32581 + Interview Questions in Mathematics

1.	Question 12 (i) ABCD is a trapezium in which AB parallel CD and AD =BC (see the given figure). Show that ∠A=∠B.
Answer» Question 12 (i) ABCD is a trapezium in which AB parallel CD and AD =BC (see the given figure). Show that $∠ A = ∠ B$ .

Discussion

2.	Give example of polynomialsp(x),g(x),q(x) and r(x), which satisfies the division algorithm and i) deg p(x)=deg q(x) ii)deg q(x)=deg r(x) iii)deg r(x)=0
Answer» Give example of polynomialsp(x),g(x),q(x) and r(x), which satisfies the division algorithm and i) deg p(x)=deg q(x) ii)deg q(x)=deg r(x) iii)deg r(x)=0

Discussion

3.	Find the sum of the following arithmetic progressions: (i) 50,46,42,... to 10 terms (ii) 1,3,5,7,... to 12 terms (iii) 3, 92,6152, ... to 25 terms (iv) 41,36,31, ... to 12 terms (v) a+b,a-b,a-3b,... to 22 terms (vi) (x−y)2,(x2+y2),(x+y)2..., to n terms (vii) x−yx+y,3x−2yx+y,5x−3yx+y,...tn n terms (viii) -26,-24,-22,... to 36 terms.
Answer» Find the sum of the following arithmetic progressions: (i) 50,46,42,... to 10 terms (ii) 1,3,5,7,... to 12 terms (iii) 3, $\frac{9}{2}, 6 \frac{15}{2}$ , ... to 25 terms (iv) 41,36,31, ... to 12 terms (v) a+b,a-b,a-3b,... to 22 terms (vi) $(x - y)^{2}, (x^{2} + y^{2}), (x + y)^{2}$ ..., to n terms (vii) $\frac{x - y}{x + y}, \frac{3 x - 2 y}{x + y}, \frac{5 x - 3 y}{x + y}$ ,...tn n terms (viii) -26,-24,-22,... to 36 terms.

Discussion

4.	An event whose probability of occurrence is 0, is called __
Answer» An event whose probability of occurrence is 0, is called __

Discussion

5.	Question 1 (ii) State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:
Answer» Question 1 (ii) State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:

Discussion

6.	I have given a test of Chapter 1 of Maths but a question has an error. My marks are 9/10 but it should be 10/10.please reply..
Answer» I have given a test of Chapter 1 of Maths but a question has an error. My marks are 9/10 but it should be 10/10.please reply..

Discussion

7.	The ratio of incomes of two persons is 11:7and ratio of their expenditures is 9:5. If each of them manages to save ₹400 per month , find their monthly incomes.
Answer» The ratio of incomes of two persons is 11:7and ratio of their expenditures is 9:5. If each of them manages to save ₹400 per month , find their monthly incomes.

Discussion

8.	Mention the proper order of identifying a point D on BC such that Ar(△ABD)Ar(△ADC)=23? 1) Join B5C and draw a line parallel to B5C from B2. 2) Identify the ratio in which the point D divides BC using the relation given. 3) Mark 5 points B1, B2, B3, B4 and B5 on BX such that they are equidistant. 4) Construct a ray BX which makes an acute angle with line segment BC. 5) The point of intersection of the parallel line from B2 with BC is the point D.
Answer» Mention the proper order of identifying a point D on BC such that $\frac{A r (△ A B D)}{A r (△ A D C)} = \frac{2}{3}$ ? 1) Join $B_{5} C$ and draw a line parallel to $B_{5} C$ from $B_{2}$ . 2) Identify the ratio in which the point D divides BC using the relation given. 3) Mark 5 points B₁, B₂, B₃, B₄ and B₅ on BX such that they are equidistant. 4) Construct a ray BX which makes an acute angle with line segment BC. 5) The point of intersection of the parallel line from B₂ with BC is the point D.

Discussion

9.	The perpendicular AD on the base BC ofABCintersects BC in D such that BD=3DC.Prove that 2AB2=2AC2+BC2
Answer» The perpendicular AD on the base BC ofABCintersects BC in D such that BD=3DC.Prove that $2 A B^{2} = 2 A C^{2} + B C^{2}$

Discussion

10.	The sum fo first 20 odd natural numbers is (a) 100 (b) 210 (c) 400 (d) 420
Answer» The sum fo first 20 odd natural numbers is (a) 100 (b) 210 (c) 400 (d) 420

Discussion

11.	Solve the following systems of equations: 2x+5y=1 60x+40y=19
Answer» Solve the following systems of equations: $\frac{2}{x} + \frac{5}{y} = 1$ $\frac{60}{x} + \frac{40}{y} = 19$

11.

