32581 + Interview Questions in Mathematics

1.	A and B are friends. A is elder to B by 5 years. B's sister C is half the age of B while A's father D is 8 years older than twice the age of B. If the present age of D is 48 years, they find the present ages of A, B and C.
Answer» A and B are friends. A is elder to B by 5 years. B's sister C is half the age of B while A's father D is 8 years older than twice the age of B. If the present age of D is 48 years, they find the present ages of A, B and C.

Discussion

2.	How many polynomials having zeroes as-7 and 2 ?
Answer» How many polynomials having zeroes as-7 and 2 ?

Discussion

3.	In the following figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that(i) AB2 = BC × BD(ii) AC2 = BC × DC(iii) AD2 = BD × CD
Answer» In the following figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that (i) AB² = BC × BD (ii) AC² = BC × DC (iii) AD² = BD × CD

3.

In the following figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that(i) AB2 = BC × BD(ii) AC2 = BC × DC(iii) AD2 = BD × CD

Answer»

In the following figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that

(i) AB² = BC × BD

(ii) AC² = BC × DC

(iii) AD² = BD × CD

Discussion

4.	In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.
Answer» In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

4.

In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

Answer»

In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

Discussion

5.	Find a cubic polynomial whose zeroes are 2, −3 and 4
Answer» Find a cubic polynomial whose zeroes are 2, −3 and 4

Discussion

6.	the number of real zeros of a polynomial of degree 5 cannot have is:-a 1b 2c 3d 5
Answer» the number of real zeros of a polynomial of degree 5 cannot have is:- a 1 b 2 c 3 d 5

Discussion

7.	A clock strikes once at 1 o'clock, twice at 2 o'clock, thrice at 3 o’clock and so on. How many times will it strike in 12 hours?
Answer» A clock strikes once at 1 o'clock, twice at 2 o'clock, thrice at 3 o’clock and so on. How many times will it strike in 12 hours?

Discussion

8.	Find the area of the minor segment of a circle of radius 42cm, if length of the correspondingc is 44cm.
Answer» Find the area of the minor segment of a circle of radius 42cm, if length of the correspondingc is 44cm.

Discussion

9.	x=a sin (wt=c) where x is displacement and t is time what are the units of a, w and c?
Answer» x=a sin (wt=c) where x is displacement and t is time what are the units of a, w and c?

Discussion

10.	Why the slope of the tangent of a curve is dy/dx ?
Answer» Why the slope of the tangent of a curve is dy/dx ?

Discussion

11.	Prove the following trigonometric identities.If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
Answer» Prove the following trigonometric identities. If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x² − y² = a² − b²

Discussion

12.	Two parallel chords 10 cm and 24 cm long are drawn on the same side of the centre of a circle of radius 13 cm. Find the distance between the chords.
Answer» Two parallel chords 10 cm and 24 cm long are drawn on the same side of the centre of a circle of radius 13 cm. Find the distance between the chords.

Discussion

13.	Find the distance between the following pairs of points:(a, b), (− a, − b)
Answer» Find the distance between the following pairs of points: (a, b), (− a, − b)

Discussion

14.	If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?
Answer» If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?

Discussion

15.	If sec 4 A= cosec (A-20 degree ) and A
Answer» If sec 4 A= cosec (A-20 degree ) and A<90 degree, then A is equal to

Discussion

16.	Question 2 For which value (s) of k will the pair of equations kx + 3y = 5 – 3, 12x + 5y = k has no solution?
Answer» Question 2 For which value (s) of k will the pair of equations kx + 3y = 5 – 3, 12x + 5y = k has no solution?

Discussion

17.

Compute the mode of the following data: [CBSE 2013] Class 0−20 20−40 40−60 60−80 80−100 Frequency 25 16 28 20 5

Answer»

Compute the mode of the following data: [CBSE 2013]

Class	0−20	20−40	40−60	60−80	80−100
Frequency	25	16	28	20	5

Discussion

18.	A chessboard contains 64 equal squares and the area of each square is 6.25 cm2. A border around the board is 2 cm wide. Find the length of the side of the chess board.
Answer» A chessboard contains 64 equal squares and the area of each square is $6.25 c m^{2}$ . A border around the board is 2 cm wide. Find the length of the side of the chess board.

