32581 + Interview Questions in Mathematics

1.	Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC. Show that the bisector of angle BAC is a perpendicular bisector of chord BC
Answer» Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC. Show that the bisector of angle BAC is a perpendicular bisector of chord BC

1.

Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC. Show that the bisector of angle BAC is a perpendicular bisector of chord BC

Answer»

Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC.

Show that the bisector of angle BAC is a perpendicular bisector of chord BC

Discussion

2.	P is the centre of the circle . Prove that ∠XPZ=2(∠XZY+∠YXZ). [3 MARKS]
Answer» P is the centre of the circle . Prove that $∠ X P Z = 2 (∠ X Z Y + ∠ Y X Z)$ . [3 MARKS]

2.

P is the centre of the circle . Prove that ∠XPZ=2(∠XZY+∠YXZ). [3 MARKS]

Answer»

P is the centre of the circle . Prove that $∠ X P Z = 2 (∠ X Z Y + ∠ Y X Z)$ . [3 MARKS]

Discussion

3.	Question 10 The students of a school decided to beautify the school on the annual day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. the flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
Answer» Question 10 The students of a school decided to beautify the school on the annual day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. the flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?

Discussion

4.	If the zeroes of the polynomial x3−3x2+x+1 are a−b,a,a+b find a and b. [3 MARKS]
Answer» If the zeroes of the polynomial $x^{3} - 3 x^{2} + x + 1$ are $a - b, a, a + b$ find $a$ and $b$ . [3 MARKS]

Discussion

5.	∣∣∣x126∣∣∣=46 Find the value of x?
Answer» $∣ ∣ ∣ \begin{matrix} x & 1 2 & 6 \end{matrix} ∣ ∣ ∣ = 46$ Find the value of x?

Discussion

6.	To draw a pair of tangents to a circle which are inclined to each other at an angle of 60o, it is required to draw tangents at the end points to those two radii of the side, the angle between which is
Answer» To draw a pair of tangents to a circle which are inclined to each other at an angle of 60^o, it is required to draw tangents at the end points to those two radii of the side, the angle between which is

Discussion

7.	The altitude AD of ΔABC, in which ∠A is obtuse and AD = 10 cm, if BD = 10 cm and CD = 10√3 cm, then ∠A =
Answer» The altitude AD of ΔABC, in which ∠A is obtuse and AD = 10 cm, if BD = 10 cm and CD = 10√3 cm, then ∠A =

Discussion

8.	There are only ___ ways in which a circle and line can interact.
Answer» There are only ___ ways in which a circle and line can interact.

Discussion

9.	Find the value of x for which (x+2),2x,(2x+3) are 3 consecutive terms of an AP
Answer» Find the value of x for which (x+2),2x,(2x+3) are 3 consecutive terms of an AP

Discussion

10.	In an arithmetic progression of 50 terms , the sum of first ten terms is 210 and the sum of last fifteen terms is 2565 . Find the arithmetic progression .
Answer» In an arithmetic progression of 50 terms , the sum of first ten terms is 210 and the sum of last fifteen terms is 2565 . Find the arithmetic progression .

Discussion

11.	The diagonal AC of the given square is 4 cm. Then, its perimeter and area will be equal to ______ and _______ respectively.
Answer» The diagonal AC of the given square is 4 cm. Then, its perimeter and area will be equal to ______ and _______ respectively.

11.

The diagonal AC of the given square is 4 cm. Then, its perimeter and area will be equal to and _ respectively.

Answer»

The diagonal AC of the given square is 4 cm. Then, its perimeter and area will be equal to ______ and _______ respectively.

Discussion

12.	Question 1 (vi) Which of the following form an AP? Justify your answer. 2,22,23,24,...
Answer» Question 1 (vi) Which of the following form an AP? Justify your answer. $2, 2^{2}, 2^{3}, 2^{4}, . . .$

Discussion

13.	When the sun is at an elevation of 50∘, the shadow of a flag post is 20 m.The height of the flag post is, [Tan 50∘=1.2]
Answer» When the sun is at an elevation of $50^{\circ},$ the shadow of a flag post is 20 m.The height of the flag post is, $[T a n 50^{\circ} = 1.2]$

Discussion

14.	Question 14 The graph of the linear equation 2x + 3y = 6 is a line which meets the X-axis at the point: A) (0, 2) B) (2, 0) C) (3, 0) D) (0, 3)
Answer» Question 14 The graph of the linear equation 2x + 3y = 6 is a line which meets the X-axis at the point: A) (0, 2) B) (2, 0) C) (3, 0) D) (0, 3)

Discussion

15.	Question 4 (vi) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (vi) 0.2, 0.22, 0.222, 0.2222 ….
Answer» Question 4 (vi) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (vi) 0.2, 0.22, 0.222, 0.2222 ….

