangle formed by these lines with the x-axis.

Question 5A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs. 16 per 100 cm2.[Assume π=227]

The two equal sides of an isosceles triangle with fixed base 2√3 cm are decreasing at the rate of 0.3 cm/sec. The rate (in sq.cm/sec) of decrease in its area, when the two equal sides are equal to base, is equal to

In the given below figure, from an external point P, a tangent PT and a secant PAB is drawn to a circle with centre O. ON is perpendicular on the chord AB. Prove that PA. PB = PT2.

86.Three concentric spherical shell have radii a b c ( (a

A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 cm3 and its diameter is 7 cm, then find the height of the toy. [CBSE 2012]

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:(i) (ii) (iii)

Question 5 In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

Find the area of ∆ABC with A(1, −4) and midpoints of sides through A being (2, −1) and (0, −1). [CBSE 2015]

Question 2 (iii) Write whether the given statement is true or false. Justify your answer. Every quadratic equation has at least two roots.