32581 + Interview Questions in Mathematics

1.	If the volume of a right circular cone of height 9 cm is 48π cm3, find the diameter of its base.
Answer» If the volume of a right circular cone of height $9 c m$ is $48 π c m^{3}$ , find the diameter of its base.

Discussion

2.	If AD, BE and CF are the medians of an equilateral triangle ABC, then the true statement is -
Answer» If AD, BE and CF are the medians of an equilateral triangle ABC, then the true statement is -

2.

If AD, BE and CF are the medians of an equilateral triangle ABC, then the true statement is -

Answer»

If AD, BE and CF are the medians of an equilateral triangle ABC, then the true statement is -

Discussion

3.	If the perpendicular distances of two chords are equal from the centre of a circle then the length of the two chords is
Answer» If the perpendicular distances of two chords are equal from the centre of a circle then the length of the two chords is

Discussion

4.	Is there any chance that frequency of a gicen table will be in increasing order ?
Answer» Is there any chance that frequency of a gicen table will be in increasing order ?

Discussion

5.	Find the sum of the series 22 + 42 + 62 + 82 +................ 20 terms ___
Answer» Find the sum of the series $2^{2}$ + $4^{2}$ + $6^{2}$ + $8^{2}$ +................ 20 terms ___

Discussion

6.	Find the equation of a line which has the y-intercept 4, and is perpendicular to the line 2 – 3y = 7. Find the coordinates of the point where it cuts the -axis.
Answer» Find the equation of a line which has the y-intercept 4, and is perpendicular to the line 2 – 3y = 7. Find the coordinates of the point where it cuts the -axis.

Discussion

7.	By investing in 1623% stock at 64, one earns Rs. 1500. The investment made is:
Answer» By investing in $16 \frac{2}{3} %$ stock at 64, one earns Rs. 1500. The investment made is:

Discussion

8.	Question 4 Find two consecutive positive integers, sum of whose squares is 365.
Answer» Question 4 Find two consecutive positive integers, sum of whose squares is 365.

Discussion

9.	In the above figure, O is the centre of the circle, FD is a tangent at C.Then, which of the following statements are true?
Answer» In the above figure, O is the centre of the circle, FD is a tangent at C.Then, which of the following statements are true?

Discussion

10.	‘P’ is a point on axis Q (8, 2). If length of PQ = 10 unit find coordinates of P.
Answer» ‘P’ is a point on axis Q (8, 2). If length of PQ = 10 unit find coordinates of P.

Discussion

11.	The ratio of total surface area and lateral surface area of cone is 3:2 and its height is 6 meters. Find its volume of the cone ?
Answer» The ratio of total surface area and lateral surface area of cone is 3:2 and its height is 6 meters. Find its volume of the cone ?

Discussion

12.	Question 10 In what ratio does the X-axis divide the line segment joining the points (-4,-6) and (-1,7)? Find the coordinates of the points of division.
Answer» Question 10 In what ratio does the X-axis divide the line segment joining the points (-4,-6) and (-1,7)? Find the coordinates of the points of division.

Discussion

13.	If the angle of elevation of a cloud from a point 200 m above a lake is 30∘ and the angle of depression of the reflection of the cloud in the lake from the same point is 60∘, then the height of the cloud above the lake is:
Answer» If the angle of elevation of a cloud from a point 200 m above a lake is $30^{\circ}$ and the angle of depression of the reflection of the cloud in the lake from the same point is $60^{\circ}$ , then the height of the cloud above the lake is:

Discussion

14.	Which of the following is a factor of (x+y)3−(x3+y3)?
Answer» Which of the following is a factor of $(x + y)^{3} - (x^{3} + y^{3})$ ?

Discussion

15.	In the adjoining figure, A, B, and C are three points on a circle O. If angle AOB = 90° and angle BOC = 120°, then angle ABC is:
Answer» In the adjoining figure, A, B, and C are three points on a circle O. If angle AOB = 90° and angle BOC = 120°, then angle ABC is:

15.