Discussion

16.	3tanθ+cotθ=5cosec θ. Solve for θ, 0 ≤ θ ≤ 90. __ (in degrees)
Answer» $3 t a n θ + c o t θ = 5 c o s e c θ$ . Solve for $θ$ , 0 ≤ $θ$ ≤ 90. __ (in degrees)

16.

3tanθ+cotθ=5cosec θ. Solve for θ, 0 ≤ θ ≤ 90. __ (in degrees)

Answer»

$3 t a n θ + c o t θ = 5 c o s e c θ$ . Solve for $θ$ , 0 ≤ $θ$ ≤ 90.

__ (in degrees)

Discussion

17.	Question 6 A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks towards the building. Find the distance he walked towards the building.
Answer» Question 6 A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from $30^{\circ} t o 60^{\circ}$ as he walks towards the building. Find the distance he walked towards the building.

Discussion

18.	AB is the diameter of a circle with centre O. The value of y is ___
Answer» AB is the diameter of a circle with centre O. The value of y is ___

18.

AB is the diameter of a circle with centre O. The value of y is ___

Answer»

AB is the diameter of a circle with centre O.

The value of y is ___

Discussion

19.	Find the height of an equilateral triangle of side 12 cm.
Answer» Find the height of an equilateral triangle of side 12 cm.

Discussion

20.	Which of the following parameters given in the figure are enough to construct the figure (choose the minimum number of parameters possible): Distance AO = d Radius of the bigger circle (with center A) = R Radius of the smaller circle (with center B) = r ∠POA = θ Note that other than the parameters given in an option, nothing else is given and you have to come up with the figure as given above.
Answer» Which of the following parameters given in the figure are enough to construct the figure (choose the minimum number of parameters possible): Distance AO = d Radius of the bigger circle (with center A) = R Radius of the smaller circle (with center B) = r $∠$ POA = $θ$ Note that other than the parameters given in an option, nothing else is given and you have to come up with the figure as given above.

20.

Which of the following parameters given in the figure are enough to construct the figure (choose the minimum number of parameters possible): Distance AO = d Radius of the bigger circle (with center A) = R Radius of the smaller circle (with center B) = r ∠POA = θ Note that other than the parameters given in an option, nothing else is given and you have to come up with the figure as given above.

Answer»

Which of the following parameters given in the figure are enough to construct the figure (choose the minimum number of parameters possible):

Distance AO = d

Radius of the bigger circle (with center A) = R

Radius of the smaller circle (with center B) = r

$∠$ POA = $θ$

Note that other than the parameters given in an option, nothing else is given and you have to come up with the figure as given above.

Discussion

21.	The monthly consumption of petrol is given city wise in the following table : CityMonthly consumption(in Lakhs)NewDelhi30Mumbai28Chennai22Bengaluru33Kolkata32Baroda23 Find the Mean(average) consumption.
Answer» The monthly consumption of petrol is given city wise in the following table : $\begin{matrix} City & Monthly consumption(in Lakhs) N e w D e l h i & 30 M u m b a i & 28 C h e n n a i & 22 B e n g a l u r u & 33 K o l k a t a & 32 B a r o d a & 23 \end{matrix}$ Find the Mean(average) consumption.

21.

The monthly consumption of petrol is given city wise in the following table : CityMonthly consumption(in Lakhs)NewDelhi30Mumbai28Chennai22Bengaluru33Kolkata32Baroda23 Find the Mean(average) consumption.

Answer»

The monthly consumption of petrol is given city wise in the following table :

$\begin{matrix} City & Monthly consumption(in Lakhs) N e w D e l h i & 30 M u m b a i & 28 C h e n n a i & 22 B e n g a l u r u & 33 K o l k a t a & 32 B a r o d a & 23 \end{matrix}$

Find the Mean(average) consumption.

