32581 + Interview Questions in Mathematics

1.	Question 9ABCD is a trapezium in which AB \|\| DC and its diagonals intersect each other at the point O. Show that AOBO=CODO.
Answer» Question 9 ABCD is a trapezium in which AB \|\| DC and its diagonals intersect each other at the point O. Show that $\frac{A O}{B O} = \frac{C O}{D O}$ .

Discussion

2.	38. a/ax-1 + b/bx-1 = a+b
Answer» 38. a/ax-1 + b/bx-1 = a+b

Discussion

3.	In the given figure, there are two concentric circles with center O such that AP is tangent to the bigger circle and AB is tangent to the smaller circle. If ∠APB=∠ABP=30∘,OA=3 cm and OP =5 cm, then, radius of the smaller circle is
Answer» In the given figure, there are two concentric circles with center O such that AP is tangent to the bigger circle and AB is tangent to the smaller circle. If $∠ A P B = ∠ A B P = 30^{\circ}, O A = 3$ cm and OP =5 cm, then, radius of the smaller circle is

Discussion

4.	The probability of winning a game is 25, the probability of losing is__. (in decimal form)
Answer» The probability of winning a game is $\frac{2}{5}$ , the probability of losing is__. (in decimal form)

Discussion

5.	Solve(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Answer» Solve (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

5.

Solve(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Answer»

Solve

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Discussion

6.	Question 5 (√3+1)(3−cot 30∘)=tan3 60∘−2 sin 60∘
Answer» Question 5 $(\sqrt{3} + 1) (3 - c o t 30^{\circ}) = t a n^{3} 60^{\circ} - 2 s i n 60^{\circ}$

Discussion

7.	In ΔABC, ∠A=60∘,∠B=45∘ and AB= 10cm as shown in the figure. Then find the area of the triangle.
Answer» In $Δ A B C$ , $∠ A = 60^{\circ}, ∠ B = 45^{\circ} a n d A B = 10 c m$ as shown in the figure. Then find the area of the triangle.

7.

In ΔABC, ∠A=60∘,∠B=45∘ and AB= 10cm as shown in the figure. Then find the area of the triangle.

Answer»

In $Δ A B C$ , $∠ A = 60^{\circ}, ∠ B = 45^{\circ} a n d A B = 10 c m$ as shown in the figure. Then find the area of the triangle.

Discussion

8.	Question 20In figure, ∠OAB=30∘ and ∠OCB=57∘. Find ∠BOC and ∠AOC.
Answer» Question 20 In figure, $∠ O A B = 30^{\circ} a n d ∠ O C B = 57^{\circ} . F i n d ∠ B O C a n d ∠ A O C$ .

Discussion

9.	In the given figure, a circle touches all the four sides of a quadrilateral ABCD with AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.
Answer» In the given figure, a circle touches all the four sides of a quadrilateral ABCD with AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.

Discussion

10.

The weekly observations on cost of living index in a certain city for the year 2004 − 2005 are given below. Compute the weekly cost of living index. Cost of living Index Number of Students Cost of living Index Number of Students 1400−1500 1500−1600 1600−1700 5 10 20 1700−1800 1800−1900 1900−2000 9 6 2

Answer» The weekly observations on cost of living index in a certain city for the year 2004 − 2005 are given below. Compute the weekly cost of living index.

Cost of living Index	Number of Students	Cost of living Index	Number of Students
1400−1500 1500−1600 1600−1700	5 10 20	1700−1800 1800−1900 1900−2000	9 6 2

Discussion

11.	Nabin and Sandip started a business by investing Rs. 9000 and Rs. 12000 respectively. After a year, they make a profit of Rs. 1400. Then, Nabin will get a profit of ________.
Answer» Nabin and Sandip started a business by investing Rs. 9000 and Rs. 12000 respectively. After a year, they make a profit of Rs. 1400. Then, Nabin will get a profit of ________.

