32581 + Interview Questions in Mathematics

1.	Displacement of a body can be zero even when the distance travelled is not zero. Explain.
Answer» Displacement of a body can be zero even when the distance travelled is not zero. Explain.

Discussion

2.	Question 26 ___ is charged on the sale of an item by the government and is added to the bill amount.
Answer» Question 26 ___ is charged on the sale of an item by the government and is added to the bill amount.

2.

Question 26 ___ is charged on the sale of an item by the government and is added to the bill amount.

Answer»

Question 26

___ is charged on the sale of an item by the government and is added to the bill amount.

Discussion

3.	A ten metre rope tied to a balloon makes an angle of 60∘ with the ground. The height of the balloon above the ground is .......................
Answer» A ten metre rope tied to a balloon makes an angle of $60^{\circ}$ with the ground. The height of the balloon above the ground is .......................

Discussion

4.	Kiran deposited Rs. 200 per month in a recurring deposit account for 3 years. Find the amount payable to him on maturity, if the rate of interest is 11% p. a.
Answer» Kiran deposited Rs. 200 per month in a recurring deposit account for 3 years. Find the amount payable to him on maturity, if the rate of interest is 11% p. a.

Discussion

5.	Match the equations of lines with their corresponding solutions.
Answer» Match the equations of lines with their corresponding solutions.

Discussion

6.	The ratio in which (4,5) divides the line segment joining the points (2,3) and (7,8) is
Answer» The ratio in which (4,5) divides the line segment joining the points (2,3) and (7,8) is

Discussion

7.	If x is a positive real number , then there exists an irrational number y such that
Answer» If x is a positive real number , then there exists an irrational number y such that

Discussion

8.	If the sum of n terms of an A.P. is 3n2+5n and Tm= 164, m=?
Answer» If the sum of n terms of an A.P. is 3 $n^{2}$ +5n and $T_{m}$ = 164, m=?

Discussion

9.	Find the value of k for which x2–4x+k=0 has equal roots.
Answer» Find the value of k for which $x^{2} - 4 x + k = 0$ has equal roots.

Discussion

10.	In the given right angled isosceles triangle ABC, if AC = 10 cm then the area of triangle (in cm2) is ___.
Answer» In the given right angled isosceles triangle ABC, if AC = 10 cm then the area of triangle (in $c m^{2}$ ) is ___.

10.

In the given right angled isosceles triangle ABC, if AC = 10 cm then the area of triangle (in cm2) is ___.

Answer»

In the given right angled isosceles triangle ABC, if AC = 10 cm then the area of triangle (in $c m^{2}$ ) is ___.

Discussion

11.	Solve: (i)25 + 22 + 19 + 16 + ... + x = 115 (ii) 1 + 4 + 7 + 10 + ... + x = 590
Answer» Solve: (i)25 + 22 + 19 + 16 + ... + x = 115 (ii) 1 + 4 + 7 + 10 + ... + x = 590

Discussion

12.	If the zeros of the polynomial f(x)=x3−3x2+x+1 are (a-b), a and (a+b), find a and b.
Answer» If the zeros of the polynomial $f (x) = x^{3} - 3 x^{2} + x + 1$ are (a-b), a and (a+b), find a and b.

Discussion

13.	The following table gives the production yield per hectare of wheat of 100 farms of a village. Production yield(kg/ha)50−5555−6060−6565−7070−7575−80Number of farms2812243816 Change the distribution to a 'more than type' distribution and draw its ogive.Using ogive,find the median of the given data.
Answer» The following table gives the production yield per hectare of wheat of 100 farms of a village. $\begin{matrix} P r o d u c t i o n y i e l d (k g / h a) & 50 - 55 & 55 - 60 & 60 - 65 & 65 - 70 & 70 - 75 & 75 - 80 N u m b e r o f f a r m s & 2 & 8 & 12 & 24 & 38 & 16 \end{matrix}$ Change the distribution to a 'more than type' distribution and draw its ogive.Using ogive,find the median of the given data.

13.

The following table gives the production yield per hectare of wheat of 100 farms of a village. Production yield(kg/ha)50−5555−6060−6565−7070−7575−80Number of farms2812243816 Change the distribution to a 'more than type' distribution and draw its ogive.Using ogive,find the median of the given data.

Answer»

The following table gives the production yield per hectare of wheat of 100 farms of a village.