In the adjoining figure, A, B, and C are three points on a circle O. If angle AOB = 90° and angle BOC = 120°, then angle ABC is:

Answer»

In the adjoining figure, A, B, and C are three points on a circle O. If angle AOB = 90° and angle BOC = 120°, then angle ABC is:

Discussion

16.	Question 13 If (a,b) is the mid-point of the line segment joining the points A(10, -6), B(k, 4) and a-2b=18. Then find the value of k and the distance AB.
Answer» Question 13 If (a,b) is the mid-point of the line segment joining the points A(10, -6), B(k, 4) and a-2b=18. Then find the value of k and the distance AB.

Discussion

17.	The entry of the variable for which the value of the polynomial is 0 is called __ of the polynomial.
Answer» The entry of the variable for which the value of the polynomial is 0 is called __ of the polynomial.

Discussion

18.	Two die are thrown simultaneously. How many outcomes are possible for the sum of the values? Are these outcomes equally likely? Explain. [4 MARKS]
Answer» Two die are thrown simultaneously. How many outcomes are possible for the sum of the values? Are these outcomes equally likely? Explain. [4 MARKS]

Discussion

19.	In the given figure, PT is a tangent drawn from an external point T to the circle with centre O and PQ is the diameter of the circle. Point Q and T are joined by a line which is intersecting the circle at R. If∠POR=78∘, then find ∠PTR.
Answer» $In the given figure, PT is a tangent drawn from an external point T to the circle with centre O and PQ is the diameter of the circle. Point Q and T are joined by a line which is intersecting the circle at R. If ∠ P O R = 78^{\circ}, then find ∠ P T R .$

Discussion

20.	Question 5 (iv) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (iv) (1+secA)secA=sin2A(1−cosA) [Hint : Simplify L.H.S and R.H.S separately]
Answer» Question 5 (iv) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (iv) $\frac{(1 + s e c A)}{s e c A} = \frac{s i n^{2} A}{(1 - c o s A)}$ [Hint : Simplify L.H.S and R.H.S separately]

Discussion

21.	The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y - 4x + 3 = 0, is
Answer» The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y - 4x + 3 = 0, is

Discussion

22.	Question 1 (i) Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P. adnan738……
Answer» Question 1 (i) Fill in the blanks in the following table, given that a is the first term, d the common difference and $a_{n}$ the $n^{t h}$ term of the A.P. $\begin{matrix} a & d & n & a_{n} 7 & 3 & 8 & \dots \dots \end{matrix}$

Discussion

23.	What is the sum of the probabilities of getting a head and getting a tail when a coin is tossed once?
Answer» What is the sum of the probabilities of getting a head and getting a tail when a coin is tossed once?

Discussion

24.	The mid-point of the line segment joining (2a,4) and (−2,2b) is (1,2a+1). Then the values of a and b respectively are
Answer» The mid-point of the line segment joining $(2 a, 4)$ and $(- 2, 2 b)$ is $(1, 2 a + 1)$ . Then the values of $a$ and $b$ respectively are

Discussion

25.	Solve for x. x2−5≤x3−4
Answer» Solve for x. $\frac{x}{2} - 5 \leq \frac{x}{3} - 4$

Discussion

26.	In a right angled triangle, which of the following is true? (h=hypotenuse, a and b are the perpendicular sides)
Answer» In a right angled triangle, which of the following is true? (h=hypotenuse, a and b are the perpendicular sides)

Discussion

27.	In the given figure △ABC is equilateral. If IE = 4 cm , IB = ____.
Answer» In the given figure $△ A B C$ is equilateral. If IE = 4 cm , IB = ____.

27.

In the given figure △ABC is equilateral. If IE = 4 cm , IB = ____.

Answer»

In the given figure $△ A B C$ is equilateral. If IE = 4 cm , IB = ____.

Discussion

28.	State Pythagoras' theorem.
Answer» State Pythagoras' theorem.

Discussion

29.	Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2 BL.
Answer» Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2 BL.