Discussion

19.	Kylie buys an article for ₹ 10000 and pays 7% tax. He sells the same article for ₹ 13000 and charges 9% tax. Find the VAT paid by Kylie.
Answer» Kylie buys an article for ₹ 10000 and pays 7% tax. He sells the same article for ₹ 13000 and charges 9% tax. Find the VAT paid by Kylie.

Discussion

20.	What will be the condition for (a2−9)x2+bx+c=0 to be a quadratic equation?
Answer» What will be the condition for $(a^{2} - 9) x^{2} + b x + c = 0$ to be a quadratic equation?

Discussion

21.	How many solutions does y=2x has? Write any four solution.
Answer» How many solutions does y=2x has? Write any four solution.

Discussion

22.	Question 6In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA=30∘ . Then , AT is equal to(A) 4 cm(B) 2 cm(C) 2 √3 cm(D) 4 √3 cm
Answer» Question 6 In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and $∠ O T A = 30^{\circ}$ . Then , AT is equal to (A) 4 cm (B) 2 cm (C) 2 $\sqrt{3}$ cm (D) 4 $\sqrt{3}$ cm

Discussion

23.	A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used, at the rate of Rs 25 per metre.
Answer» A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used, at the rate of Rs 25 per metre.

Discussion

24.	Using Euclid division lemma , prove that difference of squares of 2 odd natural numbers is a multiple of 8
Answer» Using Euclid division lemma , prove that difference of squares of 2 odd natural numbers is a multiple of 8

Discussion

25.	Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.
Answer» Explain why $7 \times 11 \times 13 + 13$ and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$ are composite numbers.

Discussion

26.

The following are the ages of 300 patients getting medical treatment in a hospital on a particular day: Age (in years)10−2020−3030−4040−5050−6060−70Number of patients604255705320Form a 'less than type' cumulative frequency distribution. [CBSE 2013]

Answer»

The following are the ages of 300 patients getting medical treatment in a hospital on a particular day:

Age (in years)	10−20	20−30	30−40	40−50	50−60	60−70
Number of patients	60	42	55	70	53	20

Form a 'less than type' cumulative frequency distribution. [CBSE 2013]

Discussion

27.	Congress has enacted legislation forbidding state and local governments from raising taxes on connections that link consumers to the Internet for the next three years.
Answer» Congress has enacted legislation forbidding state and local governments from raising taxes on connections that link consumers to the Internet for the next three years.

Discussion

28.	Show that the following numbers are irrational.(i) 12(ii) 75(iii) 6+2(iv) 3-5
Answer» Show that the following numbers are irrational. (i) $\frac{1}{\sqrt{2}}$ (ii) $7 \sqrt{5}$ (iii) $6 + \sqrt{2}$ (iv) $3 - \sqrt{5}$

Discussion

29.	Find the HCF of 525 and 270 using Euclid’s division algorithm.15
Answer» Find the HCF of 525 and 270 using Euclid’s division algorithm. 15

Discussion

30.	A pendulum swings through an angle of 30∘ and describes an arc 8.8 cm in length. Find the length of pendulum in cm.
Answer» A pendulum swings through an angle of $30^{\circ}$ and describes an arc 8.8 cm in length. Find the length of pendulum in cm.

Discussion

31.	Simplify the expression-(cosec2θ−1)×(sec2θ−1)
Answer» Simplify the expression- $(c o s e c^{2} θ - 1) \times (s e c^{2} θ - 1)$

Discussion

32.

Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P. a d n an I 7 3 8 …... II − 18 ….. 10 0 III ….. − 3 18 − 5 IV − 18.9 2.5 ….. 3.6 V 3.5 0 105 …..