Discussion

12.	IF,f(x)=f(2-x) then f'(-1)+f'(3) = ?
Answer» IF,f(x)=f(2-x) then f'(-1)+f'(3) = ?

Discussion

13.	In figure, if O is the centre of a circle, PQ is a chord and the tangent PR makes an angle of 50∘ with PQ, then ∠POQ is equal to:
Answer» In figure, if O is the centre of a circle, PQ is a chord and the tangent PR makes an angle of $50^{\circ}$ with PQ, then $∠ P O Q$ is equal to:

Discussion

14.	Find the solution of the given pair of equations2x+3y=9, 3x+4y=5
Answer» Find the solution of the given pair of equations $2 x + 3 y = 9, 3 x + 4 y = 5$

Discussion

15.	A solid piece of iron of dimensions 49 × 33 × 24 cm is moulded into a sphere. The radius of the sphere is(a) 21 cm(b) 28 cm(c) 35 cm(d) none of these
Answer» A solid piece of iron of dimensions 49 × 33 × 24 cm is moulded into a sphere. The radius of the sphere is (a) 21 cm (b) 28 cm (c) 35 cm (d) none of these

Discussion

16.	∆ABC is a right triangle right-angled at A and AD ⊥ BC. Then, BDDC=(a) ABAC2(b) ABAC(c) ABAD2(d) ABAD
Answer» ∆ABC is a right triangle right-angled at A and AD ⊥ BC. Then, $\frac{BD}{DC} =$ (a) ${(\frac{AB}{AC})}^{2}$ (b) $\frac{AB}{AC}$ (c) ${(\frac{AB}{AD})}^{2}$ (d) $\frac{AB}{AD}$

Discussion

17.	Three companies are bidding on a contract. Company A is twice as likely to win as Company B, and Company B is three times as likely to win as Company C. What is the probability of company A winning the contract?
Answer» Three companies are bidding on a contract. Company A is twice as likely to win as Company B, and Company B is three times as likely to win as Company C. What is the probability of company A winning the contract?

Discussion

18.

Prepare the Transfer Vouchers in the books of Mangla Agencies, Faridabad, Haryana from the Source Vouchers: 2019 ₹ Jan.7 Purchased goods from M/s Eufora, New Delhi vide Bill No. 912, paid IGST 12% 4,700 Jan. 11 Sold goods to M/s Yardley, Faridabad, Haryana vide Bill No. 31596, charged CGST and SGST 6% each 5,000 Jan. 31 Depreciation charged on building 10% on ₹ 2,00,000 20,000

Answer» Prepare the Transfer Vouchers in the books of Mangla Agencies, Faridabad, Haryana from the Source Vouchers:

2019		₹
Jan.7	Purchased goods from M/s Eufora, New Delhi vide Bill No. 912, paid IGST 12%	4,700
Jan. 11	Sold goods to M/s Yardley, Faridabad, Haryana vide Bill No. 31596, charged CGST and SGST 6% each	5,000
Jan. 31	Depreciation charged on building 10% on ₹ 2,00,000	20,000

Discussion

19.	(x2+4x+3) can be visualised by the rectangle below. Identify the region depicting the constant term.
Answer» ( $x^{2} + 4 x + 3$ ) can be visualised by the rectangle below. Identify the region depicting the constant term.

Discussion

20.	A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see the given figure), and these are equally likely outcomes. What is the probability that it will point at(i) 8?(ii) an odd number?(iii) a number greater than 2?(iv) a number less than 9?
Answer» A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see the given figure), and these are equally likely outcomes. What is the probability that it will point at (i) 8? (ii) an odd number? (iii) a number greater than 2? (iv) a number less than 9?

20.

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see the given figure), and these are equally likely outcomes. What is the probability that it will point at(i) 8?(ii) an odd number?(iii) a number greater than 2?(iv) a number less than 9?

Answer»

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see the given figure), and these are equally likely outcomes. What is the probability that it will point at

(i) 8?

(ii) an odd number?

(iii) a number greater than 2?

(iv) a number less than 9?

