32581 + Interview Questions in Mathematics

1.	A triangle ABC has base angle 45∘. The perimeter is [2+√2]. What type of triangle is this?
Answer» A triangle ABC has base angle $45^{\circ}$ . The perimeter is [2+ $\sqrt{2}$ ]. What type of triangle is this?

Discussion

2.	If 4x+5y=23 passes through the point (2,a), then the value of a is ___
Answer» If $4 x + 5 y = 23$ passes through the point $(2, a)$ , then the value of $a$ is ___

Discussion

3.	Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: 4x−y−4=0,3x+2y−14=0.
Answer» Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: $4 x - y - 4 = 0, 3 x + 2 y - 14 = 0.$

Discussion

4.	Question 106(iv) The food table is given below information about 2 types of soup cream of tomato and sweet corn. Use these lables to answer the given questions. (all the serving are based on a 2000 calories diet.) Calculate ratio of calories from fat in sweet corn soup to the calories from fat in cream of tomato soup.
Answer» Question 106(iv) The food table is given below information about 2 types of soup cream of tomato and sweet corn. Use these lables to answer the given questions. (all the serving are based on a 2000 calories diet.) Calculate ratio of calories from fat in sweet corn soup to the calories from fat in cream of tomato soup.

4.

Question 106(iv) The food table is given below information about 2 types of soup cream of tomato and sweet corn. Use these lables to answer the given questions. (all the serving are based on a 2000 calories diet.) Calculate ratio of calories from fat in sweet corn soup to the calories from fat in cream of tomato soup.

Answer»

Question 106(iv)

The food table is given below information about 2 types of soup cream of tomato and sweet corn. Use these lables to answer the given questions. (all the serving are based on a 2000 calories diet.)
Calculate ratio of calories from fat in sweet corn soup to the calories from fat in cream of tomato soup.

Discussion

5.	Is it possible to have two numbers whose HCF is 18 and LCM is 760 ? Give reason.
Answer» Is it possible to have two numbers whose HCF is 18 and LCM is 760 ? Give reason.

Discussion

6.	If the sun's angle of elevation increases from 30∘ to 60∘, length of shadow of a post ___ .
Answer» If the sun's angle of elevation increases from $30^{\circ}$ to $60^{\circ}$ , length of shadow of a post ___ .

Discussion

7.	Solve x :4x²−2(a²+b²)x+a²b²
Answer» Solve x : $4 x ² - 2 (a ² + b ²) x + a ² b ²$

Discussion

8.	Find the quadratic polynomial, sum of whose zeros is (52) and their product is 1. Hence, find the zeros of the polynomial?
Answer» Find the quadratic polynomial, sum of whose zeros is $(\frac{5}{2})$ and their product is $1$ . Hence, find the zeros of the polynomial?

8.

Find the quadratic polynomial, sum of whose zeros is (52) and their product is 1. Hence, find the zeros of the polynomial?

Answer»

Find the quadratic polynomial, sum of whose zeros is $(\frac{5}{2})$ and their product is $1$ . Hence, find the zeros of the polynomial?

Discussion

9.	Question 5 A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle. Find the area of the circle obtained. (a) 196 cm2 (b) 212 cm2 (c) 616 cm2 (d) 644 cm2
Answer» Question 5 A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle. Find the area of the circle obtained. (a) $196 c m^{2}$ (b) $212 c m^{2}$ (c) $616 c m^{2}$ (d) $644 c m^{2}$

Discussion

10.	During a mass drill exercise, 6250 students of different schools are arranged in rows such that the number of students in each row is equal to the number of rows. In doing so, the instructor finds out that 9 children are left out. Find the number of children in each row.
Answer» During a mass drill exercise, 6250 students of different schools are arranged in rows such that the number of students in each row is equal to the number of rows. In doing so, the instructor finds out that 9 children are left out. Find the number of children in each row.

Discussion

11.	In the given figure, PA and PB are tangents drawn from an external point P to a circle. CD is the third tangent touching the circle at Q. If PB=10cm and CQ=2cm, then the length of PC is:
Answer» In the given figure, PA and PB are tangents drawn from an external point P to a circle. CD is the third tangent touching the circle at Q. If PB=10cm and CQ=2cm, then the length of PC is:

11.

