32581 + Interview Questions in Mathematics

1.	How many numbers are between 10 to 30, that leave a remainder of '2' when divided by 3?
Answer» How many numbers are between 10 to 30, that leave a remainder of '2' when divided by 3?

Discussion

2.	If triangle ABC is right angled at B and sinA=35, then find the value of cos A.
Answer» If triangle ABC is right angled at B and $s i n A = \frac{3}{5}$ , then find the value of cos A.

Discussion

3.	Which of the following is/are not the solution of log3 (x2−2)<log3 (32∣∣x∣∣−1)
Answer» Which of the following is/are not the solution of ${log}_{3} (x^{2} - 2) < {log}_{3} (\frac{3}{2} ∣ ∣ x ∣ ∣ - 1)$

Discussion

4.	Find the value of x, if it is given that lines AB and CD are parallel to each other.
Answer» Find the value of x, if it is given that lines AB and CD are parallel to each other.

4.

Find the value of x, if it is given that lines AB and CD are parallel to each other.

Answer»

Find the value of x, if it is given that lines AB and CD are parallel to each other.

Discussion

5.	If the angles subtented by a minor arc is 30 degree, then what is the angle subtended by the major arc?
Answer» If the angles subtented by a minor arc is 30 degree, then what is the angle subtended by the major arc?

Discussion

6.	Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also , find its circumradius.
Answer» Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also , find its circumradius.

Discussion

7.	The roots of the quadratic equation (x+β)(x−α)=0 are:
Answer» The roots of the quadratic equation $(x + β) (x - α) = 0$ are:

Discussion

8.	Determine k so that (3k -2), (4k-6) and (k +2) are three consecutive terms of an AP.
Answer» Determine k so that (3k -2), (4k-6) and (k +2) are three consecutive terms of an AP.

Discussion

9.	Find the sum of all integers between 50 and 500, which are divisible by 7.
Answer» Find the sum of all integers between 50 and 500, which are divisible by 7.

Discussion

10.	The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22,find the A.P.
Answer» The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22,find the A.P.

Discussion

11.	All the sides of the quadrilateral ABCD are tangential to the circle with centre M. What is the perimeter of the quadrilateral ABCD?
Answer» All the sides of the quadrilateral ABCD are tangential to the circle with centre M. What is the perimeter of the quadrilateral ABCD?

11.

All the sides of the quadrilateral ABCD are tangential to the circle with centre M. What is the perimeter of the quadrilateral ABCD?

Answer»

All the sides of the quadrilateral ABCD are tangential to the circle with centre M. What is the perimeter of the quadrilateral ABCD?

Discussion

12.	√(√12-√8)(√3+√2)/√(5+√24)
Answer» √(√12-√8)(√3+√2)/√(5+√24)

Discussion

13.	Solve: 2 tan 3 θ cos 3 θ−tan 3 θ+1=2 cos 3 θ [4 MARKS]
Answer» Solve: $2 t a n 3 θ c o s 3 θ - t a n 3 θ + 1 = 2 c o s 3 θ$ [4 MARKS]

Discussion

14.	Find the zeros of the polynomial f(x)=x3−5x2−16x+80, if its two zeros are equal in magnitude but opposite in sign. [4 MARKS]
Answer» Find the zeros of the polynomial $f (x) = x^{3} - 5 x^{2} - 16 x + 80$ , if its two zeros are equal in magnitude but opposite in sign. [4 MARKS]

Discussion

15.	Step 2 of an input is:17 victory 19 37 70 steal like tour Which of the following will be step 3?
Answer» Step 2 of an input is:17 victory 19 37 70 steal like tour Which of the following will be step 3?

15.

Step 2 of an input is:17 victory 19 37 70 steal like tour Which of the following will be step 3?

Answer»

Step 2 of an input is:17 victory 19 37 70 steal like tour

Which of the following will be step 3?

