32581 + Interview Questions in Mathematics

1.	The angle of elevation of a cloud from a point 60 m above a lake is 300 and the angle of depression of the reflection of the cloud in the lake is 600. Find the height of the cloud.
Answer» The angle of elevation of a cloud from a point 60 m above a lake is 30⁰ and the angle of depression of the reflection of the cloud in the lake is 60⁰. Find the height of the cloud.

Discussion

2.	Finding the square root of the polynomial 9x4−6x3+7x2−2x+1.
Answer» Finding the square root of the polynomial $9 x^{4} - 6 x^{3} + 7 x^{2} - 2 x + 1.$

Discussion

3.	What must be subtracted from 8x4+14x3−2x2+7x−8 so that the resulting polynomial is exactly divisible by 4x2+3x−2 [4 MARKS]
Answer» What must be subtracted from $8 x^{4} + 14 x^{3} - 2 x^{2} + 7 x - 8$ so that the resulting polynomial is exactly divisible by $4 x^{2} + 3 x - 2$ [4 MARKS]

Discussion

4.	Which term of the A.P 10,8,6,… will be the first negative term?
Answer» Which term of the A.P 10,8,6,… will be the first negative term?

Discussion

5.	Solve the following inequation: 2x−3<x+2≤2x+5 [4 MARKS]
Answer» Solve the following inequation: $2 x - 3 < x + 2 \leq 2 x + 5$ [4 MARKS]

Discussion

6.	Question 6 The ratio of the 11th term to the 18th term of an AP is 2:3. Find the ratio of the 5th term to the 21st term and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
Answer» Question 6 The ratio of the $11^{t h}$ term to the $18^{t h}$ term of an AP is 2:3. Find the ratio of the $5^{t h}$ term to the $21^{s t}$ term and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

Discussion

7.	Find the next two terms of the A.P.:- -10, -6,-2…
Answer» Find the next two terms of the A.P.:- -10, -6,-2…

Discussion

8.	If A and B are two matrices such that AB=B and BA=A, then A2+B2=
Answer» If A and B are two matrices such that AB=B and BA=A, then $A^{2} + B^{2}$ =

Discussion

9.	Which of the following cannot form a right-angled triangle, whose three sides are given below?
Answer» Which of the following cannot form a right-angled triangle, whose three sides are given below?

Discussion

10.	If ax2+bx+c=0 is a quadratic equation, then a CANNOT be
Answer» If $a x^{2} + b x + c = 0$ is a quadratic equation, then $a$ CANNOT be

Discussion

11.	Question 8 Which term of an AP : 21, 42, 63, 84, …. is 210? A) 9th B) 10th C) 11th D) 12th
Answer» Question 8 Which term of an AP : 21, 42, 63, 84, …. is 210? A) $9^{t h}$ B) $10^{t h}$ C) $11^{t h}$ D) $12^{t h}$

Discussion

12.	If the L.C.M. of 9x2+6x+1,3x2+7x+2 and 2x2+3x−2 is (x+a)(2x−b)(3x+c)2. Find value of a−b−c=
Answer» If the L.C.M. of $9 x^{2} + 6 x + 1, 3 x^{2} + 7 x + 2 a n d 2 x^{2} + 3 x - 2$ is $(x + a) (2 x - b) (3 x + c)^{2}$ . Find value of $a - b - c =$

Discussion

13.	write down the first 4 term of the sequences whose general terms are 1 ) Tn=2n + 3 2)Tn=3raise to not n +1 3)T1=2,Tn
Answer» write down the first 4 term of the sequences whose general terms are 1 ) Tn=2n + 3 2)Tn=3raise to not n +1 3)T1=2,Tn

13.

write down the first 4 term of the sequences whose general terms are 1 ) Tn=2n + 3 2)Tn=3raise to not n +1 3)T1=2,Tn

Answer»

write down the first 4 term of the sequences whose general terms are

1 ) Tn=2n + 3

2)Tn=3raise to not n +1

3)T1=2,Tn

Discussion

14.	Question 7 (ii) Solve the following pair of linear equations. (ii) ax + by = c bx + ay = 1 + c
Answer» Question 7 (ii) Solve the following pair of linear equations. (ii) ax + by = c bx + ay = 1 + c

Discussion

15.	Out of the given equations, is not a quadratic equation.
Answer» Out of the given equations, is not a quadratic equation.

