32581 + Interview Questions in Mathematics

1.	The total surface area in m2 of a cuboid with dimensions of 26 m, 14 m and 6.5 m respectively is ___ .
Answer» The total surface area in $m^{2}$ of a cuboid with dimensions of $26 m,$ $14 m$ and $6.5 m$ respectively is ___ .

Discussion

2.	Which of the following operations could make the expression x2+8x√3 a perfect square?
Answer» Which of the following operations could make the expression $x^{2} + \frac{8 x}{\sqrt{3}}$ a perfect square?

Discussion

3.	In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm. The diameter of the circle with centre O’ is 10 cm. What is the length of the tangent PC?
Answer» In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of $25 c m$ from O as shown in the figure. The radius of the circle with centre O is $7 c m$ . The diameter of the circle with centre O’ is $10 c m .$ What is the length of the tangent PC?

Discussion

4.	Find the third term from the end of the G.P. 227, 29, 23, ..................., 162.
Answer» Find the third term from the end of the G.P. $\frac{2}{27}, \frac{2}{9}, \frac{2}{3}, . . . . . . . . . . . . . . . . . . ., 162.$

Discussion

5.	The average rainfall for a week, excluding Sunday was 0.3 inches. Due to heavy rainfall on Sunday, the average for the week rises to 0.5 inch. How much rain fell on Sunday?
Answer» The average rainfall for a week, excluding Sunday was 0.3 inches. Due to heavy rainfall on Sunday, the average for the week rises to 0.5 inch. How much rain fell on Sunday?

Discussion

6.	A number consists of two digits, the sum of which is 5. If the unit's digit is multiplied by 92, it will be equal to three times of the ten's digit number. Which of these is the number?
Answer» A number consists of two digits, the sum of which is 5. If the unit's digit is multiplied by $\frac{9}{2}$ , it will be equal to three times of the ten's digit number. Which of these is the number?

Discussion

7.	If the zeros of the polynomial 2x³-5x²+37x-30,are in AP
Answer» If the zeros of the polynomial 2x³-5x²+37x-30,are in AP

Discussion

8.	Show that one and only one out of n,n+2 or n+4 is divisible by 3, where n is any positive integer.
Answer» Show that one and only one out of $n, n + 2$ or $n + 4$ is divisible by $3$ , where $n$ is any positive integer.

Discussion

9.	Solve for x: 2(x2+ 1/x2) – 9(x + 1/x) + 14 = 0
Answer» Solve for x: 2( $x^{2}$ + 1/ $x^{2}$ ) – 9(x + 1/x) + 14 = 0

9.

Solve for x: 2(x2+ 1/x2) – 9(x + 1/x) + 14 = 0

Answer»

Solve for x:

2( $x^{2}$ + 1/ $x^{2}$ ) – 9(x + 1/x) + 14 = 0

Discussion

10.	ABC is a triangle with AB=13cm,BC=15cm and CA=14cm,AD and BE are altitude from A and B to BC and AC respectively .H is the point of intersection of AD and BE then the ratio 5HD/HB is
Answer» ABC is a triangle with AB=13cm,BC=15cm and CA=14cm,AD and BE are altitude from A and B to BC and AC respectively .H is the point of intersection of AD and BE then the ratio 5HD/HB is

Discussion

11.	In a △ABC, ∠A=60∘, ∠B=30∘ and ∠C=90∘. Find the length of BC when AB = 16 m .
Answer» In a $△ A B C, ∠ A = 60^{\circ}, ∠ B = 30^{\circ} a n d ∠ C = 90^{\circ} .$ Find the length of BC when AB = 16 m .

Discussion

12.	Show that 12n cannot end with the digit 0 or 5 for any natural number n.
Answer» Show that 12ⁿ cannot end with the digit 0 or 5 for any natural number n.

Discussion

13.	by selling a pen for Rs 165, mukti gains 10%. If she had sold it for 157.50, what percentage would she have lost or gained?
Answer» by selling a pen for Rs 165, mukti gains 10%. If she had sold it for 157.50, what percentage would she have lost or gained?

Discussion

14.	The Highest Common Factor (H.C.F) of 240 and 924 is:
Answer» The Highest Common Factor (H.C.F) of 240 and 924 is:

Discussion

15.	Mass (g)10−1415−1920−2425−2930−34Frequency3410126 Construct a cumulative frequency table for the given data
Answer» $\begin{matrix} Mass (g) & 10 - 14 & 15 - 19 & 20 - 24 & 25 - 29 & 30 - 34 Frequency & 3 & 4 & 10 & 12 & 6 \end{matrix}$ Construct a cumulative frequency table for the given data

15.