Answer»

Fill in the blanks in the following table, given that a is the first term, d the common difference and a_n the n^th term of the A.P.

	a	d	n	a_n
I	7	3	8	…...
II	− 18	…..	10	0
III	…..	− 3	18	− 5
IV	− 18.9	2.5	…..	3.6
V	3.5	0	105	…..

Discussion

33.	Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
Answer» Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

Discussion

34.	ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid-points of sides AB, BC, CD, DA, respectively.A circular rangoli of radius 10 cm is drawn at the centre as shown in the given figure. Find the area of shaded portion.
Answer» ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid-points of sides AB, BC, CD, DA, respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in the given figure. Find the area of shaded portion.

34.

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid-points of sides AB, BC, CD, DA, respectively.A circular rangoli of radius 10 cm is drawn at the centre as shown in the given figure. Find the area of shaded portion.

Answer»

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid-points of sides AB, BC, CD, DA, respectively.

A circular rangoli of radius 10 cm is drawn at the centre as shown in the given figure. Find the area of shaded portion.

Discussion

35.	Expand the following(1) (2) (3) (4) (5) (6)
Answer» Expand the following (1) (2) (3) (4) (5) (6)

35.

Expand the following(1) (2) (3) (4) (5) (6)

Answer»

Expand the following

(1)

(2)

(3)

(4)

(5)

(6)

Discussion

36.	13. There exist unique positive integers a and b such that a²+ 84a + 2008 = b²
Answer» 13. There exist unique positive integers a and b such that a²+ 84a + 2008 = b²

Discussion

37.	Three consecutive natural numbers are such that the square of the middle number excceds the difference of the squares of the other two by 60. Assume the middle number to be x and form a quadratic equation satisfying's the above statement. Hence; find the three numbers.
Answer» Three consecutive natural numbers are such that the square of the middle number excceds the difference of the squares of the other two by 60. Assume the middle number to be x and form a quadratic equation satisfying's the above statement. Hence; find the three numbers.

37.

Three consecutive natural numbers are such that the square of the middle number excceds the difference of the squares of the other two by 60. Assume the middle number to be x and form a quadratic equation satisfying's the above statement. Hence; find the three numbers.

Answer»

Three consecutive natural numbers are such that the square of the middle number excceds the difference of the squares of the other two by 60.

Assume the middle number to be x and form a quadratic equation satisfying's the above statement. Hence; find the three numbers.

Discussion

38.	In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64, find n.
Answer» In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64, find n.

Discussion

39.	Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.[4 MARKS]
Answer» Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.[4 MARKS]

Discussion

40.	A restaurant POQR is being constructed in the middle of a circular lake. The circle, which has its center at O is touching the mid-points of the boundary ABCD as shown in the figure. AB=CD and AD=BC. If BC=8 cm, then the area of AQOP is
Answer» A restaurant POQR is being constructed in the middle of a circular lake. The circle, which has its center at O is touching the mid-points of the boundary ABCD as shown in the figure. AB=CD and AD=BC. If BC=8 cm, then the area of AQOP is

Discussion

41.	AB is a chord of a circle with centre O , AOC is a diameter and AT is the tangent at A as shown in . Prove that ∠BAT = ∠ACB.
Answer» AB is a chord of a circle with centre O , AOC is a diameter and AT is the tangent at A as shown in . Prove that ∠BAT = ∠ACB.

Discussion

42.	volume and surface area of a solid hemisphere are numerically equal . what is the diameter of the hemisphere
Answer» volume and surface area of a solid hemisphere are numerically equal . what is the diameter of the hemisphere

Discussion

43.

A and B are partners in a firm sharing profits and losses in the ratio of 3 : 2. Following is their Balance Sheet as at 31st March, 2019: Liabilities ₹ Assets ₹ Capital A/cs: Building 35,000 A 50,000 Machinery 25,000 B 30,000 80,000 Stock 15,000 Creditors 20,000 Debtors 15,000 Investments 5,000 Bank 5,000 1,00,000 1,00,000 C is admitted as a partner on 1st April, 2019 on the following terms:(a) C is to pay ₹ 20,000 as capital for 1/4th share. He also pays ₹ 5,000 as premium for goodwill.(b) Debtors amounted to ₹ 3,000 is to be written off as bad and a Provision of 10% is created against Doubtful Debts on the remaining amount.(c) No entry has been passed in respect of a debt of ₹ 300 recovered by A from a customer, which was previously written off as bad in previous year. The amount is to be paid by A.(d) Investments are taken over by B at their market value of ₹ 4,900 against cash payment.You are required to prepare Revaluation Account, Partner's Capital Accounts and new Balance Sheet.