$\begin{matrix} P r o d u c t i o n y i e l d (k g / h a) & 50 - 55 & 55 - 60 & 60 - 65 & 65 - 70 & 70 - 75 & 75 - 80 N u m b e r o f f a r m s & 2 & 8 & 12 & 24 & 38 & 16 \end{matrix}$

Change the distribution to a 'more than type' distribution and draw its ogive.Using ogive,find the median of the given data.

Discussion

14.	π is (a) an integer (b) a rational number (c) an irrational number (d) none of these
Answer» $π$ is (a) an integer (b) a rational number (c) an irrational number (d) none of these

14.

π is (a) an integer (b) a rational number (c) an irrational number (d) none of these

Answer»

$π$ is

(a) an integer (b) a rational number

(c) an irrational number (d) none of these

Discussion

15.	The radius of solid sphere is R. If a solid sphere of radius R2 is removed from it. Find the volume of shell formed.
Answer» The radius of solid sphere is $R$ . If a solid sphere of radius $\frac{R}{2}$ is removed from it. Find the volume of shell formed.

Discussion

16.	Solve the following systems of equations: 12(x+2y)+53(3x−2y)=−32 54(x+2y)−55(3x−2y)=6160
Answer» Solve the following systems of equations: $\frac{1}{2 (x + 2 y)} + \frac{5}{3 (3 x - 2 y)} = \frac{- 3}{2}$ $\frac{5}{4 (x + 2 y)} - \frac{5}{5 (3 x - 2 y)} = \frac{61}{60}$

16.

Solve the following systems of equations: 12(x+2y)+53(3x−2y)=−32 54(x+2y)−55(3x−2y)=6160

Answer»

Solve the following systems of equations:

$\frac{1}{2 (x + 2 y)} + \frac{5}{3 (3 x - 2 y)} = \frac{- 3}{2}$

$\frac{5}{4 (x + 2 y)} - \frac{5}{5 (3 x - 2 y)} = \frac{61}{60}$

Discussion

17.	If x2, 4 and 9 are in continued proportion, find x.
Answer» If $x^{2}$ , 4 and 9 are in continued proportion, find x.

Discussion

18.	A ladder rests against a wall at an angles α to the horizontal. Its foot is pulled away from the wall through a distance ′p′, so that it slides a distance ′q′ down the wall making an angle β with the horizontal. Show that ab=cos α−cos βsin β−sin α
Answer» A ladder rests against a wall at an angles $α$ to the horizontal. Its foot is pulled away from the wall through a distance $^{'} p^{'}$ , so that it slides a distance $^{'} q^{'}$ down the wall making an angle $β$ with the horizontal. Show that $\frac{a}{b} = \frac{c o s α - c o s β}{s i n β - s i n α}$

Discussion

19.	In the given figure AB is a flagpost 8m high. The length of the shadow is 15 m. Find the distance between the top of the flagpole to the tip of the shadow.
Answer» In the given figure AB is a flagpost 8m high. The length of the shadow is 15 m. Find the distance between the top of the flagpole to the tip of the shadow.

Discussion

20.	The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the areah of the triangle is 24 cm2, find the perimeter of the triangle.
Answer» The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the areah of the triangle is 24 $c m^{2}$ , find the perimeter of the triangle.

Discussion

21.	The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers.
Answer» The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers.

Discussion

22.	Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ∠ ACB = 90o and AC = 15 cm.
Answer» Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, $∠$ ACB = $90^{o}$ and AC = 15 cm.

22.

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ∠ ACB = 90o and AC = 15 cm.

Answer»

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, $∠$ ACB = $90^{o}$ and AC = 15 cm.

Discussion

23.	An integer is selected at random between 1 to 100. Find probability of Multiple of 8 Not multiple of 8
Answer» An integer is selected at random between 1 to 100. Find probability of Multiple of 8 Not multiple of 8

23.

An integer is selected at random between 1 to 100. Find probability of Multiple of 8 Not multiple of 8

Answer»

An integer is selected at random between 1 to 100. Find probability of

Multiple of 8

Not multiple of 8

Discussion

24.	A metallic sphere of radius 3 cm is dropped in a right circular cylindrical vessel partly filled with water, whose radius is 6 cm. lf the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?
Answer» A metallic sphere of radius 3 cm is dropped in a right circular cylindrical vessel partly filled with water, whose radius is 6 cm. lf the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

Discussion

25.	Students who took chemistry but opted neither maths nor Physics: Read the statements and choose the letters of the region which correctly represent the statement in venn diagram.
Answer» Students who took chemistry but opted neither maths nor Physics: Read the statements and choose the letters of the region which correctly represent the statement in venn diagram.