Discussion

21.	The length of the minute hand of a clock is 21 cm. The area swept by the minute hand in 10 minutes is [CBSE 2012](a) 231 cm2(b) 210 cm2(c) 126 cm2(d) 252 cm2
Answer» The length of the minute hand of a clock is 21 cm. The area swept by the minute hand in 10 minutes is [CBSE 2012] (a) 231 cm² (b) 210 cm² (c) 126 cm² (d) 252 cm²

Discussion

22.	A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distance from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?
Answer» A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distance from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?

Discussion

23.	A right circular cylinder and aright circular cone have equal bases and equal heights. If their curved surfaces are in the ratio 8 : 5, determine the ratio of the radius of the base to the height of either of them.
Answer» A right circular cylinder and aright circular cone have equal bases and equal heights. If their curved surfaces are in the ratio 8 : 5, determine the ratio of the radius of the base to the height of either of them.

Discussion

24.	A dome of building is in the form of a hemisphere, from inside it was white washed at the cost of Rs498.96 . If the cost of white washed is 2.00 per sq.mtr. Find (i) Inside surface area of the dome (ii) Volume of the air inside the dome
Answer» A dome of building is in the form of a hemisphere, from inside it was white washed at the cost of Rs498.96 . If the cost of white washed is 2.00 per sq.mtr. Find (i) Inside surface area of the dome (ii) Volume of the air inside the dome

Discussion

25.	An ogive curve is
Answer» An ogive curve is

Discussion

26.	Question 2(b):Write the names of seven angles.
Answer» Question 2(b): Write the names of seven angles .

26.

Question 2(b):Write the names of seven angles.

Answer»

Question 2(b):

Write the names of seven angles

.

Discussion

27.	Question 2 A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed.
Answer» Question 2 A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed.

Discussion

28.	if the sum of first n terms of an AP is 2n^2-n+1, then find the tenth term of the AP
Answer» if the sum of first n terms of an AP is 2n^2-n+1, then find the tenth term of the AP

Discussion

29.	The angle between the minute hand and the hour hand of a clock when the time is 4:20 P.M., is
Answer» The angle between the minute hand and the hour hand of a clock when the time is $4 : 20$ P.M., is

Discussion

30.	If D is a point on the side AB of ∆ABC such that AD : DB = 3.2 and E is a point on BC such that DE \|\| AC. Find the ratio of areas of ∆ABC and ∆BDE.
Answer» If D is a point on the side AB of ∆ABC such that AD : DB = 3.2 and E is a point on BC such that DE \|\| AC. Find the ratio of areas of ∆ABC and ∆BDE.

Discussion

31.	Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then, construct another triangle whose sides are 34 times the corresponding sides of the first triangle. [2 MARKS]
Answer» Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then, construct another triangle whose sides are $\frac{3}{4}$ times the corresponding sides of the first triangle. [2 MARKS]

Discussion

32.	Question 5 Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.
Answer» Question 5 Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.

Discussion

33.	If the sum of the zeros of the quadratic polynomial kx2 − 3x + 5 is 1, write the value of k.
Answer» If the sum of the zeros of the quadratic polynomial kx² − 3x + 5 is 1, write the value of k.

Discussion

34.	If tana = n* tanb and sina= m* sinb then prove that cos^2a= m^2-1/n^2-1.
Answer» If tana = n* tanb and sina= m* sinb then prove that cos^2a= m^2-1/n^2-1.

Discussion

35.

Find the median of the following data Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 Frequency 5 3 4 3 3 4 7 9 7 8

Answer» Find the median of the following data

Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency	5	3	4	3	3	4	7	9	7	8

Discussion

36.	To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool?
Answer» To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool?

Discussion

37.	In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120∘ then prove that OR = PR + RQ
Answer» In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120^∘ then prove that OR = PR + RQ

Discussion

38.	In the following situations does the list of numbers involved make an arithmetic progression and why?The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.
Answer» In the following situations does the list of numbers involved make an arithmetic progression and why? The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

Discussion

39.	Calculation the area of the field shown in the diagram below:[Measurements are in metre]
Answer» Calculation the area of the field shown in the diagram below: [Measurements are in metre]

39.