Answer» A and B are partners in a firm sharing profits and losses in the ratio of 3 : 2. Following is their Balance Sheet as at 31st March, 2019:


Liabilities		₹	Assets	₹
Capital A/cs:			Building	35,000
A	50,000		Machinery	25,000
B	30,000	80,000	Stock	15,000
Creditors		20,000	Debtors	15,000
			Investments	5,000
			Bank	5,000

		1,00,000		1,00,000

C is admitted as a partner on 1st April, 2019 on the following terms:

(a) C is to pay ₹ 20,000 as capital for 1/4th share. He also pays ₹ 5,000 as premium for goodwill.

(b) Debtors amounted to ₹ 3,000 is to be written off as bad and a Provision of 10% is created against Doubtful Debts on the remaining amount.

(c) No entry has been passed in respect of a debt of ₹ 300 recovered by A from a customer, which was previously written off as bad in previous year. The amount is to be paid by A.

(d) Investments are taken over by B at their market value of ₹ 4,900 against cash payment.

You are required to prepare Revaluation Account, Partner's Capital Accounts and new Balance Sheet.

Discussion

44.	7 – 9x + 2x2 is called a _________ polynomial.
Answer» 7 – 9x + 2x² is called a _________ polynomial.

Discussion

45.	In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the given figure. Find the area of the design (Shaded region).
Answer» In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the given figure. Find the area of the design (Shaded region).

45.

In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the given figure. Find the area of the design (Shaded region).

Answer»

In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the given figure. Find the area of the design (Shaded region).

Discussion

46.	Five cards − the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card is then picked up at random.(a) What is the probability that the drawn card is the queeen?(b) If the queen is drawn and put aside and a second card is drawn, find the probability that the second card is (i) an ace, (ii) a queen.
Answer» Five cards − the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card is then picked up at random. (a) What is the probability that the drawn card is the queeen? (b) If the queen is drawn and put aside and a second card is drawn, find the probability that the second card is (i) an ace, (ii) a queen.

Discussion

47.

The coordinates of A, B & C are (2 , 3); (-1 , 2) & (3 , 0). Find equation of the line through A and perpendicular to BC.

Answer»

The coordinates of A, B & C are (2 , 3); (-1 , 2) & (3 , 0).

Find equation of the line through A and perpendicular to BC.

Discussion

48.

In a single throw of a die, find the probability of getting: i) 7 ii) a number less than 7

Answer»

In a single throw of a die, find the probability of getting:

i) 7

ii) a number less than 7

Discussion

49.	When four quantities are in proportion then the product of extreme terms is equal to the product of ___ .
Answer» When four quantities are in proportion then the product of extreme terms is equal to the product of ___ .

Discussion

50.

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30 °.

Answer»

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30 °.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A and B are friends. A is elder to B by 5 years. B's sister C is half the age of B while A's father D is 8 years older than twice the age of B. If the present age of D is 48 years, they find the present ages of A, B and C.

How many polynomials having zeroes as-7 and 2 ?

In the following figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that(i) AB2 = BC × BD(ii) AC2 = BC × DC(iii) AD2 = BD × CD

In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

Find a cubic polynomial whose zeroes are 2, −3 and 4

the number of real zeros of a polynomial of degree 5 cannot have is:-a 1b 2c 3d 5

A clock strikes once at 1 o'clock, twice at 2 o'clock, thrice at 3 o’clock and so on. How many times will it strike in 12 hours?