25.

Students who took chemistry but opted neither maths nor Physics: Read the statements and choose the letters of the region which correctly represent the statement in venn diagram.

Answer»

Students who took chemistry but opted neither maths nor Physics:

Read the statements and choose the letters of the region which correctly represent the statement in venn diagram.

Discussion

26.	For any triangle ABC, which of the following statements will always hold true?
Answer» For any triangle ABC, which of the following statements will always hold true?

Discussion

27.	In figure, AB and CD are two parallel tangents to a circle with center O. ST is tangent segment between the two parallel tangents touching the circle at Q. Show that ∠SOT=90∘. [4 MARKS]
Answer» In figure, AB and CD are two parallel tangents to a circle with center O. ST is tangent segment between the two parallel tangents touching the circle at Q. Show that $∠ S O T = 90^{\circ}$ . [4 MARKS]

27.

In figure, AB and CD are two parallel tangents to a circle with center O. ST is tangent segment between the two parallel tangents touching the circle at Q. Show that ∠SOT=90∘. [4 MARKS]

Answer»

In figure, AB and CD are two parallel tangents to a circle with center O. ST is tangent segment between the two parallel tangents touching the circle at Q. Show that $∠ S O T = 90^{\circ}$ . [4 MARKS]

Discussion

28.	In a seminar, the number of participants in science,social science and mathematics are 60,84 and 108 respectively. Find the minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject.
Answer» In a seminar, the number of participants in science,social science and mathematics are 60,84 and 108 respectively. Find the minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject.

Discussion

29.	The probability of getting 53 Fridays in a leap year is:
Answer» The probability of getting 53 Fridays in a leap year is:

Discussion

30.	A contractor has two teams of workers: team A and team B. Team A can complete a job in 12 days and team B can do the same job in 36 days. Team A starts working on the job and team B joins team A after four days. The team A withdraws after two more days. For how many more days should team B work to complete the job?
Answer» A contractor has two teams of workers: team A and team B. Team A can complete a job in 12 days and team B can do the same job in 36 days. Team A starts working on the job and team B joins team A after four days. The team A withdraws after two more days. For how many more days should team B work to complete the job?

Discussion

31.	If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
Answer» If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:

Discussion

32.	All the sides of the triangle ABC are tangential to the circle with centre R. What is the perimeter of ΔABC?
Answer» All the sides of the triangle ABC are tangential to the circle with centre R. What is the perimeter of $Δ A B C$ ?

32.

All the sides of the triangle ABC are tangential to the circle with centre R. What is the perimeter of ΔABC?

Answer»

All the sides of the triangle ABC are tangential to the circle with centre R. What is the perimeter of $Δ A B C$ ?

Discussion

33.	If A and B are two square matrices of order 3 × 3 which satisfy AB = A and BA = B then (A+B)7 is
Answer» If A and B are two square matrices of order 3 $\times$ 3 which satisfy AB = A and BA = B then $(A + B)^{7}$ is

Discussion

34.	Find the non-negative root of (3x−12x+3)2−5(3x−12x+3)+4=0
Answer» Find the non-negative root of ${(\frac{3 x - 1}{2 x + 3})}^{2} - 5 (\frac{3 x - 1}{2 x + 3}) + 4 = 0$

Discussion

35.	In what ratio does the x axis divide the line segment joining the points( - 4 - 6 )and (-1,7) find the coordinates of the point of division
Answer» In what ratio does the x axis divide the line segment joining the points( - 4 - 6 )and (-1,7) find the coordinates of the point of division

Discussion

36.	Using trigonometric tables, find the value of cos37∘20′.
Answer» Using trigonometric tables, find the value of $c o s 37^{\circ} 20^{'}$ .

Discussion

37.	For the given quadrilateral, find BC + AD.
Answer» For the given quadrilateral, find BC + AD.

Discussion

38.	Identify the common difference of the given AP: a, a+d, a+2d, a+3d, ...
Answer» Identify the common difference of the given AP: a, a+d, a+2d, a+3d, ...