Solve the following systems of equations: 2x+5y=1 60x+40y=19

Answer»

Solve the following systems of equations:

$\frac{2}{x} + \frac{5}{y} = 1$

$\frac{60}{x} + \frac{40}{y} = 19$

Discussion

12.	The centre of a circle is (2a, a-7). Find the values of a if the circle passes through the point (11, -9) and has diameter 10√2 units.
Answer» The centre of a circle is (2a, a-7). Find the values of a if the circle passes through the point (11, -9) and has diameter $10 \sqrt{2} u n i t s .$

Discussion

13.	The line segment joining the points A (3, -4) and B (1, 2) is trisected at the points P(p, -2) and Q (53,q). Find the values of p and q.
Answer» The line segment joining the points A (3, -4) and B (1, 2) is trisected at the points P(p, -2) and Q $(\frac{5}{3}, q)$ . Find the values of p and q.

Discussion

14.	Find the sum of two middle terms of hte A.P.: −43,−1,−23,−13,...,413
Answer» Find the sum of two middle terms of hte A.P.: $- \frac{4}{3}, - 1, \frac{- 2}{3}, - \frac{1}{3}, . . ., 4 \frac{1}{3}$

Discussion

15.	From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of 20m high building are 45∘ and 60∘ respectively. Find the height of the transmission tower.
Answer» From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of $20 m$ high building are $45^{\circ} a n d 60^{\circ}$ respectively. Find the height of the transmission tower.

Discussion

16.	The probability that it will rain tommorow is 0.85. What is the probability that it will not rain tommorow ?
Answer» The probability that it will rain tommorow is 0.85. What is the probability that it will not rain tommorow ?

Discussion

17.	The polynomials ax3+3x2−3 and 2x3−5x+a, when divided by x - 4 leave the same remainder in each case. Find the value of a.
Answer» The polynomials $a x^{3} + 3 x^{2} - 3$ and $2 x^{3} - 5 x + a,$ when divided by x - 4 leave the same remainder in each case. Find the value of a.

Discussion

18.	A rectangle of sides parallel to coordinate axes is shown in below figure. Find the remaining vertices coordinates.
Answer» A rectangle of sides parallel to coordinate axes is shown in below figure. Find the remaining vertices coordinates.

18.

A rectangle of sides parallel to coordinate axes is shown in below figure. Find the remaining vertices coordinates.

Answer»

A rectangle of sides parallel to coordinate axes is shown in below figure. Find the remaining vertices coordinates.

Discussion

19.	solve 4/ x+3Y= 8,6/ x- 4 y=-5
Answer» solve 4/ x+3Y= 8,6/ x- 4 y=-5

Discussion

20.	What is the formula used to find the area of a sector? [1 MARK]
Answer» What is the formula used to find the area of a sector? [1 MARK]

Discussion

21.	Which of the following is the relation between mean, median and mode?
Answer» Which of the following is the relation between mean, median and mode?

Discussion

22.	At present Asha's age is 2 more than the square of her daughter Nisha's age . When Nisha grows to her mother's age ,Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both asha and nisha
Answer» At present Asha's age is 2 more than the square of her daughter Nisha's age . When Nisha grows to her mother's age ,Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both asha and nisha

Discussion

23.	Prove that (sin2A cos2B - cos2A sin2B)= (sin2A-sin2B)
Answer» Prove that (sin²A cos²B - cos²A sin²B)= (sin²A-sin²B)

Discussion

24.	C is a point on the minor arc AB of the circle with centre O. Given ∠ACB = x. Calculate ∠x , if ACBO is a parallelogram.
Answer» C is a point on the minor arc AB of the circle with centre O. Given ∠ACB = x. Calculate ∠x , if ACBO is a parallelogram.

24.

C is a point on the minor arc AB of the circle with centre O. Given ∠ACB = x. Calculate ∠x , if ACBO is a parallelogram.