Find the area of the minor segment of a circle of radius 42cm, if length of the correspondingc is 44cm.

x=a sin (wt=c) where x is displacement and t is time what are the units of a, w and c?

Why the slope of the tangent of a curve is dy/dx ?

Prove the following trigonometric identities.If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2

Two parallel chords 10 cm and 24 cm long are drawn on the same side of the centre of a circle of radius 13 cm. Find the distance between the chords.

Find the distance between the following pairs of points:(a, b), (− a, − b)

If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?

If sec 4 A= cosec (A-20 degree ) and A

Question 2 For which value (s) of k will the pair of equations kx + 3y = 5 – 3, 12x + 5y = k has no solution?

Compute the mode of the following data: [CBSE 2013] Class 0−20 20−40 40−60 60−80 80−100 Frequency 25 16 28 20 5

A chessboard contains 64 equal squares and the area of each square is 6.25 cm2. A border around the board is 2 cm wide. Find the length of the side of the chess board.

Kylie buys an article for ₹ 10000 and pays 7% tax. He sells the same article for ₹ 13000 and charges 9% tax. Find the VAT paid by Kylie.

What will be the condition for (a2−9)x2+bx+c=0 to be a quadratic equation?

How many solutions does y=2x has? Write any four solution.

Question 6In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA=30∘ . Then , AT is equal to(A) 4 cm(B) 2 cm(C) 2 √3 cm(D) 4 √3 cm

A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used, at the rate of Rs 25 per metre.

Using Euclid division lemma , prove that difference of squares of 2 odd natural numbers is a multiple of 8

Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.

The following are the ages of 300 patients getting medical treatment in a hospital on a particular day: Age (in years)10−2020−3030−4040−5050−6060−70Number of patients604255705320Form a 'less than type' cumulative frequency distribution. [CBSE 2013]

Congress has enacted legislation forbidding state and local governments from raising taxes on connections that link consumers to the Internet for the next three years.

Show that the following numbers are irrational.(i) 12(ii) 75(iii) 6+2(iv) 3-5

Find the HCF of 525 and 270 using Euclid’s division algorithm.15

A pendulum swings through an angle of 30∘ and describes an arc 8.8 cm in length. Find the length of pendulum in cm.

Simplify the expression-(cosec2θ−1)×(sec2θ−1)

Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P. a d n an I 7 3 8 …... II − 18 ….. 10 0 III ….. − 3 18 − 5 IV − 18.9 2.5 ….. 3.6 V 3.5 0 105 …..

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid-points of sides AB, BC, CD, DA, respectively.A circular rangoli of radius 10 cm is drawn at the centre as shown in the given figure. Find the area of shaded portion.

Expand the following(1) (2) (3) (4) (5) (6)

13. There exist unique positive integers a and b such that a²+ 84a + 2008 = b²

Three consecutive natural numbers are such that the square of the middle number excceds the difference of the squares of the other two by 60. Assume the middle number to be x and form a quadratic equation satisfying's the above statement. Hence; find the three numbers.

In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64, find n.

Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.[4 MARKS]

A restaurant POQR is being constructed in the middle of a circular lake. The circle, which has its center at O is touching the mid-points of the boundary ABCD as shown in the figure. AB=CD and AD=BC. If BC=8 cm, then the area of AQOP is

AB is a chord of a circle with centre O , AOC is a diameter and AT is the tangent at A as shown in . Prove that ∠BAT = ∠ACB.

volume and surface area of a solid hemisphere are numerically equal . what is the diameter of the hemisphere

7 – 9x + 2x2 is called a _________ polynomial.

In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the given figure. Find the area of the design (Shaded region).

The coordinates of A, B &amp; C are (2 , 3); (-1 , 2) &amp; (3 , 0). Find equation of the line through A and perpendicular to BC.

In a single throw of a die, find the probability of getting: i) 7 ii) a number less than 7

When four quantities are in proportion then the product of extreme terms is equal to the product of ___ .

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30 °.

The coordinates of A, B & C are (2 , 3); (-1 , 2) & (3 , 0). Find equation of the line through A and perpendicular to BC.