Discussion

39.	Sanjay has a Recurring Deposit Account in a bank of Rs 2,000 per month at the rate of 10% per annum. At the time of maturity, he receives Rs 83,100. Find the time for which account was held. [3 MARKS]
Answer» Sanjay has a Recurring Deposit Account in a bank of Rs 2,000 per month at the rate of 10% per annum. At the time of maturity, he receives Rs 83,100. Find the time for which account was held. [3 MARKS]

Discussion

40.	Choose the word that is a necessary part of the underlined word. School
Answer» Choose the word that is a necessary part of the underlined word. School

40.

Choose the word that is a necessary part of the underlined word. School

Answer»

Choose the word that is a necessary part of the underlined word.

School

Discussion

41.	In a birthday, 25 caps are required which are of conical shape. The dimensions of conical cap must be 10 cm (height) and 24 cm (radius). If the material used for making these caps is paper which is in rectangular shape. The length of paper is 24 cm, then the width of paper is ________.
Answer» In a birthday, 25 caps are required which are of conical shape. The dimensions of conical cap must be 10 cm (height) and 24 cm (radius). If the material used for making these caps is paper which is in rectangular shape. The length of paper is 24 cm, then the width of paper is ________.

Discussion

42.	The bottom, side and front areas of a rectangular box are known. The product of these area s is equal to
Answer» The bottom, side and front areas of a rectangular box are known. The product of these area s is equal to

Discussion

43.	OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. (i) If the radius of the circle is 10 cm, find the area of the rhombus. (ii) If the area of the rhombus is 32√3 cm2 find the radius of the circle.
Answer» OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. (i) If the radius of the circle is 10 cm, find the area of the rhombus. (ii) If the area of the rhombus is $32 \sqrt{3} c m^{2}$ find the radius of the circle.

43.

OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. (i) If the radius of the circle is 10 cm, find the area of the rhombus. (ii) If the area of the rhombus is 32√3 cm2 find the radius of the circle.

Answer»

OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O.

(i) If the radius of the circle is 10 cm, find the area of the rhombus.

(ii) If the area of the rhombus is $32 \sqrt{3} c m^{2}$ find the radius of the circle.

Discussion

44.	If (x + 2) is a factor of p(x) = ax3+bx2+x−6 and when p(x) is divided by (x – 2) the remainder is 4, then a + b =
Answer» If (x + 2) is a factor of p(x) = $a x^{3} + b x^{2} + x - 6$ and when p(x) is divided by (x – 2) the remainder is 4, then a + b =

Discussion

45.	Find the roots of the following quadratic equations by the factorization method. 3√2x2−5x−√2=0
Answer» Find the roots of the following quadratic equations by the factorization method. $3 \sqrt{2} x^{2} - 5 x - \sqrt{2} = 0$

Discussion

46.	Find the seventh term from the end of the series : √2, 2, 2√2, ....................,32.
Answer» Find the seventh term from the end of the series : $\sqrt{2}, 2, 2 \sqrt{2}, . . . . . . . . . . . . . . . . . . . ., 32.$

Discussion

47.	An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from her eyes is 45∘. What is the height of the tower? [2 MARKS]
Answer» An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from her eyes is $45^{\circ}$ . What is the height of the tower? [2 MARKS]

Discussion

48.	Which of the following is the exchange of goods in the present for payment in future?
Answer» Which of the following is the exchange of goods in the present for payment in future?

Discussion

49.	A chord of length 24 cm is at a distance of 5 cm from the centre of a circle. find the length of the chord of the same circle which is at a distance of 12 cm from the centre.
Answer» A chord of length 24 cm is at a distance of 5 cm from the centre of a circle. find the length of the chord of the same circle which is at a distance of 12 cm from the centre.

Discussion

50.	A (2, 4), B (3, 3) and C (7, 5) are the vertices of a Δ ABC. Find
Answer» A (2, 4), B (3, 3) and C (7, 5) are the vertices of a Δ ABC. Find

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Displacement of a body can be zero even when the distance travelled is not zero. Explain.

Question 26 ___ is charged on the sale of an item by the government and is added to the bill amount.

A ten metre rope tied to a balloon makes an angle of 60∘ with the ground. The height of the balloon above the ground is .......................

Kiran deposited Rs. 200 per month in a recurring deposit account for 3 years. Find the amount payable to him on maturity, if the rate of interest is 11% p. a.

Match the equations of lines with their corresponding solutions.