In the given figure, PA and PB are tangents drawn from an external point P to a circle. CD is the third tangent touching the circle at Q. If PB=10cm and CQ=2cm, then the length of PC is:

Answer»

In the given figure, PA and PB are tangents drawn from an external point P to a circle. CD is the third tangent touching the circle at Q. If PB=10cm and CQ=2cm, then the length of PC is:

Discussion

12.	There are several human beings and several dogs in a room. One tenth of the humans have lost a leg. The total number of feet is 77. Then the number of dogs is:
Answer» There are several human beings and several dogs in a room. One tenth of the humans have lost a leg. The total number of feet is 77. Then the number of dogs is:

Discussion

13.	Write the steps of construction to construct the tangents to a circle from an external point.
Answer» Write the steps of construction to construct the tangents to a circle from an external point.

Discussion

14.	Please explain in words and by solving the following sum: A man on a cliff observes a boat at an angle of depression 30 degrees which is sailing directly to the point beneath him. Three minutes later, the angle of depression of the boat is found to be at 60 degrees . Assuming the boat to have uniform speed find the following 1) how much more time will it take to reach the shore ; 2) the speed of the boat in master per second if the height of the cliff is 500 m. PS please answer fast my maths exams are tomorrow.
Answer» Please explain in words and by solving the following sum: A man on a cliff observes a boat at an angle of depression 30 degrees which is sailing directly to the point beneath him. Three minutes later, the angle of depression of the boat is found to be at 60 degrees . Assuming the boat to have uniform speed find the following 1) how much more time will it take to reach the shore ; 2) the speed of the boat in master per second if the height of the cliff is 500 m. PS please answer fast my maths exams are tomorrow.

Discussion

15.	Roopa buys an article for ₹ 9000 and pays a sales tax of ₹ 450 on it . Find the rate of sales tax
Answer» Roopa buys an article for ₹ 9000 and pays a sales tax of ₹ 450 on it . Find the rate of sales tax

Discussion

16.	Is it possible for the HCF and LCM of the numbers be 18,378.
Answer» Is it possible for the HCF and LCM of the numbers be 18,378.

Discussion

17.	Question 6 Is 0.2 a root of the equation x2 – 0.4 = 0? Justify your answer.
Answer» Question 6 Is 0.2 a root of the equation $x^{2}$ – 0.4 = 0? Justify your answer.

Discussion

18.	In the given circle, OP = 1 unit and ∠POQ=θ Which of the following is cosecθ from this circle?
Answer» In the given circle, OP = 1 unit and ∠POQ=θ Which of the following is $c o s e c θ$ from this circle?

Discussion

19.	Rachel buys goods worth Rs.5,500. She gets a rebate of 5% on it. After getting the rebate, sales tax 5% is charged. Find the amount she will have to pay for the goods.
Answer» Rachel buys goods worth Rs.5,500. She gets a rebate of 5% on it. After getting the rebate, sales tax 5% is charged. Find the amount she will have to pay for the goods.

Discussion

20.	How did we get 22/7 as approximate value for pi?
Answer» How did we get 22/7 as approximate value for pi?

Discussion

21.	What is sinθ × cosθ × secθ × cotθ ?
Answer» What is sin $θ$ $\times$ cos $θ$ $\times$ sec $θ$ $\times$ cot $θ$ ?

Discussion

22.	The number π + 7 is
Answer» The number π + 7 is

Discussion

23.	If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is
Answer» If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is

Discussion

24.	The sum and the product of the zeroes of a quadratic polynomial are -1/2 and 1/2 respectively, then the polynomial is:
Answer» The sum and the product of the zeroes of a quadratic polynomial are -1/2 and 1/2 respectively, then the polynomial is:

Discussion

25.	Write the first five terms of the sequences whose nth term is an=n(n+2)
Answer» Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n} = n (n + 2)$

25.

Write the first five terms of the sequences whose nth term is an=n(n+2)

Answer»

Write the first five terms of the sequences whose $n^{t h}$ term is

$a_{n} = n (n + 2)$

Discussion

26.	What is the degree of the polynomial 3x5−4x3y+5x4y2−x+1?
Answer» What is the degree of the polynomial $3 x^{5} - 4 x^{3} y + 5 x^{4} y^{2} - x + 1$ ?

Discussion

27.	Which of the following rational numbers have a terminating decimal expansion?
Answer» Which of the following rational numbers have a terminating decimal expansion?