Discussion

16.	What is the solution of the following system of linear equations? 2x+3y=12 x-y=1
Answer» What is the solution of the following system of linear equations? 2x+3y=12 x-y=1

Discussion

17.	If m sin θ=n cos θ, then show that: tan θ+cot θtan θ−cot θ=n sin θ+m cos θn sin θ−m cos θ=n2+m2n2−m2 [4 MARKS]
Answer» If $m s i n θ = n c o s θ$ , then show that: $\frac{t a n θ + c o t θ}{t a n θ - c o t θ} = \frac{n s i n θ + m c o s θ}{n s i n θ - m c o s θ} = \frac{n^{2} + m^{2}}{n^{2} - m^{2}}$ [4 MARKS]

Discussion

18.	Find the area of an isoceles triangle whose equal sides are 6cm each and unequal side is 4cm. [2 MARKS]
Answer» Find the area of an isoceles triangle whose equal sides are 6cm each and unequal side is 4cm. [2 MARKS]

Discussion

19.	Solve for x : sin−13x5+sin−14x5=sin−1x x=0,1,−1
Answer» Solve for x : $s i n^{- 1} \frac{3 x}{5} + s i n^{- 1} \frac{4 x}{5} = s i n^{- 1} x$ $x = 0, 1, - 1$

Discussion

20.	Prove that n2 -n is divisible by 2 for every positive integer n
Answer» Prove that n2 -n is divisible by 2 for every positive integer n

Discussion

21.	What is the difference between at least and at most
Answer» What is the difference between at least and at most

Discussion

22.	Form the pair of linear equation for the following problem and find its solution by elimination method. Places A and B are 100 KM apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. Is there travel towards Each Other, they meet in 1 hour. What are the speeds of the two cars?
Answer» Form the pair of linear equation for the following problem and find its solution by elimination method. Places A and B are 100 KM apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. Is there travel towards Each Other, they meet in 1 hour. What are the speeds of the two cars?

22.

Form the pair of linear equation for the following problem and find its solution by elimination method. Places A and B are 100 KM apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. Is there travel towards Each Other, they meet in 1 hour. What are the speeds of the two cars?

Answer»

Form the pair of linear equation for the following problem and find its solution by elimination method.

Places A and B are 100 KM apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. Is there travel towards Each Other, they meet in 1 hour. What are the speeds of the two cars?

Discussion

23.	If p cotθ = √q2−p2, then the value of sinθ is ___. (θ being an acute angle).
Answer» If $p c o t θ$ = $\sqrt{q^{2} - p^{2}}$ , then the value of $s i n θ$ is ___. ( $θ$ being an acute angle).

Discussion

24.	The radius of the base and the height of a right circular cylinder are 7 cm and 13.5 cm respectively. The volume of the cylinder( in cm3) is
Answer» The radius of the base and the height of a right circular cylinder are 7 cm and 13.5 cm respectively. The volume of the cylinder( in $c m^{3}$ ) is

Discussion

25.	Prove that 5+√2 is irrational
Answer» Prove that 5+√2 is irrational

Discussion

26.	A box contains 90 marbles each numbered from 1 to 90. A marble is drawn at random. The probability that marble bears a perfect square is
Answer» A box contains 90 marbles each numbered from 1 to 90. A marble is drawn at random. The probability that marble bears a perfect square is

Discussion

27.	The sum of the radii of two circles is 7 cm, and the difference of their circumferences is 8 cm. Find the circumferences of the circles.
Answer» The sum of the radii of two circles is 7 cm, and the difference of their circumferences is 8 cm. Find the circumferences of the circles.

Discussion

28.	Solve for x and y: x+y=3,4x−3y=26.
Answer» Solve for x and y: $x + y = 3, 4 x - 3 y = 26.$

28.

Solve for x and y: x+y=3,4x−3y=26.

Answer»

Solve for x and y:

$x + y = 3, 4 x - 3 y = 26.$

Discussion

29.	A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13 ? (a) 0 (b) 1 (c) 3 (d) 5
Answer» A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13 ? (a) 0 (b) 1 (c) 3 (d) 5

29.

A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13 ? (a) 0 (b) 1 (c) 3 (d) 5

Answer»

A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13 ?

(a) 0 (b) 1 (c) 3 (d) 5

Discussion

30.	A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm respectively. Find (i) the volume of water which can completely fill the bucket; (ii) the area of the metal sheet used to make the bucket.
Answer» A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm respectively. Find (i) the volume of water which can completely fill the bucket; (ii) the area of the metal sheet used to make the bucket.

30.

A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm respectively. Find (i) the volume of water which can completely fill the bucket; (ii) the area of the metal sheet used to make the bucket.

Answer»

A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm respectively. Find

(i) the volume of water which can completely fill the bucket;

(ii) the area of the metal sheet used to make the bucket.