Calculation the area of the field shown in the diagram below:[Measurements are in metre]

Answer»

Calculation the area of the field shown in the diagram below:

[Measurements are in metre]

Discussion

40.	The value of k such that 3x2+2kx+x−k−5 have the sum of the zeroes as half of their product,
Answer» The value of k such that $3 x^{2} + 2 k x + x - k - 5$ have the sum of the zeroes as half of their product,

Discussion

41.	The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum(in cm2).
Answer» The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum(in $c m^{2}$ ).

Discussion

42.	A motorbike requires 5 L of petrol to travel 220 km. How much distance will it cover using 1.5 L of petrol?
Answer» A motorbike requires 5 L of petrol to travel 220 km. How much distance will it cover using 1.5 L of petrol?

Discussion

43.	28. If 3 and 9 term of an AP 4 and -2 then find which of an AP are zeroes
Answer» 28. If 3 and 9 term of an AP 4 and -2 then find which of an AP are zeroes

Discussion

44.	A solid cube is cut into two cuboids of equal volumes. The ratio of the total surface area of the given cube and that of one of the cuboids is
Answer» A solid cube is cut into two cuboids of equal volumes. The ratio of the total surface area of the given cube and that of one of the cuboids is

Discussion

45.	A fraction becomes 12 if 5 is subtracted from its numerator and 3 is subtracted from its denominator. If the denominator of this fraction is 5 more than its numerator, find the fraction.
Answer» A fraction becomes $\frac{1}{2}$ if 5 is subtracted from its numerator and 3 is subtracted from its denominator. If the denominator of this fraction is 5 more than its numerator, find the fraction.

Discussion

46.	There are two apparent planes making an angle 60° with each other. One of the plane is at angle 15° with the actual plane and the angle of dip in this plane is 30°. What is the actual angle of dip at that place? Also find the apparent angle of dip on the other plane.
Answer» There are two apparent planes making an angle 60° with each other. One of the plane is at angle 15° with the actual plane and the angle of dip in this plane is 30°. What is the actual angle of dip at that place? Also find the apparent angle of dip on the other plane.

Discussion

47.	Find the sum of the first 10 natural numbers.
Answer» Find the sum of the first 10 natural numbers.

Discussion

48.	2tan230° sec252° sin238°cosec270°-tan220°=?(a) 2(b) 1(c) 23(d) 32
Answer» $(\frac{2 \tan^{2} 30 ° \sec^{2} 52 ° \sin^{2} 38 °}{{cosec}^{2} 70 ° - \tan^{2} 20 °}) = ?$ (a) 2 (b) 1 (c) $\frac{2}{3}$ (d) $\frac{3}{2}$

Discussion

49.	The tops of two towers of height x and y, standing on level ground, subtend angles of 30∘ and 60∘ respectively at the centre of the line joining their feet, then find the ratio of x, y.
Answer» The tops of two towers of height x and y, standing on level ground, subtend angles of $30^{\circ}$ and $60^{\circ}$ respectively at the centre of the line joining their feet, then find the ratio of x, y.

Discussion

50.	38. Equation of the circle on the line joining the points (1, -3) and (2, 5) as diameter is
Answer» 38. Equation of the circle on the line joining the points (1, -3) and (2, 5) as diameter is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 9ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AOBO=CODO.

38. a/ax-1 + b/bx-1 = a+b

In the given figure, there are two concentric circles with center O such that AP is tangent to the bigger circle and AB is tangent to the smaller circle. If ∠APB=∠ABP=30∘,OA=3 cm and OP =5 cm, then, radius of the smaller circle is

The probability of winning a game is 25, the probability of losing is__. (in decimal form)

Solve(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Question 5 (√3+1)(3−cot 30∘)=tan3 60∘−2 sin 60∘

In ΔABC, ∠A=60∘,∠B=45∘ and AB= 10cm as shown in the figure. Then find the area of the triangle.

Question 20In figure, ∠OAB=30∘ and ∠OCB=57∘. Find ∠BOC and ∠AOC.

In the given figure, a circle touches all the four sides of a quadrilateral ABCD with AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.