Discussion

16.	A stadium is in circular shape. Within the stadium some areas have been allotted for a hockey court and a javelin range, as given in the figure. Assume the shape of the hockey court and the javelin range to be square and triangle, resp. The curators would like to accommodate a few more sports in the stadium. Help them by measuring the unallocated region within the stadium.(the radius of the stadium is 200 mts.)
Answer» A stadium is in circular shape. Within the stadium some areas have been allotted for a hockey court and a javelin range, as given in the figure. Assume the shape of the hockey court and the javelin range to be square and triangle, resp. The curators would like to accommodate a few more sports in the stadium. Help them by measuring the unallocated region within the stadium.(the radius of the stadium is 200 mts.)

16.

A stadium is in circular shape. Within the stadium some areas have been allotted for a hockey court and a javelin range, as given in the figure. Assume the shape of the hockey court and the javelin range to be square and triangle, resp. The curators would like to accommodate a few more sports in the stadium. Help them by measuring the unallocated region within the stadium.(the radius of the stadium is 200 mts.)

Answer»

A stadium is in circular shape. Within the stadium some areas have been allotted for a hockey court and a javelin range, as given in the figure. Assume the shape of the hockey court and the javelin range to be square and triangle, resp. The curators would like to accommodate a few more sports in the stadium. Help them by measuring the unallocated region within the stadium.(the radius of the stadium is 200 mts.)

Discussion

17.	Question 4 (iv) Choose the correct option. Justify your choice. (iv) 1+tan2A1+cot2A (A) sec2A (B) -1 (C) cot2A (D) tan2A
Answer» Question 4 (iv) Choose the correct option. Justify your choice. (iv) $\frac{1 + t a n^{2} A}{1 + c o t^{2} A}$ (A) $s e c^{2} A$ (B) -1 (C) $c o t^{2} A$ (D) $t a n^{2} A$

Discussion

18.	Find the radius of the circle.
Answer» Find the radius of the circle.

18.

Find the radius of the circle.

Answer»

Find the radius of the circle.

Discussion

19.	Question 1 (iv) 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. adnan(iv)−18.92.5……3.6
Answer» Question 1 (iv) 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. $\begin{matrix} a & d & n & a_{n} (i v) & - 18.9 & 2.5 & \dots \dots & 3.6 \end{matrix}$

Discussion

20.	Find the mean using step-deviation. Class IntervalFrequency0−1016010−2020020−3032030−4048040−5030050−60140 [4 MARKS]
Answer» Find the mean using step-deviation. $\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y 0 - 10 & 160 10 - 20 & 200 20 - 30 & 320 30 - 40 & 480 40 - 50 & 300 50 - 60 & 140 \end{matrix}$ [4 MARKS]

Discussion

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

Discussion

22.	Question 1(iii) Find the roots of the following quadratic equations by factorisation: (iii) √2x2+7x+5√2=0
Answer» Question 1(iii) Find the roots of the following quadratic equations by factorisation: (iii) $\sqrt{2} x^{2} + 7 x + 5 \sqrt{2} = 0$

Discussion

23.	(1+tanA tanB)2+(tanA − tanB)2sec2A sec2B= ___
Answer» $\frac{(1 + t a n A t a n B)^{2} + (t a n A - t a n B)^{2}}{{s e c}^{2} A {s e c}^{2} B} =$ ___

Discussion

24.	tan2 θ+cot2 θ+2=
Answer» $t a n^{2} θ + c o t^{2} θ + 2 =$

Discussion

25.	The sides of ΔABC are 6 cm, 8 cm and 10 cm. Find the sides of the larger triangle which is similar to ΔABC if the ratio of corresponding sides is 2.
Answer» The sides of $Δ ABC$ are $6 c m, 8 c m$ and $10 c m .$ Find the sides of the larger triangle which is similar to $Δ ABC$ if the ratio of corresponding sides is 2.