Discussion

30.	Given the linear equation y+3=0, write another equation in two variables such that the geometrical representation of the pair so formed is i) Parallel lines
Answer» Given the linear equation y+3=0, write another equation in two variables such that the geometrical representation of the pair so formed is i) Parallel lines

Discussion

31.	A vertical stick of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
Answer» A vertical stick of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Discussion

32.	Examine if x = 4, y = 1 is a solution of 3x + 2y = 12 [2 MARKS]
Answer» Examine if x = 4, y = 1 is a solution of 3x + 2y = 12 [2 MARKS]

Discussion

33.	Find the zeroes of the polynomial x2−2.
Answer» $Find the zeroes of the polynomial x^{2} - 2.$

Discussion

34.	Find the value of constant if x = - 4 is a zero of quadratic equation 4x2–mx+5=0. [2 MARKS]
Answer» Find the value of constant if x = - 4 is a zero of quadratic equation $4 x^{2} - m x + 5 = 0$ . [2 MARKS]

Discussion

35.	Among the following, the terminating rational number is .
Answer» Among the following, the terminating rational number is .

Discussion

36.	If the line y=√3x+k touches the circle x2+y2=16, then find the value of k.
Answer» If the line $y = \sqrt{3} x + k$ touches the circle $x^{2} + y^{2} = 16$ , then find the value of k.

Discussion

37.	A right triangle is formed by connecting the 3 coordinates A, B and C. If AB and BC are parallel to the coordinate axes as shown in figure, find the distance BC.
Answer» A right triangle is formed by connecting the 3 coordinates A, B and C. If AB and BC are parallel to the coordinate axes as shown in figure, find the distance BC.

Discussion

38.	Find the roots of the equation 2x2–5x+3=0, by factorisation method.
Answer» Find the roots of the equation $2 x^{2} - 5 x + 3 = 0$ , by factorisation method.

Discussion

39.	Find the sum of the following geometric series : (i) 0.15 + 0.015 + 0.0015 + ..... to 8 terms ; (ii) √2+1√2+12√2+..... to 8 terms ; (iii) 29−13+12−34+..... to 5 terms. (iv) (x+y)+(x2+xy+y2)+(x3+x2y+xy+y3)+.... to n terms ; (v) 35+452+353+454+..... to 2n terms ; (vi) a1+i+a(1+i)2+a(1+i)3+....+a(1+i)n (vii) 1,−a,a2,−a3,........ to n terms (a≠1) (viii) x3,x5,x7,.... to n terms (ix) √7,√21,3√7,.... to n terms
Answer» Find the sum of the following geometric series : (i) 0.15 + 0.015 + 0.0015 + ..... to 8 terms ; (ii) $\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2 \sqrt{2}} + . . . . .$ to 8 terms ; (iii) $\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . . .$ to 5 terms. (iv) $(x + y) + (x^{2} + x y + y^{2}) + (x^{3} + x^{2} y + x y + y^{3}) + . . . .$ to n terms ; (v) $\frac{3}{5} + \frac{4}{5^{2}} + \frac{3}{5^{3}} + \frac{4}{5^{4}} + . . . . .$ to 2n terms ; (vi) $\frac{a}{1 + i} + \frac{a}{(1 + i)^{2}} + \frac{a}{(1 + i)^{3}} + . . . . + \frac{a}{(1 + i)^{n}}$ (vii) $1, - a, a^{2}, - a^{3}, . . . . . . . .$ to n terms $(a \neq 1)$ (viii) $x^{3}, x^{5}, x^{7}, . . . .$ to n terms (ix) $\sqrt{7}, \sqrt{21}, 3 \sqrt{7}, . . . .$ to n terms

39.

Find the sum of the following geometric series : (i) 0.15 + 0.015 + 0.0015 + ..... to 8 terms ; (ii) √2+1√2+12√2+..... to 8 terms ; (iii) 29−13+12−34+..... to 5 terms. (iv) (x+y)+(x2+xy+y2)+(x3+x2y+xy+y3)+.... to n terms ; (v) 35+452+353+454+..... to 2n terms ; (vi) a1+i+a(1+i)2+a(1+i)3+....+a(1+i)n (vii) 1,−a,a2,−a3,........ to n terms (a≠1) (viii) x3,x5,x7,.... to n terms (ix) √7,√21,3√7,.... to n terms

Answer»

Find the sum of the following geometric series :

(i) 0.15 + 0.015 + 0.0015 + ..... to 8 terms ;

(ii) $\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2 \sqrt{2}} + . . . . .$ to 8 terms ;

(iii) $\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . . .$ to 5 terms.