Nabin and Sandip started a business by investing Rs. 9000 and Rs. 12000 respectively. After a year, they make a profit of Rs. 1400. Then, Nabin will get a profit of ________.

IF,f(x)=f(2-x) then f'(-1)+f'(3) = ?

In figure, if O is the centre of a circle, PQ is a chord and the tangent PR makes an angle of 50∘ with PQ, then ∠POQ is equal to:

Find the solution of the given pair of equations2x+3y=9, 3x+4y=5

A solid piece of iron of dimensions 49 × 33 × 24 cm is moulded into a sphere. The radius of the sphere is(a) 21 cm(b) 28 cm(c) 35 cm(d) none of these

∆ABC is a right triangle right-angled at A and AD ⊥ BC. Then, BDDC=(a) ABAC2(b) ABAC(c) ABAD2(d) ABAD

Three companies are bidding on a contract. Company A is twice as likely to win as Company B, and Company B is three times as likely to win as Company C. What is the probability of company A winning the contract?

(x2+4x+3) can be visualised by the rectangle below. Identify the region depicting the constant term.

The length of the minute hand of a clock is 21 cm. The area swept by the minute hand in 10 minutes is [CBSE 2012](a) 231 cm2(b) 210 cm2(c) 126 cm2(d) 252 cm2

A right circular cylinder and aright circular cone have equal bases and equal heights. If their curved surfaces are in the ratio 8 : 5, determine the ratio of the radius of the base to the height of either of them.

A dome of building is in the form of a hemisphere, from inside it was white washed at the cost of Rs498.96 . If the cost of white washed is 2.00 per sq.mtr. Find (i) Inside surface area of the dome (ii) Volume of the air inside the dome

An ogive curve is

Question 2(b):Write the names of seven angles.​​

Question 2 A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed.

if the sum of first n terms of an AP is 2n^2-n+1, then find the tenth term of the AP

The angle between the minute hand and the hour hand of a clock when the time is 4:20 P.M., is

If D is a point on the side AB of ∆ABC such that AD : DB = 3.2 and E is a point on BC such that DE || AC. Find the ratio of areas of ∆ABC and ∆BDE.

Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then, construct another triangle whose sides are 34 times the corresponding sides of the first triangle. [2 MARKS]

Question 5 Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.

If the sum of the zeros of the quadratic polynomial kx2 − 3x + 5 is 1, write the value of k.

If tana = n* tanb and sina= m* sinb then prove that cos^2a= m^2-1/n^2-1.

Find the median of the following data Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 Frequency 5 3 4 3 3 4 7 9 7 8

In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120∘ then prove that OR = PR + RQ

In the following situations does the list of numbers involved make an arithmetic progression and why?The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

Calculation the area of the field shown in the diagram below:[Measurements are in metre]

The value of k such that 3x2+2kx+x−k−5 have the sum of the zeroes as half of their product,

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum(in cm2).

A motorbike requires 5 L of petrol to travel 220 km. How much distance will it cover using 1.5 L of petrol?

28. If 3 and 9 term of an AP 4 and -2 then find which of an AP are zeroes

A solid cube is cut into two cuboids of equal volumes. The ratio of the total surface area of the given cube and that of one of the cuboids is

A fraction becomes 12 if 5 is subtracted from its numerator and 3 is subtracted from its denominator. If the denominator of this fraction is 5 more than its numerator, find the fraction.

There are two apparent planes making an angle 60° with each other. One of the plane is at angle 15° with the actual plane and the angle of dip in this plane is 30°. What is the actual angle of dip at that place? Also find the apparent angle of dip on the other plane.

Find the sum of the first 10 natural numbers.

2tan230° sec252° sin238°cosec270°-tan220°=?(a) 2(b) 1(c) 23(d) 32

The tops of two towers of height x and y, standing on level ground, subtend angles of 30∘ and 60∘ respectively at the centre of the line joining their feet, then find the ratio of x, y.

38. Equation of the circle on the line joining the points (1, -3) and (2, 5) as diameter is

Question 2(b):Write the names of seven angles.