Discussion

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

Discussion

29.	Hundred rupee shares of a company are available in the market at a premium of Rs 20. Find the rate of dividend given by the company when a man's return on his investment is 15 percent.
Answer» Hundred rupee shares of a company are available in the market at a premium of Rs 20. Find the rate of dividend given by the company when a man's return on his investment is 15 percent.

Discussion

30.	In tossing of 3 coins, the probability of getting exactly 1 head is:
Answer» In tossing of 3 coins, the probability of getting exactly 1 head is:

Discussion

31.	x∝y and x∝1z. if y = 5, z = 4 , then x = 3. Now, if y = 30 and z = 16 ,then x =
Answer» $x \propto y and x \propto \frac{1}{z} .$ if y = 5, z = 4 , then x = 3. Now, if y = 30 and z = 16 ,then x =

Discussion

32.	A box contains some black balls & 30 white balls. If the probability of drawing a black ball is 2/5th of a white ball, find the number of black balls in the box.
Answer» A box contains some black balls & 30 white balls. If the probability of drawing a black ball is ²/₅^thof a white ball, find the number of black balls in the box.

Discussion

33.	If tan θ, 2 tan θ + 2, 3 tan θ + 3 are in G.P. then the value of 7−5 cot θ9−4 √sec2 θ−1 is
Answer» If tan $θ$ , 2 tan $θ$ + 2, 3 tan $θ$ + 3 are in G.P. then the value of $\frac{7 - 5 c o t θ}{9 - 4 \sqrt{s e c^{2} θ - 1}}$ is

Discussion

34.	When any natural number is divided by 10, what are the possible remainders?
Answer» When any natural number is divided by 10, what are the possible remainders?

Discussion

35.	The square of a number is decreased by 15 which is equal to twice the original number. Which of the following are true about the numbers?
Answer» The square of a number is decreased by 15 which is equal to twice the original number. Which of the following are true about the numbers?

Discussion

36.	Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.
Answer» Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.

Discussion

37.	If -3 is a root of both the Quadratic equations 2x2 + px - 15 = 0, and p(x2 + x) + q = 0, then the value of q if the equation containing it has equal roots is.
Answer» If -3 is a root of both the Quadratic equations 2x² + px - 15 = 0, and p(x² + x) + q = 0, then the value of q if the equation containing it has equal roots is.

Discussion

38.	The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a smaller sphere of diameter 3.5 cm. How many can such spheres be obtained? [4 MARKS]
Answer» The surface area of a solid metallic sphere is $616 c m^{2}$ . It is melted and recast into a smaller sphere of diameter 3.5 cm. How many can such spheres be obtained? [4 MARKS]

Discussion

39.	A jar contains 8 white marbles, 10 orange marbles, and some red marbles. If the probability of picking a red marble is 1 in 4, then how many red marbles are there? [4 MARKS]
Answer» A jar contains 8 white marbles, 10 orange marbles, and some red marbles. If the probability of picking a red marble is 1 in 4, then how many red marbles are there? [4 MARKS]

Discussion

40.	The annual incomes of A and B are in the ratio 3 : 4 and their annual expenditures are in the ratio 5 : 7. If each saves Rs. 5,000: find their annual incomes.
Answer» The annual incomes of A and B are in the ratio 3 : 4 and their annual expenditures are in the ratio 5 : 7. If each saves Rs. 5,000: find their annual incomes.

Discussion

41.	Which term of the AP 72, 63, 54 .......... will equal to 0?
Answer» Which term of the AP 72, 63, 54 .......... will equal to 0?

Discussion

42.	The arithmetic mean of the following data is
Answer» The arithmetic mean of the following data is

42.

The arithmetic mean of the following data is

Answer»

The arithmetic mean of the following data is

Discussion

43.	Value of a machine depreciates every year at the rate of 15%. If its present value is Rs 4800, what will be its value after 3 years?
Answer» Value of a machine depreciates every year at the rate of 15%. If its present value is Rs 4800, what will be its value after 3 years?

Discussion

44.	A lady has only 25-paisa and 50-paisa coins in her purse. If she has 50 coins in all total and the amount she has is Rs.19.50, how many coins of each kind does she have?
Answer» A lady has only 25-paisa and 50-paisa coins in her purse. If she has 50 coins in all total and the amount she has is Rs.19.50, how many coins of each kind does she have?

