32581 + Interview Questions in Mathematics

1.	Two coins are tossed simultaneously. Find the probability of getting i) 2 heads ii) 2 tails iii) at least one head iv) at most one tail
Answer» Two coins are tossed simultaneously. Find the probability of getting i) 2 heads ii) 2 tails iii) at least one head iv) at most one tail

Discussion

2.	Question 10 An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
Answer» Question 10 An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

Discussion

3.	Two concentric circles are of radii 7 cm and r cm respectively, where r > 7. A chord of the larger Circle, of length 48 cm, touches the smaller circle. Find the value of r.
Answer» Two concentric circles are of radii 7 cm and r cm respectively, where r > 7. A chord of the larger Circle, of length 48 cm, touches the smaller circle. Find the value of r.

Discussion

4.	In ∆ABC, D and E are points on side AB and AC respectively such that DE \|\| BC and AD : DB = 3 : 1. If EA = 3.3 cm, then AC =(a) 1.1 cm(b) 4 cm(c) 4.4 cm(d) 5.5 cm
Answer» In ∆ABC, D and E are points on side AB and AC respectively such that DE \|\| BC and AD : DB = 3 : 1. If EA = 3.3 cm, then AC = (a) 1.1 cm (b) 4 cm (c) 4.4 cm (d) 5.5 cm

Discussion

5.	If the probability of winning a game is 0.3, what is the probability of losing it?
Answer» If the probability of winning a game is 0.3, what is the probability of losing it?

Discussion

6.	Choose the correct answer of the following question:A solid is hemispherical at the bottom and conical (of same radius) above it. If the surface areas of the two parts are equal, then the ratio of its radius and the slant height of the conical part is(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1 [CBSE 2011]
Answer» Choose the correct answer of the following question: A solid is hemispherical at the bottom and conical (of same radius) above it. If the surface areas of the two parts are equal, then the ratio of its radius and the slant height of the conical part is (a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1 [CBSE 2011]

Discussion

7.	Prove that the line segment joining the point of contact of two parallel tangents of a circle passes through its centre
Answer» Prove that the line segment joining the point of contact of two parallel tangents of a circle passes through its centre

Discussion

8.	For the given distinct values x1, x2, x3 .....xn occurring with frequencies f1, f2, f3, ... fn respectively. The mean deviation about mean would be
Answer» For the given distinct values x₁, x₂, x₃ .....x_n occurring with frequencies f₁, f₂, f₃, ... f_n respectively. The mean deviation about mean would be

Discussion

9.	Let f(x) = x2-1, 0 0<x<2 and 2x+3, 2≤x<3, The quadratic equation whose roots are limx→2−f(x),and limx→2+f(x)
Answer» Let f(x) = $x^{2}$ -1, 0 0<x<2 and 2x+3, 2 $\leq$ x<3, The quadratic equation whose roots are ${lim}_{x \to 2^{-}} f (x), a n d {lim}_{x \to 2^{+}} f (x)$

Discussion

10.	Solve each of the following quadratic equations:2x2-x+18=0
Answer» Solve each of the following quadratic equations: $2 x^{2} - x + \frac{1}{8} = 0$

Discussion

11.	A milk tank is in the form of a cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in liters that can be stored in the tank.
Answer» A milk tank is in the form of a cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in liters that can be stored in the tank.

Discussion

12.	if alpha and beta are two zeroes of the polynomial 2x^2+x-6 then form a quadratic equation whose zeroes are 2 alpha and 2 beta
Answer» if alpha and beta are two zeroes of the polynomial 2x^2+x-6 then form a quadratic equation whose zeroes are 2 alpha and 2 beta

Discussion

13.	Ashu is x years old while his mother Mrs Veena is x2 years old. Five years hence Mrs Veena will be three times old as Ashu. Find their present ages.
Answer» Ashu is x years old while his mother Mrs Veena is $x^{2}$ years old. Five years hence Mrs Veena will be three times old as Ashu. Find their present ages.

Discussion

14.	A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs.0.35 per cm2. [Use]
Answer» A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs.0.35 per cm². [Use]

14.