Mass (g)10−1415−1920−2425−2930−34Frequency3410126 Construct a cumulative frequency table for the given data

Answer»

$\begin{matrix} Mass (g) & 10 - 14 & 15 - 19 & 20 - 24 & 25 - 29 & 30 - 34 Frequency & 3 & 4 & 10 & 12 & 6 \end{matrix}$

Construct a cumulative frequency table for the given data

Discussion

16.	Find the rate per cent at which a sum of money becomes 125/64 of itself in 3 years.
Answer» Find the rate per cent at which a sum of money becomes 125/64 of itself in 3 years.

Discussion

17.	From a point A, the length of a tangent to a circle is 8 cm and distance of A from the circle is 10 cm. The length of the diameter of the circle is
Answer» From a point A, the length of a tangent to a circle is 8 cm and distance of A from the circle is 10 cm. The length of the diameter of the circle is

17.

From a point A, the length of a tangent to a circle is 8 cm and distance of A from the circle is 10 cm. The length of the diameter of the circle is

Answer»

From a point A, the length of a tangent to a circle is 8 cm and distance of A from the circle is 10 cm. The length of the diameter of the circle is

Discussion

18.	The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30o than when it is 60o. Find the height of the tower.
Answer» The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30^o than when it is 60^o. Find the height of the tower.

18.

The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30o than when it is 60o. Find the height of the tower.

Answer»

The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30^o than when it is 60^o. Find the height of the tower.

Discussion

19.	There are 21 girls and 33 boys in a classroom. I want to randomly select one student to become the class leader. If I want to find the probability that the selected student is a girl, the number of favourable outcomes is ___.
Answer» There are 21 girls and 33 boys in a classroom. I want to randomly select one student to become the class leader. If I want to find the probability that the selected student is a girl, the number of favourable outcomes is ___.

Discussion

20.	If AB is a chord of a circle and P and Q are two points on the circle different from A and B, then:
Answer» If AB is a chord of a circle and P and Q are two points on the circle different from A and B, then:

Discussion

21.	Time taken by Hussain Bolt to go around the track for the respective rounds is given below Round numberTime taken in sec144242343442 Find the average time taken by him for the four rounds.
Answer» Time taken by Hussain Bolt to go around the track for the respective rounds is given below $\begin{matrix} Round number & Time taken in sec 1 & 44 2 & 42 3 & 43 4 & 42 \end{matrix}$ Find the average time taken by him for the four rounds.

21.

Time taken by Hussain Bolt to go around the track for the respective rounds is given below Round numberTime taken in sec144242343442 Find the average time taken by him for the four rounds.

Answer»

Time taken by Hussain Bolt to go around the track for the respective rounds is given below

$\begin{matrix} Round number & Time taken in sec 1 & 44 2 & 42 3 & 43 4 & 42 \end{matrix}$

Find the average time taken by him for the four rounds.

Discussion

22.	A certain amount of 1 rupee, 50 paisa and 25 paise coins make up Rs. 93.75. The number of coins of each denomination is in the ratio 3 : 4 : 5 respectively. The number of coins of each denomination respectively are:
Answer» A certain amount of 1 rupee, 50 paisa and 25 paise coins make up Rs. 93.75. The number of coins of each denomination is in the ratio 3 : 4 : 5 respectively. The number of coins of each denomination respectively are:

Discussion

23.	Solve equation, given below, using factorisation method: 5x−2−3x+6=4x
Answer» Solve equation, given below, using factorisation method: $\frac{5}{x - 2} - \frac{3}{x + 6} = \frac{4}{x}$

23.

Solve equation, given below, using factorisation method: 5x−2−3x+6=4x

Answer»

Solve equation, given below, using factorisation method:

$\frac{5}{x - 2} - \frac{3}{x + 6} = \frac{4}{x}$

Discussion

24.	The sum of the coefficients of the polynomial is zero. Mention one of its linear factor.
Answer» The sum of the coefficients of the polynomial is zero. Mention one of its linear factor.