Discussion

31.	In the given figure, O is center of the circle and TP is the tangent to the circle from an external point T. If ∠PBT=30∘, prove that BA:AT=2:1.
Answer» In the given figure, $O$ is center of the circle and $T P$ is the tangent to the circle from an external point $T .$ If $∠ P B T = 30^{\circ}$ , prove that $B A : A T = 2 : 1.$

31.

In the given figure, O is center of the circle and TP is the tangent to the circle from an external point T. If ∠PBT=30∘, prove that BA:AT=2:1.

Answer»

In the given figure, $O$ is center of the circle and $T P$ is the tangent to the circle from an external point $T .$ If $∠ P B T = 30^{\circ}$ , prove that $B A : A T = 2 : 1.$

Discussion

32.	Question 2 The distance (in km) of 40 engineers from their residence to their place of work were found as follows: 5310202511137123119101217181131171627978351215183121429615157612 Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main feature do you observe from this tabular representation?
Answer» Question 2 The distance (in km) of 40 engineers from their residence to their place of work were found as follows: $\begin{matrix} 5 & 3 & 10 & 20 & 25 & 11 & 13 & 7 & 12 & 31 19 & 10 & 12 & 17 & 18 & 11 & 31 & 17 & 16 & 2 7 & 9 & 7 & 8 & 3 & 5 & 12 & 15 & 18 & 3 12 & 14 & 2 & 9 & 6 & 15 & 15 & 7 & 6 & 12 \end{matrix}$ Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main feature do you observe from this tabular representation?

Discussion

33.	Find three solutions for the equations (i) 2x - y = -5 (ii) y - 3x = 7
Answer» Find three solutions for the equations (i) 2x - y = -5 (ii) y - 3x = 7

Discussion

34.	A bag contains cards numbered from 2 to 90. A card is drawn at random. Find the probability that the card drawn is a perfect square.
Answer» A bag contains cards numbered from 2 to 90. A card is drawn at random. Find the probability that the card drawn is a perfect square.

Discussion

35.	Find the values of cot θ and cosec θ in the figure given above.
Answer» Find the values of $cot θ and cosec θ$ in the figure given above.

Discussion

36.	When a boat goea upstream for a distance of 24 km and downstream for 24 km with a speed of 18km/h,the time difference is 1 hour.Find the speed of the stream? please answer this question with all the steps clearly with reason for each and everything
Answer» When a boat goea upstream for a distance of 24 km and downstream for 24 km with a speed of 18km/h,the time difference is 1 hour.Find the speed of the stream? please answer this question with all the steps clearly with reason for each and everything

36.

When a boat goea upstream for a distance of 24 km and downstream for 24 km with a speed of 18km/h,the time difference is 1 hour.Find the speed of the stream? please answer this question with all the steps clearly with reason for each and everything

Answer»

When a boat goea upstream for a distance of 24 km and downstream for 24 km with a speed of 18km/h,the time difference is 1 hour.Find the speed of the stream?

please answer this question with all the steps clearly with reason for each and everything

Discussion

37.	Solve for x:- x^2 +5x - (a^2+a-6)=0
Answer» Solve for x:- x^2 +5x - (a^2+a-6)=0

37.

Solve for x:- x^2 +5x - (a^2+a-6)=0

Answer»

Solve for x:-

x^2 +5x - (a^2+a-6)=0

Discussion

38.	if A and B are two odd positive integers such that a is greater than B then prove that one of the two numbers a + b upon Two And A minus b upon 2 is odd and the other is even.
Answer» if A and B are two odd positive integers such that a is greater than B then prove that one of the two numbers a + b upon Two And A minus b upon 2 is odd and the other is even.

Discussion

39.	If ad is not equal to bc, then find whether the pair of linear equation ax+by =p and cx+dy=q has no solution, unique solution or infinitely many solutions.
Answer» If ad is not equal to bc, then find whether the pair of linear equation ax+by =p and cx+dy=q has no solution, unique solution or infinitely many solutions.

Discussion

40.	Prove that the areas of two similar triangles are in the ratio of the squares of their corresponding: [4 MARKS] (i) altitudes (ii) Medians (iii) Angle bisector segments
Answer» Prove that the areas of two similar triangles are in the ratio of the squares of their corresponding: [4 MARKS] (i) altitudes (ii) Medians (iii) Angle bisector segments

Discussion

41.	Show that the semi Vertical angle of the right circular cone of given total surface area and maximum volume is sin-¹ 1/√3 (i.e sin inverse 1 by √3).
Answer» Show that the semi Vertical angle of the right circular cone of given total surface area and maximum volume is sin-¹ 1/√3 (i.e sin inverse 1 by √3).