Answer»

C is a point on the minor arc AB of the circle with centre O. Given ∠ACB = x. Calculate ∠x , if ACBO is a parallelogram.

Discussion

25.	The condition for two sets A and B to be disjoint is
Answer» The condition for two sets A and B to be disjoint is

Discussion

26.	In the given figure, BD bisects ∠ABC and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then x = ___ and y = ___.
Answer» In the given figure, BD bisects $∠ A B C$ and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then x = ___ and y = ___.

26.

In the given figure, BD bisects ∠ABC and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then x = _ and y = _.

Answer»

In the given figure, BD bisects $∠ A B C$ and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then x = ___ and y = ___.

Discussion

27.	Determine the general term of an A.P. whose 7th term is –1 and 16th term 17.
Answer» Determine the general term of an A.P. whose $7^{t h}$ term is –1 and $16^{t h}$ term 17.

Discussion

28.	A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy( in cm2) if the height of the conical part is 12 cm. ___
Answer» A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy( in $c m^{2}$ ) if the height of the conical part is 12 cm. ___

Discussion

29.	If A and B are any two 2×2 matrices such that AB =BA=B IS NOT A zero matrix , what can you say about the matrix A?
Answer» If A and B are any two 2×2 matrices such that AB =BA=B IS NOT A zero matrix , what can you say about the matrix A?

Discussion

30.	√2x+√3y=0,√3x-√8y=0 solve by elimination method
Answer» √2x+√3y=0,√3x-√8y=0 solve by elimination method

Discussion

31.	Question1 (v) Answer the following and justify v) Can the quadratic polynomial x2+kx+k have equal zeroes for some odd integer k > 1?
Answer» Question1 (v) Answer the following and justify v) Can the quadratic polynomial $x^{2} + k x + k$ have equal zeroes for some odd integer k > 1?

Discussion

32.	The image of point (3, 2) under the operation Mo.My is
Answer» The image of point (3, 2) under the operation $M_{o} . M_{y}$ is

Discussion

33.	A furniture shop has six identical steel cabinets of brand A and four identical steel cabinets of brand B. Three customers buy one cabinet each. Then the probability that two or more cabinets of brand A have been sold
Answer» A furniture shop has six identical steel cabinets of brand A and four identical steel cabinets of brand B. Three customers buy one cabinet each. Then the probability that two or more cabinets of brand A have been sold

Discussion

34.	If three consecutive term of an ap are 2K,K+4,3K+5. FIND THE VALUES OF K AND WRITE THE AP
Answer» If three consecutive term of an ap are 2K,K+4,3K+5. FIND THE VALUES OF K AND WRITE THE AP

34.

If three consecutive term of an ap are 2K,K+4,3K+5. FIND THE VALUES OF K AND WRITE THE AP

Answer»

If three consecutive term of an ap are

2K,K+4,3K+5. FIND THE VALUES OF K AND WRITE THE

AP

Discussion

35.	How many terms are there in the series : (i) 4, 7 , 10, 13, ................ , 148 ? (ii) 0.5, 0.53, 0.56, .................... , 1.1 ? (iii) 34,1,114,....................,3?
Answer» How many terms are there in the series : (i) 4, 7 , 10, 13, ................ , 148 ? (ii) 0.5, 0.53, 0.56, .................... , 1.1 ? (iii) $\frac{3}{4}, 1, 1 \frac{1}{4}, . . . . . . . . . . . . . . . . . . . ., 3 ?$

35.

How many terms are there in the series : (i) 4, 7 , 10, 13, ................ , 148 ? (ii) 0.5, 0.53, 0.56, .................... , 1.1 ? (iii) 34,1,114,....................,3?

Answer»

How many terms are there in the series :

(i) 4, 7 , 10, 13, ................ , 148 ?

(ii) 0.5, 0.53, 0.56, .................... , 1.1 ?