Discussion

22.	The height of a triangle is 7 m more than its base. If the area of the triangle is 39 sq.m. , then find its height.
Answer» The height of a triangle is 7 m more than its base. If the area of the triangle is 39 sq.m. , then find its height.

Discussion

23.	If p, q and r are the roots of a cubic polynomial ax3+bx2+cx+d, then what will be the value of pq + qr + rp?
Answer» If p, q and r are the roots of a cubic polynomial $a x^{3} + b x^{2} + c x + d$ , then what will be the value of pq + qr + rp?

Discussion

24.	Question 3 Obtain all other zeroes of 3x4+6x3−2x2−10x−5, if two of its zeroes are √53 and −√53.
Answer» Question 3 Obtain all other zeroes of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5$ , if two of its zeroes are $\sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$ .

Discussion

25.	The zeros of mn(x2+1)=(m2+n2)x are:
Answer» The zeros of $m n (x^{2} + 1) = (m^{2} + n^{2}) x$ are:

Discussion

26.	Question 19 If the distance between the points (4,p) and (1,0) is 5, then the value of p is (A) 4 only (B) ±4 (C) −4 only (D) 0
Answer» Question 19 If the distance between the points (4,p) and (1,0) is 5, then the value of p is (A) $4 o n l y$ (B) $\pm 4$ (C) $- 4 o n l y$ (D) $0$

Discussion

27.	What is the value of the polynomial x2−3x+5 at x=3?
Answer» What is the value of the polynomial $x^{2} - 3 x + 5$ at $x = 3 ?$

Discussion

28.	AD is the median of △ ABC. If area of △ ADB = 22.5 sq cm, then the area of △ABC = ____ sq cm.
Answer» AD is the median of △ ABC. If area of △ ADB = 22.5 sq cm, then the area of △ABC = ____ sq cm.

Discussion

29.	If BP:PC = 1:2 and area Δ CPQ = 20 sq.cm, then which of the shaded regions has an area of 40sq.cm.
Answer» If BP:PC = 1:2 and area $Δ$ CPQ = 20 sq.cm, then which of the shaded regions has an area of 40sq.cm.

Discussion

30.	The income of a man A is twice the income of B. The income B is thrice that of C. Given that the sum of income of A, B and C is Rs.72000, find the income of A?
Answer» The income of a man A is twice the income of B. The income B is thrice that of C. Given that the sum of income of A, B and C is Rs.72000, find the income of A?

Discussion

31.	Factorise : [4 MARKS] 1)x3−2x2−x+2 2)2y3+y2−2y−1
Answer» Factorise : [4 MARKS] $1) x^{3} - 2 x^{2} - x + 2$ $2) 2 y^{3} + y^{2} - 2 y - 1$

Discussion

32.	Question 2 (i) Write whether the following statements are true or false. Justify your answers. Every quadratic equation has exactly one root.
Answer» Question 2 (i) Write whether the following statements are true or false. Justify your answers. Every quadratic equation has exactly one root.

Discussion

33.	Which of the following is a polynomial expression in one variable?
Answer» Which of the following is a polynomial expression in one variable?

Discussion

34.	The angles of elevation of the top of a tower from two points at distances of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Show that the height of the tower is 6 metres.
Answer» The angles of elevation of the top of a tower from two points at distances of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Show that the height of the tower is 6 metres.

Discussion

35.	Question 9 If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the point P and Q, prove that PQ is a diameter of the circle.
Answer» Question 9 If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the point P and Q, prove that PQ is a diameter of the circle.

Discussion

36.	One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number, which is a multiple of 7, is (a) 17 (b) 18 (c) 15 (d) 740
Answer» One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number, which is a multiple of 7, is (a) $\frac{1}{7}$ (b) $\frac{1}{8}$ (c) $\frac{1}{5}$ (d) $\frac{7}{40}$

Discussion

37.	2 sin2 63o+1+2 sin2 27o3 cos2 17o−2+3 cos2 73o = ? (a) 32 (a) 23 (c) 2 (d) 3
Answer» $\frac{2 s i n^{2} 63^{o} + 1 + 2 s i n^{2} 27^{o}}{3 c o s^{2} 17^{o} - 2 + 3 c o s^{2} 73^{o}}$ = ? (a) $\frac{3}{2}$ (a) $\frac{2}{3}$ (c) 2 (d) 3

37.