Discussion

42.	A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone. [3 MARKS]
Answer» A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone. [3 MARKS]

Discussion

43.	Juice is filled upto 64 cm in a cylindrical container of radius 30 cm. It is served in small cylindrical cups of radius 6 cm and height 16 cm. If each cup is sold at Rs. 3, how much money can be earned by selling the juice?
Answer» Juice is filled upto 64 cm in a cylindrical container of radius 30 cm. It is served in small cylindrical cups of radius 6 cm and height 16 cm. If each cup is sold at Rs. 3, how much money can be earned by selling the juice?

Discussion

44.	In the following figure, XY is parallel to BC AX =9 cm, XB =4.5 cm and BC =18 cm. Then, AYYC = ___
Answer» In the following figure, XY is parallel to BC AX =9 cm, XB =4.5 cm and BC =18 cm. Then, $\frac{A Y}{Y C}$ = ___

44.

In the following figure, XY is parallel to BC AX =9 cm, XB =4.5 cm and BC =18 cm. Then, AYYC = ___

Answer»

In the following figure, XY is parallel to BC AX =9 cm, XB =4.5 cm and BC =18 cm.

Then, $\frac{A Y}{Y C}$ = ___

Discussion

45.	Identify the figure that completes the pattern
Answer» Identify the figure that completes the pattern

45.

Identify the figure that completes the pattern

Answer»

Identify the figure that completes the pattern

Discussion

46.	Let ω be a complex cube root of unity with ω≠0 and P=[pij] be an n×n matrix with Pij=ωi+j. Then P2=0 when n is equal to
Answer» Let $ω$ be a complex cube root of unity with $ω \neq 0$ and $P = [p_{i j}]$ be an $n \times n$ matrix with $P_{i j} = ω^{i + j}$ . Then $P^{2} = 0$ when n is equal to

Discussion

47.	The mean and median of same data are 24 and 26 respectively. The value of mode is :
Answer» The mean and median of same data are 24 and 26 respectively. The value of mode is :

Discussion

48.	In Fig. 6, find the area of the shaded region [Use π = 3.14]
Answer» In Fig. 6, find the area of the shaded region [Use $π$ = 3.14]

Discussion

49.	A pan is of the shape of the frustum of a cone. The diameters of its circular ends are 42 cm and 28 cm respectively and its vertical height is √51 cm. (Use π = 22/7) What is the area of the foil required to be pasted on the walls of the pan?
Answer» A pan is of the shape of the frustum of a cone. The diameters of its circular ends are 42 cm and 28 cm respectively and its vertical height is √51 cm. (Use π = ²²/₇) What is the area of the foil required to be pasted on the walls of the pan?

49.

A pan is of the shape of the frustum of a cone. The diameters of its circular ends are 42 cm and 28 cm respectively and its vertical height is √51 cm. (Use π = 22/7) What is the area of the foil required to be pasted on the walls of the pan?

Answer»

A pan is of the shape of the frustum of a cone. The diameters of its circular ends are 42 cm and 28 cm respectively and its vertical height is √51 cm. (Use π = ²²/₇)

What is the area of the foil required to be pasted on the walls of the pan?

Discussion

50.	A point O is at a distance of 10 cm from the centre of a circle of radius 6 cm. How many tangents can be drawn from point O to the circle?
Answer» A point O is at a distance of 10 cm from the centre of a circle of radius 6 cm. How many tangents can be drawn from point O to the circle?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

How many numbers are between 10 to 30, that leave a remainder of '2' when divided by 3?

If triangle ABC is right angled at B and sinA=35, then find the value of cos A.

Which of the following is/are not the solution of log3 (x2−2)&lt;log3 (32∣∣x∣∣−1)

Find the value of x, if it is given that lines AB and CD are parallel to each other.

If the angles subtented by a minor arc is 30 degree, then what is the angle subtended by the major arc?

Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also , find its circumradius.

The roots of the quadratic equation (x+β)(x−α)=0 are:

Determine k so that (3k -2), (4k-6) and (k +2) are three consecutive terms of an AP.

Find the sum of all integers between 50 and 500, which are divisible by 7.