Discussion

25.	If each edge of a cube, of volume V, is doubled, then the volume of the new cube is
Answer» If each edge of a cube, of volume V, is doubled, then the volume of the new cube is

Discussion

26.	I have a doubt in maths as they told tht a number is terminating whn there is 2(power n)×5(power m) if for example there is a number which contains both the number tht is 2(power n) × 5(power n ) in addition to another number will tht particular decimal b terminating??????? Pls answer this and thanku for answering!!!
Answer» I have a doubt in maths as they told tht a number is terminating whn there is 2(power n)×5(power m) if for example there is a number which contains both the number tht is 2(power n) × 5(power n ) in addition to another number will tht particular decimal b terminating??????? Pls answer this and thanku for answering!!!

Discussion

27.	Explain why (17×5×11×3×2+2×11) is a composite number?
Answer» Explain why $(17 \times 5 \times 11 \times 3 \times 2 + 2 \times 11)$ is a composite number?

Discussion

28.	The line segment joining the points M (5, 7) and N (-3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.
Answer» The line segment joining the points M (5, 7) and N (-3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.

Discussion

29.	For solving each pair of equations, use the method of eliminations by equating coefficients: 3x−y=23 x3+y4=4
Answer» For solving each pair of equations, use the method of eliminations by equating coefficients: $3 x - y = 23$ $\frac{x}{3} + \frac{y}{4} = 4$

29.

For solving each pair of equations, use the method of eliminations by equating coefficients: 3x−y=23 x3+y4=4

Answer»

For solving each pair of equations, use the method of eliminations by equating coefficients:

$3 x - y = 23$

$\frac{x}{3} + \frac{y}{4} = 4$

Discussion

30.	What is the value of cosec(90−θ)?
Answer» What is the value of $c o s e c (90 - θ)$ ?

Discussion

31.	Which of these following equations have x=−3,y=2 as solutions?
Answer» Which of these following equations have $x = - 3, y = 2$ as solutions?

Discussion

32.	If a + b + c = 0, then the value of a2bc+b2ac+c2ab is:
Answer» If a + b + c = 0, then the value of $\frac{a^{2}}{b c} + \frac{b^{2}}{a c} + \frac{c^{2}}{a b}$ is:

Discussion

33.	In an equilateral ΔABC, D is a point on side BC such that BD =13BC. Prove that 9(AD)2=7(AB)2. OR Prove that, in a right triangle, the square on the hyporenuse is equal to the sum of the squares on the other two sides.
Answer» In an equilateral $Δ A B C,$ D is a point on side BC such that BD $= \frac{1}{3}$ BC. Prove that $9 (A D)^{2} = 7 (A B)^{2}$ . OR Prove that, in a right triangle, the square on the hyporenuse is equal to the sum of the squares on the other two sides.

Discussion

34.	Directions:- Study the following information carefully to answer the question given below. A, C, D, I, L, P and M are sitting in a straight line facing North. (a) P sits fourth to the right of A and C sits second to the left of P. D sits in the middle and is second to the right of M. (b) I sits at the farthest possible distance from P (five persons sits between I and P). How many persons sit between A and L?
Answer» Directions:- Study the following information carefully to answer the question given below. A, C, D, I, L, P and M are sitting in a straight line facing North. (a) P sits fourth to the right of A and C sits second to the left of P. D sits in the middle and is second to the right of M. (b) I sits at the farthest possible distance from P (five persons sits between I and P). How many persons sit between A and L?

Discussion

35.	Product of two number a and b is 192. If there HCF is 4 what is their LCM
Answer» Product of two number $a$ and $b$ is 192. If there HCF is 4 what is their LCM

Discussion

36.	Find the value of a and b so that x4+ x3+ 8x2+ax+ b is divisible by . x2+1.
Answer» Find the value of a and b so that x⁴+ x³+ 8x²+ax+ b is divisible by . x²+1.

Discussion

37.	A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. 1500 after 4 years of service andRs. 1800 after 10 years of service, what was his starting salary and what is the annual increment?
Answer» A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. 1500 after 4 years of service andRs. 1800 after 10 years of service, what was his starting salary and what is the annual increment?

Discussion

38.	Find the value of b, if (x - 3) is a factor of x3−9x2 - bx + 81 = 0
Answer» Find the value of b, if (x - 3) is a factor of $x^{3} - 9 x^{2}$ - bx + 81 = 0

Discussion

39.	Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. OR A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
Answer» Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. OR A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

Discussion

40.	For what value of k will k+9, 2k−1 and 2k+7 are the consecutive terms of an A.P.?
Answer» For what value of k will $k + 9, 2 k - 1$ and $2 k + 7$ are the consecutive terms of an A.P.?

Discussion

41.	How many terms of series 54,51,48,....... Be taken so that their sum is 513? Explain the double answer.
Answer» How many terms of series 54,51,48,....... Be taken so that their sum is 513? Explain the double answer.