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs.0.35 per cm2. [Use]

Answer»

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs.0.35 per cm². [Use]

Discussion

15.	Two numbers are in the ratio 5:7. Their difference is 10. Find the numbers.
Answer» Two numbers are in the ratio $5 : 7$ . Their difference is $10$ . Find the numbers.

Discussion

16.	The difference in the areas of the regular hexagon circumscribing a circle of radius 10 cm and the regular hexagon inscribed in the circle is ___________.
Answer» The difference in the areas of the regular hexagon circumscribing a circle of radius 10 cm and the regular hexagon inscribed in the circle is ___________.

Discussion

17.	How to prove that 3+2√5 is irrational.
Answer» How to prove that 3+2√5 is irrational.

Discussion

18.	All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is(i) a red card,(ii) a face card,(iii) a card of clubs.
Answer» All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is (i) a red card, (ii) a face card, (iii) a card of clubs.

Discussion

19.	Mr. Ravi opened a recurring deposit account in a bank. He deposited in the installment of Rs. 2500 per month for two years. At the time of maturity he received an amount of Rs. 67,500. Calculate the total interest earned by Mr. Ravi.
Answer» Mr. Ravi opened a recurring deposit account in a bank. He deposited in the installment of Rs. 2500 per month for two years. At the time of maturity he received an amount of Rs. 67,500. Calculate the total interest earned by Mr. Ravi.

Discussion

20.	If the pth term of an AP is q and the qth term is p, then nth term of the A.P is:
Answer» If the $p^{t h}$ term of an AP is $q$ and the $q^{t h}$ term is $p$ , then $n^{t h}$ term of the A.P is:

Discussion

21.	Nikhila spent 5% of her monthly income in her children's education, invested 18% in shares, deposited 3% in a bank, and used 44% for her expenses. She's left with a balance of ₹15,000. Calculate the amount she invested in shares.
Answer» Nikhila spent 5% of her monthly income in her children's education, invested 18% in shares, deposited 3% in a bank, and used 44% for her expenses. She's left with a balance of ₹15,000. Calculate the amount she invested in shares.

Discussion

22.	Mr. Michel invested ₹ 52000 on ₹ 100 shares at a discount of 20% paying 8% dividend. Find his annual dividend.
Answer» Mr. Michel invested ₹ 52000 on ₹ 100 shares at a discount of 20% paying $8 %$ dividend. Find his annual dividend.

Discussion

23.	48. A solid right circular cone if radius 3 cm and slant height 5 cm is cut by a plane through the vertex of the cone into 2 exact pieces. Find the TSA of a single piece
Answer» 48. A solid right circular cone if radius 3 cm and slant height 5 cm is cut by a plane through the vertex of the cone into 2 exact pieces. Find the TSA of a single piece

Discussion

24.	The sum of four consecutive terms in an AP is 32 and the ratio of the product of the first and last terms to the product of two middle terms is 7:15, find the numbers
Answer» The sum of four consecutive terms in an AP is 32 and the ratio of the product of the first and last terms to the product of two middle terms is 7:15, find the numbers

Discussion

25.	In the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region. [Use π= 3.14] [CBSE 2014]
Answer» In the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region. [Use π= 3.14] [CBSE 2014]

Discussion

26.	Evaluate each of the followingsin 60 cos 30° + cos 60° sin 30°
Answer» Evaluate each of the following sin 60 cos 30° + cos 60° sin 30°

Discussion

27.	If the perimeter of a sector of a circle of radius 6.5 cm is 29 cm, then its area is(a) 58 cm2(b) 52 cm2(c) 25 cm2(d) 56 cm2
Answer» If the perimeter of a sector of a circle of radius 6.5 cm is 29 cm, then its area is (a) 58 cm² (b) 52 cm² (c) 25 cm² (d) 56 cm²

Discussion

28.	A man invested Rs.45000 in 15% rs.100 shares quotes at Rs.125. when the market value of these shares rose to Rs.140, he sold some shares, just enough to raise Rs.8400. Calculate The number of shares, he still holds. The dividend due to him on these remaining shares.
Answer» A man invested Rs.45000 in 15% rs.100 shares quotes at Rs.125. when the market value of these shares rose to Rs.140, he sold some shares, just enough to raise Rs.8400. Calculate The number of shares, he still holds. The dividend due to him on these remaining shares.