(iv) $(x + y) + (x^{2} + x y + y^{2}) + (x^{3} + x^{2} y + x y + y^{3}) + . . . .$ to n terms ;

(v) $\frac{3}{5} + \frac{4}{5^{2}} + \frac{3}{5^{3}} + \frac{4}{5^{4}} + . . . . .$ to 2n terms ;

(vi) $\frac{a}{1 + i} + \frac{a}{(1 + i)^{2}} + \frac{a}{(1 + i)^{3}} + . . . . + \frac{a}{(1 + i)^{n}}$

(vii) $1, - a, a^{2}, - a^{3}, . . . . . . . .$ to n terms $(a \neq 1)$

(viii) $x^{3}, x^{5}, x^{7}, . . . .$ to n terms

(ix) $\sqrt{7}, \sqrt{21}, 3 \sqrt{7}, . . . .$ to n terms

Discussion

40.	Write an equation of line passing through the point representing solution of the pair of linear equations x+y=2 and 2x−y=1. How many such lines can we find?.
Answer» Write an equation of line passing through the point representing solution of the pair of linear equations $x + y = 2$ and $2 x - y = 1$ . How many such lines can we find?.

Discussion

41.	Select the expression you will get for x and y if you solve the following equations using the cross multiplication method. √3x=2 x3=7−y5
Answer» Select the expression you will get for x and y if you solve the following equations using the cross multiplication method. $\sqrt{3} x = 2$ $\frac{x}{3} = 7 - \frac{y}{5}$

Discussion

42.	If a, b ,c are real numbers such that ac \neq 0, then show that at least one of the equatiions ax2+bx+c=0 and −ax2+bx+c=0
Answer» If a, b ,c are real numbers such that ac \neq 0, then show that at least one of the equatiions $a x^{2} + b x + c = 0$ and $- a x^{2} + b x + c = 0$

Discussion

43.	Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3, respectively.
Answer» Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3, respectively.

Discussion

44.	Factorize : x2−8x+16
Answer» Factorize : $x^{2} - 8 x + 16$

Discussion

45.	ABC is an equilateral triangle of side 4a. Length of its altitude is .
Answer» ABC is an equilateral triangle of side 4a. Length of its altitude is .

Discussion

46.	The length of the tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre is ___ cm.
Answer» The length of the tangent drawn to a circle with radius $7 c m$ from a point $25 c m$ away from the centre is ___ $c m .$

Discussion

47.	A tent of height 77 dm is in the form a right circular cylindrer of diameter 36 m and height 44 dm surrounded by a right circular cone. Find the cost of the canvas at Rs.3.50 per m^2.
Answer» A tent of height 77 dm is in the form a right circular cylindrer of diameter 36 m and height 44 dm surrounded by a right circular cone. Find the cost of the canvas at Rs.3.50 per m^2.

Discussion

48.	A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student A takes food for 20 days, he has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charge and the cost of food per day.
Answer» A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student A takes food for 20 days, he has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charge and the cost of food per day.

Discussion

49.	Pavan completely filled water in a cylindrical vessel of radius 7 cm and height 14 cm. Then he gently dropped a spherical ball of radius 0.7 cm. By how much should the height of glass be increased if he doesn't want water to overflow when the spherical ball is dropped into it? Give the answer in micrometres and correct up to 2 decimal places. 1 m=10−6μm
Answer» Pavan completely filled water in a cylindrical vessel of radius 7 cm and height 14 cm. Then he gently dropped a spherical ball of radius 0.7 cm. By how much should the height of glass be increased if he doesn't want water to overflow when the spherical ball is dropped into it? Give the answer in micrometres and correct up to 2 decimal places. $1 m = 10^{- 6} μ m$

Discussion

50.	Solve the following pair of equations: 7x−8y=−12 −4x+2y=3
Answer» Solve the following pair of equations: $7 x - 8 y = - 12$ $- 4 x + 2 y = 3$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the volume of a right circular cone of height 9 cm is 48π cm3, find the diameter of its base.

If AD, BE and CF are the medians of an equilateral triangle ABC, then the true statement is -

If the perpendicular distances of two chords are equal from the centre of a circle then the length of the two chords is

Is there any chance that frequency of a gicen table will be in increasing order ?