Discussion

42.	How many terms of the series 3, 9, 27 . . . . . . . will add up to 363? __
Answer» How many terms of the series 3, 9, 27 . . . . . . . will add up to 363? __

Discussion

43.	If the roots of equation x2−bxax−c = m−1m+1 are equal but opposite in sign, then the value of m will be
Answer» If the roots of equation $\frac{x^{2} - b x}{a x - c}$ = $\frac{m - 1}{m + 1}$ are equal but opposite in sign, then the value of m will be

Discussion

44.	The mode of a frequency distribution can be determined graphically from ________.
Answer» The mode of a frequency distribution can be determined graphically from ________.

Discussion

45.	The diameter of a cylinder is 28 cm and its height is 20 cm. The total surface area of the cylinder is (a) 2993 cm2 (b) 2992 cm2 (c) 2292 cm2 (d) 2229 cm2
Answer» The diameter of a cylinder is 28 cm and its height is 20 cm. The total surface area of the cylinder is (a) 2993 $c m^{2}$ (b) 2992 $c m^{2}$ (c) 2292 $c m^{2}$ (d) 2229 $c m^{2}$

45.

The diameter of a cylinder is 28 cm and its height is 20 cm. The total surface area of the cylinder is (a) 2993 cm2 (b) 2992 cm2 (c) 2292 cm2 (d) 2229 cm2

Answer»

The diameter of a cylinder is 28 cm and its height is 20 cm. The total surface area of the cylinder is

(a) 2993 $c m^{2}$ (b) 2992 $c m^{2}$ (c) 2292 $c m^{2}$ (d) 2229 $c m^{2}$

Discussion

46.	Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60∘ to each other.
Answer» Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of $60^{\circ}$ to each other.

Discussion

47.	Give the relation between circumference and radius of a circle.
Answer» Give the relation between circumference and radius of a circle.

Discussion

48.	Find the value of k for which each of the following systems of equations have infinitely many solution: (9-19) 2x + 3y - 5 =0 6x + ky - 15 = 0
Answer» Find the value of k for which each of the following systems of equations have infinitely many solution: (9-19) 2x + 3y - 5 =0 6x + ky - 15 = 0

48.

Find the value of k for which each of the following systems of equations have infinitely many solution: (9-19) 2x + 3y - 5 =0 6x + ky - 15 = 0

Answer»

Find the value of k for which each of the following systems of equations have infinitely many solution: (9-19)

2x + 3y - 5 =0

6x + ky - 15 = 0

Discussion

49.	Question 6 In the following question out of the four options only one is correct, write the correct answer: The value of x, for which the expressions 3x-4 and 2x+1 become equal, is: (a) -3 (b) 0 (c) 5 (d) 1
Answer» Question 6 In the following question out of the four options only one is correct, write the correct answer: The value of x, for which the expressions 3x-4 and 2x+1 become equal, is: (a) -3 (b) 0 (c) 5 (d) 1

49.

Question 6 In the following question out of the four options only one is correct, write the correct answer: The value of x, for which the expressions 3x-4 and 2x+1 become equal, is: (a) -3 (b) 0 (c) 5 (d) 1

Answer»

Question 6

In the following question out of the four options only one is correct, write the correct answer:

The value of x, for which the expressions 3x-4 and 2x+1 become equal, is:

(a) -3

(b) 0

(c) 5

(d) 1

Discussion

50.	Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex of an equilateral triangle of side 12 cm as centre and a sector of circle of radius 6 cm with centre B is made. [ Use √3=1.73andπ=3.14.]
Answer» Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex of an equilateral triangle of side 12 cm as centre and a sector of circle of radius 6 cm with centre B is made. [ Use $\sqrt{3} = 1.73 a n d π = 3.14$ .]

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The total surface area in m2 of a cuboid with dimensions of 26 m, 14 m and 6.5 m respectively is ___ .

Which of the following operations could make the expression x2+8x√3 a perfect square?

In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm. The diameter of the circle with centre O’ is 10 cm. What is the length of the tangent PC?

Find the third term from the end of the G.P. 227, 29, 23, ..................., 162.

The average rainfall for a week, excluding Sunday was 0.3 inches. Due to heavy rainfall on Sunday, the average for the week rises to 0.5 inch. How much rain fell on Sunday?

A number consists of two digits, the sum of which is 5. If the unit's digit is multiplied by 92, it will be equal to three times of the ten's digit number. Which of these is the number?