The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22,find the A.P.

All the sides of the quadrilateral ABCD are tangential to the circle with centre M. What is the perimeter of the quadrilateral ABCD?

√(√12-√8)(√3+√2)/√(5+√24)

Solve: 2 tan 3 θ cos 3 θ−tan 3 θ+1=2 cos 3 θ [4 MARKS]

Find the zeros of the polynomial f(x)=x3−5x2−16x+80, if its two zeros are equal in magnitude but opposite in sign. [4 MARKS]

Step 2 of an input is:17 victory 19 37 70 steal like tour Which of the following will be step 3?

What is the solution of the following system of linear equations? 2x+3y=12 x-y=1

If m sin θ=n cos θ, then show that: tan θ+cot θtan θ−cot θ=n sin θ+m cos θn sin θ−m cos θ=n2+m2n2−m2 [4 MARKS]

Find the area of an isoceles triangle whose equal sides are 6cm each and unequal side is 4cm. [2 MARKS]

Solve for x : sin−13x5+sin−14x5=sin−1x x=0,1,−1

Prove that n2 -n is divisible by 2 for every positive integer n

What is the difference between at least and at most

If p cotθ = √q2−p2, then the value of sinθ is ___. (θ being an acute angle).

The radius of the base and the height of a right circular cylinder are 7 cm and 13.5 cm respectively. The volume of the cylinder( in cm3) is

Prove that 5+√2 is irrational

A box contains 90 marbles each numbered from 1 to 90. A marble is drawn at random. The probability that marble bears a perfect square is

The sum of the radii of two circles is 7 cm, and the difference of their circumferences is 8 cm. Find the circumferences of the circles.

Solve for x and y: x+y=3,4x−3y=26.

A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13 ? (a) 0 (b) 1 (c) 3 (d) 5

A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm respectively. Find (i) the volume of water which can completely fill the bucket; (ii) the area of the metal sheet used to make the bucket.

In the given figure, O is center of the circle and TP is the tangent to the circle from an external point T. If ∠PBT=30∘, prove that BA:AT=2:1.

Find three solutions for the equations (i) 2x - y = -5 (ii) y - 3x = 7

A bag contains cards numbered from 2 to 90. A card is drawn at random. Find the probability that the card drawn is a perfect square.

Find the values of cot θ and cosec θ in the figure given above.

When a boat goea upstream for a distance of 24 km and downstream for 24 km with a speed of 18km/h,the time difference is 1 hour.Find the speed of the stream? please answer this question with all the steps clearly with reason for each and everything

Solve for x:- x^2 +5x - (a^2+a-6)=0

if A and B are two odd positive integers such that a is greater than B then prove that one of the two numbers a + b upon Two And A minus b upon 2 is odd and the other is even.

If ad is not equal to bc, then find whether the pair of linear equation ax+by =p and cx+dy=q has no solution, unique solution or infinitely many solutions.

Prove that the areas of two similar triangles are in the ratio of the squares of their corresponding: [4 MARKS] (i) altitudes (ii) Medians (iii) Angle bisector segments

Show that the semi Vertical angle of the right circular cone of given total surface area and maximum volume is sin-¹ 1/√3 (i.e sin inverse 1 by √3).

A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone. [3 MARKS]

Juice is filled upto 64 cm in a cylindrical container of radius 30 cm. It is served in small cylindrical cups of radius 6 cm and height 16 cm. If each cup is sold at Rs. 3, how much money can be earned by selling the juice?

In the following figure, XY is parallel to BC AX =9 cm, XB =4.5 cm and BC =18 cm. Then, AYYC = ___

Identify the figure that completes the pattern

Let ω be a complex cube root of unity with ω≠0 and P=[pij] be an n×n matrix with Pij=ωi+j. Then P2=0 when n is equal to

The mean and median of same data are 24 and 26 respectively. The value of mode is :

In Fig. 6, find the area of the shaded region [Use π = 3.14]

A pan is of the shape of the frustum of a cone. The diameters of its circular ends are 42 cm and 28 cm respectively and its vertical height is √51 cm. (Use π = 22/7) What is the area of the foil required to be pasted on the walls of the pan?

A point O is at a distance of 10 cm from the centre of a circle of radius 6 cm. How many tangents can be drawn from point O to the circle?

Which of the following is/are not the solution of log3 (x2−2)<log3 (32∣∣x∣∣−1)