(iii) $\frac{3}{4}, 1, 1 \frac{1}{4}, . . . . . . . . . . . . . . . . . . . ., 3 ?$

Discussion

36.	Leela buys an article for ₹ 12000 and pays 7% tax. She sells the same article for ₹ 15000 and charges 9% tax. Find the VAT paid by Leela
Answer» Leela buys an article for ₹ 12000 and pays 7% tax. She sells the same article for ₹ 15000 and charges 9% tax. Find the VAT paid by Leela

Discussion

37.	What is a locus
Answer» What is a locus

Discussion

38.	PQR is a right angle triangle right angled at q. X and Y are points on PQ and QR such that PX: XQ = 1:2 and QY : YR = 2:1. prove that 9(PY^2 + XR^2) = 13PR^2
Answer» PQR is a right angle triangle right angled at q. X and Y are points on PQ and QR such that PX: XQ = 1:2 and QY : YR = 2:1. prove that 9(PY^2 + XR^2) = 13PR^2

Discussion

39.	An arc of a circle is of length 5π cm and the sector bounded around it has an area of 20π sq cm. Find the radius of the circle.
Answer» An arc of a circle is of length 5π cm and the sector bounded around it has an area of 20π sq cm. Find the radius of the circle.

Discussion

40.	If the first term of a G.P. is 5 and the common ratio is -5, then 3125 is the ____ term.
Answer» If the first term of a G.P. is 5 and the common ratio is -5, then 3125 is the ____ term.

Discussion

41.	An AP consists of 50 terms of which the third term is 12 and the last term is 106. Find the 29th term. ___
Answer» An AP consists of 50 terms of which the third term is 12 and the last term is 106. Find the $29^{t h}$ term. ___

Discussion

42.	Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour.
Answer» Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour.

Discussion

43.	Nature of root(s) of x−1x−1=x+42x+2 will be:
Answer» Nature of root(s) of $\frac{x - 1}{x - 1} = \frac{x + 4}{2 x + 2}$ will be:

Discussion

44.	Find the factors of x2 - 5x + 4
Answer» Find the factors of $x^{2}$ - 5x + 4

Discussion

45.	Aarti selects a card from a pack of well shuffled 52 playing cards. She needs an ace to win the game. The probability of Aarti losing the game is
Answer» Aarti selects a card from a pack of well shuffled 52 playing cards. She needs an ace to win the game. The probability of Aarti losing the game is

Discussion

46.	How does the banking system help the public to start a business?
Answer» How does the banking system help the public to start a business?

Discussion

47.	If tan4θ=cot(θ−10∘), where 4θ and(θ−10∘) are acute angles then the value of θ in degrees is ___.
Answer» If $t a n 4 θ = c o t (θ - 10^{\circ})$ , where $4 θ$ and $(θ - 10^{\circ})$ are acute angles then the value of $θ$ in degrees is ___.

Discussion

48.	What will be the cost for surfing a square water tank with sides 20 m surrounded by four semi-circular grassy plots, given that cost for surfing per m2 is Rs.2.5?
Answer» What will be the cost for surfing a square water tank with sides 20 m surrounded by four semi-circular grassy plots, given that cost for surfing per m²is Rs.2.5?

Discussion

49.	Solutions of which of the inequalities comprising a system in variable x are represented on number lines as given below, (black color is taken in consideration)
Answer» Solutions of which of the inequalities comprising a system in variable x are represented on number lines as given below, (black color is taken in consideration)

49.

Solutions of which of the inequalities comprising a system in variable x are represented on number lines as given below, (black color is taken in consideration)

Answer»

Solutions of which of the inequalities comprising a system in variable x are represented on number lines as given below, (black color is taken in consideration)

Discussion

50.	The roots of the equation x2 - √3 x – x + √3 = 0 are :
Answer» The roots of the equation x² - √3 x – x + √3 = 0 are :

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 12 (i) ABCD is a trapezium in which AB parallel CD and AD =BC (see the given figure). Show that ∠A=∠B.

Give example of polynomialsp(x),g(x),q(x) and r(x), which satisfies the division algorithm and i) deg p(x)=deg q(x) ii)deg q(x)=deg r(x) iii)deg r(x)=0

An event whose probability of occurrence is 0, is called __

Question 1 (ii) State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:

I have given a test of Chapter 1 of Maths but a question has an error. My marks are 9/10 but it should be 10/10.please reply..

The ratio of incomes of two persons is 11:7and ratio of their expenditures is 9:5. If each of them manages to save ₹400 per month , find their monthly incomes.