2 sin2 63o+1+2 sin2 27o3 cos2 17o−2+3 cos2 73o = ? (a) 32 (a) 23 (c) 2 (d) 3

Answer»

$\frac{2 s i n^{2} 63^{o} + 1 + 2 s i n^{2} 27^{o}}{3 c o s^{2} 17^{o} - 2 + 3 c o s^{2} 73^{o}}$ = ?

(a) $\frac{3}{2}$ (a) $\frac{2}{3}$ (c) 2 (d) 3

Discussion

38.	If 2x+3y=9xy and 4x+9y=21xy,find the values of x and y.
Answer» If $\frac{2}{x} + \frac{3}{y} = \frac{9}{x y} a n d \frac{4}{x} + \frac{9}{y} = \frac{21}{x y}$ ,find the values of x and y.

Discussion

39.	What is the volume of water that can be filled in a hemispherical bowl of radius 10 cm.
Answer» What is the volume of water that can be filled in a hemispherical bowl of radius 10 cm.

Discussion

40.	From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30∘ and 45∘ respectively. The width of the river is 12m. What is the height of the bridge?
Answer» From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30^{\circ}$ and $45^{\circ}$ respectively. The width of the river is 12m. What is the height of the bridge?

Discussion

41.	The HCF of 1848, 3058 and 242 is ___.
Answer» The HCF of 1848, 3058 and 242 is ___.

Discussion

42.	Find the coordinates of points which trisect the line segment joining (1, –2) and (–3, 4).
Answer» Find the coordinates of points which trisect the line segment joining (1, –2) and (–3, 4).

Discussion

43.	Solve for x and y: (i) (3x-7)+2iy=-5y+(5+x)i (ii) (x+iy)(2-3i)=4+i
Answer» Solve for x and y: (i) (3x-7)+2iy=-5y+(5+x)i (ii) (x+iy)(2-3i)=4+i

Discussion

44.	Sonal's mother age is thrice of sonal. After 10 years she will be just twice of her daughter age. What are there ages
Answer» Sonal's mother age is thrice of sonal. After 10 years she will be just twice of her daughter age. What are there ages

Discussion

45.	Question 28 If the sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, then find the sum of first 10 terms.
Answer» Question 28 If the sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, then find the sum of first 10 terms.

Discussion

46.	Water is filled in a cubical tank of side 10m is transferred completely to a cuboidal tank of length 5m and breadth 10 and height h. Find the height of the cuboidal tank (in metre).
Answer» Water is filled in a cubical tank of side 10m is transferred completely to a cuboidal tank of length 5m and breadth 10 and height h. Find the height of the cuboidal tank (in metre).

Discussion

47.	Find the unknown length 'Y' in the given figure.
Answer» Find the unknown length 'Y' in the given figure.

47.

Find the unknown length 'Y' in the given figure.

Answer»

Find the unknown length 'Y' in the given figure.

Discussion

48.	A point P (3, 5) is reflected in the x - axis and then in the origin. The image P' will be
Answer» A point P (3, 5) is reflected in the x - axis and then in the origin. The image P' will be

Discussion

49.	A square of side 4cm is inscribed in a circle. Find the area enclosed between the circle and square.
Answer» A square of side 4cm is inscribed in a circle. Find the area enclosed between the circle and square.

Discussion

50.	The highest power of 2 by which the product of first 100 counting numbers can be divided without any remainder is
Answer» The highest power of 2 by which the product of first 100 counting numbers can be divided without any remainder is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC. Show that the bisector of angle BAC is a perpendicular bisector of chord BC

P is the centre of the circle . Prove that ∠XPZ=2(∠XZY+∠YXZ). [3 MARKS]

If the zeroes of the polynomial x3−3x2+x+1 are a−b,a,a+b find a and b. [3 MARKS]

∣∣∣x126∣∣∣=46 Find the value of x?

To draw a pair of tangents to a circle which are inclined to each other at an angle of 60o, it is required to draw tangents at the end points to those two radii of the side, the angle between which is

The altitude AD of ΔABC, in which ∠A is obtuse and AD = 10 cm, if BD = 10 cm and CD = 10√3 cm, then ∠A =

There are only ___ ways in which a circle and line can interact.