Discussion

26.	Factorise x2–5x+6 by using the Factor Theorem.
Answer» Factorise $x^{2} - 5 x + 6$ by using the Factor Theorem.

Discussion

27.	The circles x2+y2−6x+6y+17=0 and x2+y2−6x−2y+1=0, a common exterior tangent is drawn thus forming a curvilinear triangle.The radius of the circle inscribed in this triangle is
Answer» $T h e c i r c l e s x^{2} + y^{2} - 6 x + 6 y + 17 = 0 a n d x^{2} + y^{2} - 6 x - 2 y + 1 = 0, a c o m m o n e x t e r i o r t a n g e n t i s d r a w n t h u s f o r m i n g a c u r v i l i n e a r t r i a n g l e . T h e r a d i u s o f t h e c i r c l e i n s c r i b e d i n t h i s t r i a n g l e i s$

Discussion

28.	D and E are points on the sides AB and AC respectively of a △ABC such that DE \|\| BC and DE divides △ABC into two parts that are equal in area. Find BDAB.
Answer» D and E are points on the sides AB and AC respectively of a $△$ ABC such that DE \|\| BC and DE divides $△$ ABC into two parts that are equal in area. Find $\frac{B D}{A B}$ .

28.

D and E are points on the sides AB and AC respectively of a △ABC such that DE || BC and DE divides △ABC into two parts that are equal in area. Find BDAB.

Answer»

D and E are points on the sides AB and AC respectively of a $△$ ABC such that DE || BC and DE divides $△$ ABC into two parts that are equal in area. Find $\frac{B D}{A B}$ .

Discussion

29.	ABCD is a square with side a. With centres A, B, C and D four circles are drawn such that each circle touches externally two of the remaining three circles. Let δ be the area of the region in the interior of the square and exterior of the circles. Then the maximum value of δ is:
Answer» ABCD is a square with side a. With centres A, B, C and D four circles are drawn such that each circle touches externally two of the remaining three circles. Let $δ$ be the area of the region in the interior of the square and exterior of the circles. Then the maximum value of $δ$ is:

Discussion

30.	Osho was instructed to make a hexagonal pyramid during math lab. To construct such a pyramid he would require one hexagonal base and ___ isosceles triangles.
Answer» Osho was instructed to make a hexagonal pyramid during math lab. To construct such a pyramid he would require one hexagonal base and ___ isosceles triangles.

Discussion

31.	In the figure below, two tangents are drawn from a point P to a circle meeting it at points A and C. If ∠AOC=120∘, what is the value of ∠APC?
Answer» In the figure below, two tangents are drawn from a point P to a circle meeting it at points A and C. If $∠ A O C = 120^{\circ}$ , what is the value of $∠ A P C$ ?

Discussion

32.	(2,0) is a point on the line joining the points (2x2,4x) and (2y2,4y). Then,
Answer» $(2, 0)$ is a point on the line joining the points $(2 x^{2}, 4 x)$ and $(2 y^{2}, 4 y)$ . Then,

Discussion

33.	What is the solution for the following pair of linear equations? 12x−1y=−1 1x+12y=8 (Given: x≠0 and y≠0)
Answer» What is the solution for the following pair of linear equations? $\frac{1}{2 x} - \frac{1}{y} = - 1$ $\frac{1}{x} + \frac{1}{2 y} = 8$ (Given: $x \neq 0 a n d y \neq 0)$

Discussion

34.	Tick the correct answer in the following. Area of a sector of angle p∘ of a circle with radius R is: 1. p∘180∘×2πR 2. p∘360∘×πR2 3. p∘360∘×2πR 4. p∘720∘×2πR2
Answer» Tick the correct answer in the following. Area of a sector of angle $p^{\circ}$ of a circle with radius $R$ is: 1. $\frac{p^{\circ}}{180^{\circ}} \times 2 π R$ 2. $\frac{p^{\circ}}{360^{\circ}} \times π R^{2}$ 3. $\frac{p^{\circ}}{360^{\circ}} \times 2 π R$ 4. $\frac{p^{\circ}}{720^{\circ}} \times 2 π R^{2}$

Discussion

35.	A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a spade card.
Answer» A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a spade card.