If the zeros of the polynomial 2x³-5x²+37x-30,are in AP

Show that one and only one out of n,n+2 or n+4 is divisible by 3, where n is any positive integer.

Solve for x: 2(x2+ 1/x2) – 9(x + 1/x) + 14 = 0

ABC is a triangle with AB=13cm,BC=15cm and CA=14cm,AD and BE are altitude from A and B to BC and AC respectively .H is the point of intersection of AD and BE then the ratio 5HD/HB is

In a △ABC, ∠A=60∘, ∠B=30∘ and ∠C=90∘. Find the length of BC when AB = 16 m .

Show that 12n cannot end with the digit 0 or 5 for any natural number n.

by selling a pen for Rs 165, mukti gains 10%. If she had sold it for 157.50, what percentage would she have lost or gained?

The Highest Common Factor (H.C.F) of 240 and 924 is:

Mass (g)10−1415−1920−2425−2930−34Frequency3410126 Construct a cumulative frequency table for the given data

Find the rate per cent at which a sum of money becomes 125/64 of itself in 3 years.

From a point A, the length of a tangent to a circle is 8 cm and distance of A from the circle is 10 cm. The length of the diameter of the circle is

The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30o than when it is 60o. Find the height of the tower.

There are 21 girls and 33 boys in a classroom. I want to randomly select one student to become the class leader. If I want to find the probability that the selected student is a girl, the number of favourable outcomes is ___.

If AB is a chord of a circle and P and Q are two points on the circle different from A and B, then:

Time taken by Hussain Bolt to go around the track for the respective rounds is given below Round numberTime taken in sec144242343442 Find the average time taken by him for the four rounds.

A certain amount of 1 rupee, 50 paisa and 25 paise coins make up Rs. 93.75. The number of coins of each denomination is in the ratio 3 : 4 : 5 respectively. The number of coins of each denomination respectively are:

Solve equation, given below, using factorisation method: 5x−2−3x+6=4x

The sum of the coefficients of the polynomial is zero. Mention one of its linear factor.

If each edge of a cube, of volume V, is doubled, then the volume of the new cube is

Explain why (17×5×11×3×2+2×11) is a composite number?

The line segment joining the points M (5, 7) and N (-3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.

For solving each pair of equations, use the method of eliminations by equating coefficients: 3x−y=23 x3+y4=4

What is the value of cosec(90−θ)?

Which of these following equations have x=−3,y=2 as solutions?

If a + b + c = 0, then the value of a2bc+b2ac+c2ab is:

In an equilateral ΔABC, D is a point on side BC such that BD =13BC. Prove that 9(AD)2=7(AB)2. OR Prove that, in a right triangle, the square on the hyporenuse is equal to the sum of the squares on the other two sides.

Product of two number a and b is 192. If there HCF is 4 what is their LCM

Find the value of a and b so that x​​​​​​4+ x​​​​​​3+ 8x2+ax+ b is divisible by . x​​​​​​2+1.

A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. 1500 after 4 years of service andRs. 1800 after 10 years of service, what was his starting salary and what is the annual increment?

Find the value of b, if (x - 3) is a factor of x3−9x2 - bx + 81 = 0

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. OR A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

For what value of k will k+9, 2k−1 and 2k+7 are the consecutive terms of an A.P.?

How many terms of series 54,51,48,....... Be taken so that their sum is 513? Explain the double answer.

How many terms of the series 3, 9, 27 . . . . . . . will add up to 363? __

If the roots of equation x2−bxax−c = m−1m+1 are equal but opposite in sign, then the value of m will be

The mode of a frequency distribution can be determined graphically from ________.

The diameter of a cylinder is 28 cm and its height is 20 cm. The total surface area of the cylinder is (a) 2993 cm2 (b) 2992 cm2 (c) 2292 cm2 (d) 2229 cm2

Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60∘ to each other.

Give the relation between circumference and radius of a circle.

Find the value of k for which each of the following systems of equations have infinitely many solution: (9-19) 2x + 3y - 5 =0 6x + ky - 15 = 0

Question 6 In the following question out of the four options only one is correct, write the correct answer: The value of x, for which the expressions 3x-4 and 2x+1 become equal, is: (a) -3 (b) 0 (c) 5 (d) 1

Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex of an equilateral triangle of side 12 cm as centre and a sector of circle of radius 6 cm with centre B is made. [ Use √3=1.73andπ=3.14.]

Find the value of a and b so that x4+ x3+ 8x2+ax+ b is divisible by . x2+1.