Find the value of x for which (x+2),2x,(2x+3) are 3 consecutive terms of an AP

In an arithmetic progression of 50 terms , the sum of first ten terms is 210 and the sum of last fifteen terms is 2565 . Find the arithmetic progression .

The diagonal AC of the given square is 4 cm. Then, its perimeter and area will be equal to ______ and _______ respectively.

Question 1 (vi) Which of the following form an AP? Justify your answer. 2,22,23,24,...

When the sun is at an elevation of 50∘, the shadow of a flag post is 20 m.The height of the flag post is, [Tan 50∘=1.2]

Question 14 The graph of the linear equation 2x + 3y = 6 is a line which meets the X-axis at the point: A) (0, 2) B) (2, 0) C) (3, 0) D) (0, 3)

Question 4 (vi) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (vi) 0.2, 0.22, 0.222, 0.2222 ….

3tanθ+cotθ=5cosec θ. Solve for θ, 0 ≤ θ ≤ 90. __ (in degrees)

Question 6 A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks towards the building. Find the distance he walked towards the building.

AB is the diameter of a circle with centre O. The value of y is ___

Find the height of an equilateral triangle of side 12 cm.

The monthly consumption of petrol is given city wise in the following table : CityMonthly consumption(in Lakhs)NewDelhi30Mumbai28Chennai22Bengaluru33Kolkata32Baroda23 Find the Mean(average) consumption.

The height of a triangle is 7 m more than its base. If the area of the triangle is 39 sq.m. , then find its height.

If p, q and r are the roots of a cubic polynomial ax3+bx2+cx+d, then what will be the value of pq + qr + rp?

Question 3 Obtain all other zeroes of 3x4+6x3−2x2−10x−5, if two of its zeroes are √53 and −√53.

The zeros of mn(x2+1)=(m2+n2)x are:

Question 19 If the distance between the points (4,p) and (1,0) is 5, then the value of p is (A) 4 only (B) ±4 (C) −4 only (D) 0

What is the value of the polynomial x2−3x+5 at x=3?

AD is the median of △ ABC. If area of △ ADB = 22.5 sq cm, then the area of △ABC = ____ sq cm.

If BP:PC = 1:2 and area Δ CPQ = 20 sq.cm, then which of the shaded regions has an area of 40sq.cm.

The income of a man A is twice the income of B. The income B is thrice that of C. Given that the sum of income of A, B and C is Rs.72000, find the income of A?

Factorise : [4 MARKS] 1)x3−2x2−x+2 2)2y3+y2−2y−1

Question 2 (i) Write whether the following statements are true or false. Justify your answers. Every quadratic equation has exactly one root.

Which of the following is a polynomial expression in one variable?

The angles of elevation of the top of a tower from two points at distances of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Show that the height of the tower is 6 metres.

Question 9 If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the point P and Q, prove that PQ is a diameter of the circle.

One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number, which is a multiple of 7, is (a) 17 (b) 18 (c) 15 (d) 740

2 sin2 63o+1+2 sin2 27o3 cos2 17o−2+3 cos2 73o = ? (a) 32 (a) 23 (c) 2 (d) 3

If 2x+3y=9xy and 4x+9y=21xy,find the values of x and y.

What is the volume of water that can be filled in a hemispherical bowl of radius 10 cm.

From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30∘ and 45∘ respectively. The width of the river is 12m. What is the height of the bridge?

The HCF of 1848, 3058 and 242 is ___.

Find the coordinates of points which trisect the line segment joining (1, –2) and (–3, 4).

Solve for x and y: (i) (3x-7)+2iy=-5y+(5+x)i (ii) (x+iy)(2-3i)=4+i

Sonal's mother age is thrice of sonal. After 10 years she will be just twice of her daughter age. What are there ages

Question 28 If the sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, then find the sum of first 10 terms.

Water is filled in a cubical tank of side 10m is transferred completely to a cuboidal tank of length 5m and breadth 10 and height h. Find the height of the cuboidal tank (in metre).

Find the unknown length 'Y' in the given figure.

A point P (3, 5) is reflected in the x - axis and then in the origin. The image P' will be

A square of side 4cm is inscribed in a circle. Find the area enclosed between the circle and square.

The highest power of 2 by which the product of first 100 counting numbers can be divided without any remainder is

The diagonal AC of the given square is 4 cm. Then, its perimeter and area will be equal to and _ respectively.