Discussion

45.	A(−3,−3),B(2,−2),C(2,3) and D(−4,4) are the vertices of quadrilateral ABCD. Then the point of intersection of its diagonals is
Answer» $A (- 3, - 3), B (2, - 2), C (2, 3)$ and $D (- 4, 4)$ are the vertices of quadrilateral $A B C D$ . Then the point of intersection of its diagonals is

45.

A(−3,−3),B(2,−2),C(2,3) and D(−4,4) are the vertices of quadrilateral ABCD. Then the point of intersection of its diagonals is

Answer»

$A (- 3, - 3), B (2, - 2), C (2, 3)$ and $D (- 4, 4)$ are the vertices of quadrilateral $A B C D$ . Then the point of intersection of its diagonals is

Discussion

46.	The ratio of corresponding sides for the pair of triangles whose construction is given as follows : Triangle ABC of dimensions AB = 4cm, BC = 5 cm and ∠B= 60o. The ray BX is drawn from B making an acute angle with AB. Five points B1, B2, B3, B4 and B5 are located on the ray such that BB1 = B1B2 = B2B3 = B3B4 = B4B5. B4 is joined to A and a line parallel to B4A is drawn through B5 to intersect the extended line AB at A'. Another line is drawn through A' parallel to AC, intersecting the extended line BC at C'. Find the ratio of the corresponding sides of ΔABC and ΔA′BC′.
Answer» The ratio of corresponding sides for the pair of triangles whose construction is given as follows : Triangle ABC of dimensions AB = 4cm, BC = 5 cm and ∠B= 60^o. The ray BX is drawn from B making an acute angle with AB. Five points B1, B2, B3, B4 and B5 are located on the ray such that BB1 = B1B2 = B2B3 = B3B4 = B4B5. B4 is joined to A and a line parallel to B4A is drawn through B5 to intersect the extended line AB at A'. Another line is drawn through A' parallel to AC, intersecting the extended line BC at C'. Find the ratio of the corresponding sides of $Δ A B C$ and $Δ A^{'} B C^{'}$ .

Discussion

47.	Solve the following quadratic equation by factorization. 3x+1−12=23x−1,x≠−1,13
Answer» Solve the following quadratic equation by factorization. $\frac{3}{x + 1} - \frac{1}{2} = \frac{2}{3 x - 1}, x \neq - 1, \frac{1}{3}$

Discussion

48.	A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius.The radius of hemisphere is 3.5cm and the total wood used in the making of toy is 16656cm3.Find the height of the toy.Also,find the cost of painting the hemispherical part of the toy at the rate of Rs.10 per cm2.(Take π= 22/7)
Answer» A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius.The radius of hemisphere is $3.5 c m$ and the total wood used in the making of toy is 166 $\frac{5}{6} c m^{3}$ .Find the height of the toy.Also,find the cost of painting the hemispherical part of the toy at the rate of Rs. $10$ per $c m^{2}$ . $(T a k e π = 22 / 7)$

Discussion

49.	Initially the origin was at X=0 and position of a particle at point P was given as X=−3 m, if origin is shifted by 1 unit to the left, then position of point P with respect to new origin will be:
Answer» Initially the origin was at $X = 0$ and position of a particle at point $P$ was given as $X = - 3 m$ , if origin is shifted by $1$ unit to the left, then position of point $P$ with respect to new origin will be:

Discussion

50.	sin (45o + θ) - cos (45o − θ) = ? (a) 2 sin θ (a) 2 sin θ (c) 0 (d) 1
Answer» sin $(45^{o} + θ)$ - cos $(45^{o} - θ)$ = ? (a) 2 sin $θ$ (a) 2 sin $θ$ (c) 0 (d) 1

50.

sin (45o + θ) - cos (45o − θ) = ? (a) 2 sin θ (a) 2 sin θ (c) 0 (d) 1

Answer»

sin $(45^{o} + θ)$ - cos $(45^{o} - θ)$ = ?

(a) 2 sin $θ$ (a) 2 sin $θ$ (c) 0 (d) 1

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A triangle ABC has base angle 45∘. The perimeter is [2+√2]. What type of triangle is this?

If 4x+5y=23 passes through the point (2,a), then the value of a is ___

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: 4x−y−4=0,3x+2y−14=0.

Is it possible to have two numbers whose HCF is 18 and LCM is 760 ? Give reason.

If the sun's angle of elevation increases from 30∘ to 60∘, length of shadow of a post ___ .