The perpendicular AD on the base BC ofABCintersects BC in D such that BD=3DC.Prove that 2AB2=2AC2+BC2

The sum fo first 20 odd natural numbers is (a) 100 (b) 210 (c) 400 (d) 420

Solve the following systems of equations: 2x+5y=1 60x+40y=19

The centre of a circle is (2a, a-7). Find the values of a if the circle passes through the point (11, -9) and has diameter 10√2 units.

The line segment joining the points A (3, -4) and B (1, 2) is trisected at the points P(p, -2) and Q (53,q). Find the values of p and q.

Find the sum of two middle terms of hte A.P.: −43,−1,−23,−13,...,413

From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of 20m high building are 45∘ and 60∘ respectively. Find the height of the transmission tower.

The probability that it will rain tommorow is 0.85. What is the probability that it will not rain tommorow ?

The polynomials ax3+3x2−3 and 2x3−5x+a, when divided by x - 4 leave the same remainder in each case. Find the value of a.

A rectangle of sides parallel to coordinate axes is shown in below figure. Find the remaining vertices coordinates.

solve 4/ x+3Y= 8,6/ x- 4 y=-5

What is the formula used to find the area of a sector? [1 MARK]

Which of the following is the relation between mean, median and mode?

At present Asha's age is 2 more than the square of her daughter Nisha's age . When Nisha grows to her mother's age ,Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both asha and nisha

Prove that (sin2A cos2B - cos2A sin2B)= (sin2A-sin2B)

C is a point on the minor arc AB of the circle with centre O. Given ∠ACB = x. Calculate ∠x , if ACBO is a parallelogram.﻿

The condition for two sets A and B to be disjoint is

In the given figure, BD bisects ∠ABC and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then x = ___ and y = ___.

Determine the general term of an A.P. whose 7th term is –1 and 16th term 17.

If A and B are any two 2×2 matrices such that AB =BA=B IS NOT A zero matrix , what can you say about the matrix A?

√2x+√3y=0,√3x-√8y=0 solve by elimination method

Question1 (v) Answer the following and justify v) Can the quadratic polynomial x2+kx+k have equal zeroes for some odd integer k &gt; 1?

The image of point (3, 2) under the operation Mo.My is

A furniture shop has six identical steel cabinets of brand A and four identical steel cabinets of brand B. Three customers buy one cabinet each. Then the probability that two or more cabinets of brand A have been sold

If three consecutive term of an ap are 2K,K+4,3K+5. FIND THE VALUES OF K AND WRITE THE AP

How many terms are there in the series : (i) 4, 7 , 10, 13, ................ , 148 ? (ii) 0.5, 0.53, 0.56, .................... , 1.1 ? (iii) 34,1,114,....................,3?

Leela buys an article for ₹ 12000 and pays 7% tax. She sells the same article for ₹ 15000 and charges 9% tax. Find the VAT paid by Leela

What is a locus

PQR is a right angle triangle right angled at q. X and Y are points on PQ and QR such that PX: XQ = 1:2 and QY : YR = 2:1. prove that 9(PY^2 + XR^2) = 13PR^2

An arc of a circle is of length 5π cm and the sector bounded around it has an area of 20π sq cm. Find the radius of the circle.

If the first term of a G.P. is 5 and the common ratio is -5, then 3125 is the ____ term.

An AP consists of 50 terms of which the third term is 12 and the last term is 106. Find the 29th term. ___

Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour.

Nature of root(s) of x−1x−1=x+42x+2 will be:

Find the factors of x2 - 5x + 4

Aarti selects a card from a pack of well shuffled 52 playing cards. She needs an ace to win the game. The probability of Aarti losing the game is

How does the banking system help the public to start a business?

If tan4θ=cot(θ−10∘), where 4θ and(θ−10∘) are acute angles then the value of θ in degrees is ___.

What will be the cost for surfing a square water tank with sides 20 m surrounded by four semi-circular grassy plots, given that cost for surfing per m2 is Rs.2.5?

Solutions of which of the inequalities comprising a system in variable x are represented on number lines as given below, (black color is taken in consideration)

The roots of the equation x2 - √3 x – x + √3 = 0 are :

C is a point on the minor arc AB of the circle with centre O. Given ∠ACB = x. Calculate ∠x , if ACBO is a parallelogram.

In the given figure, BD bisects ∠ABC and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then x = _ and y = _.

Question1 (v) Answer the following and justify v) Can the quadratic polynomial x2+kx+k have equal zeroes for some odd integer k > 1?