28.

A man invested Rs.45000 in 15% rs.100 shares quotes at Rs.125. when the market value of these shares rose to Rs.140, he sold some shares, just enough to raise Rs.8400. Calculate The number of shares, he still holds. The dividend due to him on these remaining shares.

Answer»

A man invested Rs.45000 in 15% rs.100 shares quotes at Rs.125. when the market value of these shares rose to Rs.140, he sold some shares, just enough to raise Rs.8400. Calculate

The number of shares, he still holds.
The dividend due to him on these remaining shares.

Discussion

29.	If a and b are distinct real numbers, show that the quadratic equation 2(a2+b2)x2+2(a+b)x+1=0 has no real roots.
Answer» If a and b are distinct real numbers, show that the quadratic equation $2 (a^{2} + b^{2}) x^{2} + 2 (a + b) x + 1 = 0$ has no real roots.

Discussion

30.	The value of limx→−1cos2−cos2xx2−\|x\| is
Answer» The value of $lim x \to - 1 \frac{cos 2 - cos 2 x}{x^{2} - \| x \|}$ is

Discussion

31.	Prove the following trigonometric identities.If cosec θ − sin θ = a3, sec θ − cos θ = b3, prove that a2 b2 (a2 + b2) = 1
Answer» Prove the following trigonometric identities. If cosec θ − sin θ = a³, sec θ − cos θ = b³, prove that a² b² (a² + b²) = 1

Discussion

32.

Find the mean of each of the following frequency distributions : Class interval: 0-6 6-12 12-18 18-24 24-30 Frequency: 6 8 10 9 7

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

Class interval:	0-6	6-12	12-18	18-24	24-30
Frequency:	6	8	10	9	7

Discussion

33.	If a dozen of bananas cost ₹ 24, while 10 apples cost ₹ 100, then how many times an apple is costlier than a banana?
Answer» If a dozen of bananas cost ₹ 24, while 10 apples cost ₹ 100, then how many times an apple is costlier than a banana?

Discussion

34.	The cost of painting the four walls of a room 12 m long at ₹30 per m2 is ₹7560 and the cost of covering the floor with mat at ₹25 per m2 is ₹2700. Find the dimensions of the room.
Answer» The cost of painting the four walls of a room 12 m long at ₹30 per m² is ₹7560 and the cost of covering the floor with mat at ₹25 per m² is ₹2700. Find the dimensions of the room.

Discussion

35.	Find the sum of the n terms of the series 1+3+7+15+31+⋯n terms.
Answer» Find the sum of the n terms of the series $1 + 3 + 7 + 15 + 31 + \dots n$ terms.

Discussion

36.	Two dice are thrown together. The probability of getting the same number on the both dice is [CBSE 2012](a) 12(b) 13(c) 16(d) 112
Answer» Two dice are thrown together. The probability of getting the same number on the both dice is [CBSE 2012] (a) $\frac{1}{2}$ (b) $\frac{1}{3}$ (c) $\frac{1}{6}$ (d) $\frac{1}{12}$

Discussion

37.	Solve x2+x+1√2=0
Answer» Solve $x^{2} + x + \frac{1}{\sqrt{2}} = 0$

37.

Solve x2+x+1√2=0

Answer»

Solve

$x^{2} + x + \frac{1}{\sqrt{2}} = 0$

Discussion

38.	A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are α and β respectively. Prove that the height of the tower is h tan αtan β−tan α [3 MARKS]
Answer» A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are $α$ and $β$ respectively. Prove that the height of the tower is $\frac{h t a n α}{t a n β - t a n α}$ [3 MARKS]

Discussion

39.	Fill in the blanks with the correct rational numbers.46,, ,1924
Answer» Fill in the blanks with the correct rational numbers. $\frac{4}{6}$ ,, , $\frac{19}{24}$

Discussion

40.	Find the value of K for which the roots of equation: 2kxsquare-40x+25=0, are equal and real.?
Answer» Find the value of K for which the roots of equation: 2kxsquare-40x+25=0, are equal and real.?

Discussion

41.	Find the next number in the following sequence: 41.00, 38.50, 36.00, 33.50...
Answer» Find the next number in the following sequence: 41.00, 38.50, 36.00, 33.50...