Find the sum of the series 22 + 42 + 62 + 82 +................ 20 terms ___

Find the equation of a line which has the y-intercept 4, and is perpendicular to the line 2 – 3y = 7. Find the coordinates of the point where it cuts the -axis.

By investing in 1623% stock at 64, one earns Rs. 1500. The investment made is:

Question 4 Find two consecutive positive integers, sum of whose squares is 365.

In the above figure, O is the centre of the circle, FD is a tangent at C.Then, which of the following statements are true?

‘P’ is a point on axis Q (8, 2). If length of PQ = 10 unit find coordinates of P.

The ratio of total surface area and lateral surface area of cone is 3:2 and its height is 6 meters. Find its volume of the cone ?

Question 10 In what ratio does the X-axis divide the line segment joining the points (-4,-6) and (-1,7)? Find the coordinates of the points of division.

If the angle of elevation of a cloud from a point 200 m above a lake is 30∘ and the angle of depression of the reflection of the cloud in the lake from the same point is 60∘, then the height of the cloud above the lake is:

Which of the following is a factor of (x+y)3−(x3+y3)?

In the adjoining figure, A, B, and C are three points on a circle O. If angle AOB = 90° and angle BOC = 120°, then angle ABC is:

Question 13 If (a,b) is the mid-point of the line segment joining the points A(10, -6), B(k, 4) and a-2b=18. Then find the value of k and the distance AB.

The entry of the variable for which the value of the polynomial is 0 is called __ of the polynomial.

Two die are thrown simultaneously. How many outcomes are possible for the sum of the values? Are these outcomes equally likely? Explain. [4 MARKS]

In the given figure, PT is a tangent drawn from an external point T to the circle with centre O and PQ is the diameter of the circle. Point Q and T are joined by a line which is intersecting the circle at R. If∠POR=78∘, then find ∠PTR.

Question 5 (iv) Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (iv) (1+secA)secA=sin2A(1−cosA) [Hint : Simplify L.H.S and R.H.S separately]

The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y - 4x + 3 = 0, is

Question 1 (i) Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P. adnan738……

What is the sum of the probabilities of getting a head and getting a tail when a coin is tossed once?

The mid-point of the line segment joining (2a,4) and (−2,2b) is (1,2a+1). Then the values of a and b respectively are

Solve for x. x2−5≤x3−4

In a right angled triangle, which of the following is true? (h=hypotenuse, a and b are the perpendicular sides)

In the given figure △ABC is equilateral. If IE = 4 cm , IB = ____.

State Pythagoras' theorem.

Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2 BL.

Given the linear equation y+3=0, write another equation in two variables such that the geometrical representation of the pair so formed is i) Parallel lines

A vertical stick of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Examine if x = 4, y = 1 is a solution of 3x + 2y = 12 [2 MARKS]

Find the zeroes of the polynomial x2−2.

Find the value of constant if x = - 4 is a zero of quadratic equation 4x2–mx+5=0. [2 MARKS]

Among the following, the terminating rational number is .

If the line y=√3x+k touches the circle x2+y2=16, then find the value of k.

A right triangle is formed by connecting the 3 coordinates A, B and C. If AB and BC are parallel to the coordinate axes as shown in figure, find the distance BC.

Find the roots of the equation 2x2–5x+3=0, by factorisation method.

Write an equation of line passing through the point representing solution of the pair of linear equations x+y=2 and 2x−y=1. How many such lines can we find?.

Select the expression you will get for x and y if you solve the following equations using the cross multiplication method. √3x=2 x3=7−y5

If a, b ,c are real numbers such that ac \neq 0, then show that at least one of the equatiions ax2+bx+c=0 and −ax2+bx+c=0

Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3, respectively.

Factorize : x2−8x+16

ABC is an equilateral triangle of side 4a. Length of its altitude is .

The length of the tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre is ___ cm.

A tent of height 77 dm is in the form a right circular cylindrer of diameter 36 m and height 44 dm surrounded by a right circular cone. Find the cost of the canvas at Rs.3.50 per m^2.

Solve the following pair of equations: 7x−8y=−12 −4x+2y=3