The ratio in which (4,5) divides the line segment joining the points (2,3) and (7,8) is

If x is a positive real number , then there exists an irrational number y such that

If the sum of n terms of an A.P. is 3n2+5n and Tm= 164, m=?

Find the value of k for which x2–4x+k=0 has equal roots.

In the given right angled isosceles triangle ABC, if AC = 10 cm then the area of triangle (in cm2) is ___.

Solve: (i)25 + 22 + 19 + 16 + ... + x = 115 (ii) 1 + 4 + 7 + 10 + ... + x = 590

If the zeros of the polynomial f(x)=x3−3x2+x+1 are (a-b), a and (a+b), find a and b.

π is (a) an integer (b) a rational number (c) an irrational number (d) none of these

The radius of solid sphere is R. If a solid sphere of radius R2 is removed from it. Find the volume of shell formed.

Solve the following systems of equations: 12(x+2y)+53(3x−2y)=−32 54(x+2y)−55(3x−2y)=6160

If x2, 4 and 9 are in continued proportion, find x.

A ladder rests against a wall at an angles α to the horizontal. Its foot is pulled away from the wall through a distance ′p′, so that it slides a distance ′q′ down the wall making an angle β with the horizontal. Show that ab=cos α−cos βsin β−sin α

In the given figure AB is a flagpost 8m high. The length of the shadow is 15 m. Find the distance between the top of the flagpole to the tip of the shadow.

The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the areah of the triangle is 24 cm2, find the perimeter of the triangle.

The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers.

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ∠ ACB = 90o and AC = 15 cm.

An integer is selected at random between 1 to 100. Find probability of Multiple of 8 Not multiple of 8

A metallic sphere of radius 3 cm is dropped in a right circular cylindrical vessel partly filled with water, whose radius is 6 cm. lf the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

Students who took chemistry but opted neither maths nor Physics: Read the statements and choose the letters of the region which correctly represent the statement in venn diagram.

For any triangle ABC, which of the following statements will always hold true?

In figure, AB and CD are two parallel tangents to a circle with center O. ST is tangent segment between the two parallel tangents touching the circle at Q. Show that ∠SOT=90∘. [4 MARKS]

In a seminar, the number of participants in science,social science and mathematics are 60,84 and 108 respectively. Find the minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject.

The probability of getting 53 Fridays in a leap year is:

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:

All the sides of the triangle ABC are tangential to the circle with centre R. What is the perimeter of ΔABC?

If A and B are two square matrices of order 3 × 3 which satisfy AB = A and BA = B then (A+B)7 is

Find the non-negative root of (3x−12x+3)2−5(3x−12x+3)+4=0

In what ratio does the x axis divide the line segment joining the points( - 4 - 6 )and (-1,7) find the coordinates of the point of division

Using trigonometric tables, find the value of cos37∘20′.

For the given quadrilateral, find BC + AD.

Identify the common difference of the given AP: a, a+d, a+2d, a+3d, ...

Sanjay has a Recurring Deposit Account in a bank of Rs 2,000 per month at the rate of 10% per annum. At the time of maturity, he receives Rs 83,100. Find the time for which account was held. [3 MARKS]

Choose the word that is a necessary part of the underlined word. School

In a birthday, 25 caps are required which are of conical shape. The dimensions of conical cap must be 10 cm (height) and 24 cm (radius). If the material used for making these caps is paper which is in rectangular shape. The length of paper is 24 cm, then the width of paper is ________.

The bottom, side and front areas of a rectangular box are known. The product of these area s is equal to

OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. (i) If the radius of the circle is 10 cm, find the area of the rhombus. (ii) If the area of the rhombus is 32√3 cm2 find the radius of the circle.

If (x + 2) is a factor of p(x) = ax3+bx2+x−6 and when p(x) is divided by (x – 2) the remainder is 4, then a + b =

Find the roots of the following quadratic equations by the factorization method. 3√2x2−5x−√2=0

Find the seventh term from the end of the series : √2, 2, 2√2, ....................,32.

An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from her eyes is 45∘. What is the height of the tower? [2 MARKS]

Which of the following is the exchange of goods in the present for payment in future?

A chord of length 24 cm is at a distance of 5 cm from the centre of a circle. find the length of the chord of the same circle which is at a distance of 12 cm from the centre.

A (2, 4), B (3, 3) and C (7, 5) are the vertices of a Δ ABC. Find