Discussion

42.	Prove the following:(sin5A-sin7A+sin8A-sin4A)/(cos4A+cos7A-cos5A-cos8A)=tan A
Answer» Prove the following: (sin5A-sin7A+sin8A-sin4A)/(cos4A+cos7A-cos5A-cos8A)=tan A

Discussion

43.	Find the value of x in each of the following :tan x = sin 45° cos 45° + sin 30°
Answer» Find the value of x in each of the following : tan x = sin 45° cos 45° + sin 30°

Discussion

44.	In the given figure, ∠ABC=90∘ and BM is a median drawn from B to AC, AB=8 cm and BC=6 cm. Then, choose the correct option(s).
Answer» In the given figure, $∠ A B C = 90^{\circ}$ and $B M$ is a median drawn from $B$ to $A C, A B = 8 c m$ and $B C = 6 c m .$ Then, choose the correct option(s).

44.

In the given figure, ∠ABC=90∘ and BM is a median drawn from B to AC, AB=8 cm and BC=6 cm. Then, choose the correct option(s).

Answer»

In the given figure, $∠ A B C = 90^{\circ}$ and $B M$ is a median drawn from $B$ to $A C, A B = 8 c m$ and $B C = 6 c m .$ Then, choose the correct option(s).

Discussion

45.	What is sin θ in the given right triangle, right angled at B?
Answer» What is sin $θ$ in the given right triangle, right angled at B?

45.

What is sin θ in the given right triangle, right angled at B?

Answer»

What is sin $θ$ in the given right triangle, right angled at B?

Discussion

46.	Question 18A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ……… as shown the n figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take π=227)
Answer» Question 18 A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ……… as shown the n figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take $π = \frac{22}{7})$

Discussion

47.	Find the roots of the quadratic equation ax2+bx+c=0.
Answer» Find the roots of the quadratic equation $a x^{2} + b x + c = 0$ .

Discussion

48.	Prove the following trigonometric identities.1+cos Asin A=sin A1-cos A
Answer» Prove the following trigonometric identities. $\frac{1 + \cos A}{\sin A} = \frac{\sin A}{1 - \cos A}$

Discussion

49.	What is the value of (cos267o−sin223o)?
Answer» What is the value of $(c o s^{2} 67^{o} - s i n^{2} 23^{o})$ ?

Discussion

50.	If the difference between the two conjugate angles is 100 , then find the angles
Answer» If the difference between the two conjugate angles is 100 , then find the angles

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Two coins are tossed simultaneously. Find the probability of getting i) 2 heads ii) 2 tails iii) at least one head iv) at most one tail

Question 10 An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

Two concentric circles are of radii 7 cm and r cm respectively, where r &gt; 7. A chord of the larger Circle, of length 48 cm, touches the smaller circle. Find the value of r.

In ∆ABC, D and E are points on side AB and AC respectively such that DE || BC and AD : DB = 3 : 1. If EA = 3.3 cm, then AC =(a) 1.1 cm(b) 4 cm(c) 4.4 cm(d) 5.5 cm

If the probability of winning a game is 0.3, what is the probability of losing it?

Prove that the line segment joining the point of contact of two parallel tangents of a circle passes through its centre

For the given distinct values x1, x2, x3 .....xn occurring with frequencies f1, f2, f3, ... fn respectively. The mean deviation about mean would be

Let f(x) = x2-1, 0 0&lt;x&lt;2 and 2x+3, 2≤x&lt;3, The quadratic equation whose roots are limx→2−f(x),and limx→2+f(x)

Solve each of the following quadratic equations:2x2-x+18=0

A milk tank is in the form of a cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in liters that can be stored in the tank.

if alpha and beta are two zeroes of the polynomial 2x^2+x-6 then form a quadratic equation whose zeroes are 2 alpha and 2 beta

Ashu is x years old while his mother Mrs Veena is x2 years old. Five years hence Mrs Veena will be three times old as Ashu. Find their present ages.

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs.0.35 per cm2. [Use]

Two numbers are in the ratio 5:7. Their difference is 10. Find the numbers.

The difference in the areas of the regular hexagon circumscribing a circle of radius 10 cm and the regular hexagon inscribed in the circle is ___________.