Solve x :4x²−2(a²+b²)x+a²b²

Find the quadratic polynomial, sum of whose zeros is (52) and their product is 1. Hence, find the zeros of the polynomial?

Question 5 A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle. Find the area of the circle obtained. (a) 196 cm2 (b) 212 cm2 (c) 616 cm2 (d) 644 cm2

During a mass drill exercise, 6250 students of different schools are arranged in rows such that the number of students in each row is equal to the number of rows. In doing so, the instructor finds out that 9 children are left out. Find the number of children in each row.

In the given figure, PA and PB are tangents drawn from an external point P to a circle. CD is the third tangent touching the circle at Q. If PB=10cm and CQ=2cm, then the length of PC is:

There are several human beings and several dogs in a room. One tenth of the humans have lost a leg. The total number of feet is 77. Then the number of dogs is:

Write the steps of construction to construct the tangents to a circle from an external point.

Roopa buys an article for ₹ 9000 and pays a sales tax of ₹ 450 on it . Find the rate of sales tax

Is it possible for the HCF and LCM of the numbers be 18,378.

Question 6 Is 0.2 a root of the equation x2 – 0.4 = 0? Justify your answer.

In the given circle, OP = 1 unit and ∠POQ=θ Which of the following is cosecθ from this circle?

Rachel buys goods worth Rs.5,500. She gets a rebate of 5% on it. After getting the rebate, sales tax 5% is charged. Find the amount she will have to pay for the goods.

How did we get 22/7 as approximate value for pi?

What is sinθ × cosθ × secθ × cotθ ?

The number π + 7 is

If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is

The sum and the product of the zeroes of a quadratic polynomial are -1/2 and 1/2 respectively, then the polynomial is:

Write the first five terms of the sequences whose nth term is an=n(n+2)

What is the degree of the polynomial 3x5−4x3y+5x4y2−x+1?

Which of the following rational numbers have a terminating decimal expansion?

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

Hundred rupee shares of a company are available in the market at a premium of Rs 20. Find the rate of dividend given by the company when a man's return on his investment is 15 percent.

In tossing of 3 coins, the probability of getting exactly 1 head is:

x∝y and x∝1z. if y = 5, z = 4 , then x = 3. Now, if y = 30 and z = 16 ,then x =

A box contains some black balls &amp; 30 white balls. If the probability of drawing a black ball is 2/5th of a white ball, find the number of black balls in the box.

If tan θ, 2 tan θ + 2, 3 tan θ + 3 are in G.P. then the value of 7−5 cot θ9−4 √sec2 θ−1 is

When any natural number is divided by 10, what are the possible remainders?

The square of a number is decreased by 15 which is equal to twice the original number. Which of the following are true about the numbers?

Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.

If -3 is a root of both the Quadratic equations 2x2 + px - 15 = 0, and p(x2 + x) + q = 0, then the value of q if the equation containing it has equal roots is.

The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a smaller sphere of diameter 3.5 cm. How many can such spheres be obtained? [4 MARKS]

A jar contains 8 white marbles, 10 orange marbles, and some red marbles. If the probability of picking a red marble is 1 in 4, then how many red marbles are there? [4 MARKS]

The annual incomes of A and B are in the ratio 3 : 4 and their annual expenditures are in the ratio 5 : 7. If each saves Rs. 5,000: find their annual incomes.

Which term of the AP 72, 63, 54 .......... will equal to 0?

The arithmetic mean of the following data is

Value of a machine depreciates every year at the rate of 15%. If its present value is Rs 4800, what will be its value after 3 years?

A lady has only 25-paisa and 50-paisa coins in her purse. If she has 50 coins in all total and the amount she has is Rs.19.50, how many coins of each kind does she have?

A(−3,−3),B(2,−2),C(2,3) and D(−4,4) are the vertices of quadrilateral ABCD. Then the point of intersection of its diagonals is

Solve the following quadratic equation by factorization. 3x+1−12=23x−1,x≠−1,13

Initially the origin was at X=0 and position of a particle at point P was given as X=−3 m, if origin is shifted by 1 unit to the left, then position of point P with respect to new origin will be:

sin (45o + θ) - cos (45o − θ) = ? (a) 2 sin θ (a) 2 sin θ (c) 0 (d) 1

A box contains some black balls & 30 white balls. If the probability of drawing a black ball is 2/5th of a white ball, find the number of black balls in the box.