How to prove that 3+2√5 is irrational.

All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is(i) a red card,(ii) a face card,(iii) a card of clubs.

Mr. Ravi opened a recurring deposit account in a bank. He deposited in the installment of Rs. 2500 per month for two years. At the time of maturity he received an amount of Rs. 67,500. Calculate the total interest earned by Mr. Ravi.

If the pth term of an AP is q and the qth term is p, then nth term of the A.P is:

Nikhila spent 5% of her monthly income in her children's education, invested 18% in shares, deposited 3% in a bank, and used 44% for her expenses. She's left with a balance of ₹15,000. Calculate the amount she invested in shares.

Mr. Michel invested ₹ 52000 on ₹ 100 shares at a discount of 20% paying 8% dividend. Find his annual dividend.

48. A solid right circular cone if radius 3 cm and slant height 5 cm is cut by a plane through the vertex of the cone into 2 exact pieces. Find the TSA of a single piece

The sum of four consecutive terms in an AP is 32 and the ratio of the product of the first and last terms to the product of two middle terms is 7:15, find the numbers

In the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region. [Use π= 3.14] [CBSE 2014]

Evaluate each of the followingsin 60 cos 30° + cos 60° sin 30°

If the perimeter of a sector of a circle of radius 6.5 cm is 29 cm, then its area is(a) 58 cm2(b) 52 cm2(c) 25 cm2(d) 56 cm2

A man invested Rs.45000 in 15% rs.100 shares quotes at Rs.125. when the market value of these shares rose to Rs.140, he sold some shares, just enough to raise Rs.8400. Calculate The number of shares, he still holds. The dividend due to him on these remaining shares.

If a and b are distinct real numbers, show that the quadratic equation 2(a2+b2)x2+2(a+b)x+1=0 has no real roots.

The value of limx→−1cos2−cos2xx2−|x| is

Prove the following trigonometric identities.If cosec θ − sin θ = a3, sec θ − cos θ = b3, prove that a2 b2 (a2 + b2) = 1

Find the mean of each of the following frequency distributions : Class interval: 0-6 6-12 12-18 18-24 24-30 Frequency: 6 8 10 9 7

If a dozen of bananas cost ₹ 24, while 10 apples cost ₹ 100, then how many times an apple is costlier than a banana?

The cost of painting the four walls of a room 12 m long at ₹30 per m2 is ₹7560 and the cost of covering the floor with mat at ₹25 per m2 is ₹2700. Find the dimensions of the room.

Find the sum of the n terms of the series 1+3+7+15+31+⋯n terms.

Two dice are thrown together. The probability of getting the same number on the both dice is [CBSE 2012](a) 12(b) 13(c) 16(d) 112

Solve x2+x+1√2=0

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are α and β respectively. Prove that the height of the tower is h tan αtan β−tan α [3 MARKS]

Fill in the blanks with the correct rational numbers.46,, ,1924

Find the value of K for which the roots of equation: 2kxsquare-40x+25=0, are equal and real.?

Find the next number in the following sequence: 41.00, 38.50, 36.00, 33.50...

Prove the following:(sin5A-sin7A+sin8A-sin4A)/(cos4A+cos7A-cos5A-cos8A)=tan A

Find the value of x in each of the following :tan x = sin 45° cos 45° + sin 30°

In the given figure, ∠ABC=90∘ and BM is a median drawn from B to AC, AB=8 cm and BC=6 cm. Then, choose the correct option(s).

What is sin θ in the given right triangle, right angled at B?

Question 18A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ……… as shown the n figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take π=227)

Find the roots of the quadratic equation ax2+bx+c=0.

Prove the following trigonometric identities.1+cos Asin A=sin A1-cos A

What is the value of (cos267o−sin223o)?

If the difference between the two conjugate angles is 100 , then find the angles

Two concentric circles are of radii 7 cm and r cm respectively, where r > 7. A chord of the larger Circle, of length 48 cm, touches the smaller circle. Find the value of r.

Let f(x) = x2-1, 0 0<x<2 and 2x+3, 2≤x<3, The quadratic equation whose roots are limx→2−f(x),and limx→2+f(x)