Discussion

36.	Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, ∠A=70o, PR=9cm, ∠P=70o and PQ=4.5cm. Show that ΔABC∼ΔPQR and state the similarity criterion.
Answer» Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, $∠ A = 70^{o}, P R = 9 c m, ∠ P = 70^{o} a n d P Q = 4.5 c m$ . Show that $Δ A B C \sim Δ P Q R$ and state the similarity criterion.

Discussion

37.	In figure, ∠BAC=90∘ and segment AD⊥BC. Prove that AD2=BD×DC. [3 MARKS]
Answer» In figure, $∠ B A C = 90^{\circ}$ and segment $A D ⊥ B C$ . Prove that ${A D}^{2} = B D \times D C$ . [3 MARKS]

37.

In figure, ∠BAC=90∘ and segment AD⊥BC. Prove that AD2=BD×DC. [3 MARKS]

Answer»

In figure, $∠ B A C = 90^{\circ}$ and segment $A D ⊥ B C$ . Prove that ${A D}^{2} = B D \times D C$ . [3 MARKS]

Discussion

38.	Represent 57 in decimal form. [2 MARKS]
Answer» Represent $\frac{5}{7}$ in decimal form. [2 MARKS]

Discussion

39.	Which of the following is correct about the nature of the roots of x2−3x+2=0?
Answer» Which of the following is correct about the nature of the roots of $x^{2} - 3 x + 2 = 0$ ?

Discussion

40.	In the equation ax+by+c=0, the line is parallel to x axis when a = .
Answer» In the equation $a x + b y + c = 0,$ the line is parallel to $x$ axis when $a$ = .

Discussion

41.	Find the area of the shaded region in Fig. 2, where areas drawn with centres A, B, C and D intersed in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π=3.14]
Answer» Find the area of the shaded region in Fig. 2, where areas drawn with centres A, B, C and D intersed in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use $π = 3.14$ ]

Discussion

42.	The 14th term of an AP is twice its 8th. If its 6th term is -8, then find the sum of its first 20 terms.
Answer» The $14^{t h}$ term of an AP is twice its $8^{t h}$ . If its $6^{t h}$ term is -8, then find the sum of its first 20 terms.

Discussion

43.	The curved surface area of a hemisphere is 308 m2. Find the volume and the total surface area of the hemisphere.
Answer» The curved surface area of a hemisphere is $308 m^{2}$ . Find the volume and the total surface area of the hemisphere.

Discussion

44.	Find the difference between the sum of first 100 natural numbers and the sum of even numbers from 1 to 100.
Answer» Find the difference between the sum of first 100 natural numbers and the sum of even numbers from 1 to 100.

Discussion

45.	A chord PQ of length 12 cm subtends an angle of 120∘ at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.
Answer» A chord PQ of length 12 cm subtends an angle of $120^{\circ}$ at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.

Discussion

46.	In the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region [ Use π = 3.14.]
Answer» In the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region [ Use $π$ = 3.14.]

46.

In the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region [ Use π = 3.14.]

Answer»

In the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region [ Use $π$ = 3.14.]

Discussion

47.	A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be filled into cylindrical-shaped bottles each of diameter 5 cm and height 6 cm. Find the number of bottles necessary to empty the bowl.
Answer» A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be filled into cylindrical-shaped bottles each of diameter 5 cm and height 6 cm. Find the number of bottles necessary to empty the bowl.

Discussion

48.	A TV tower stands vertically on a bank of canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60∘. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30∘. Find the height of the tower and the width of the canal.
Answer» A TV tower stands vertically on a bank of canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^{\circ}$ . From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is $30^{\circ}$ . Find the height of the tower and the width of the canal.

Discussion

49.

Solve each of the following systems of equations by the method of cross-multiplication: 6(ax+by)=3a+2b 6(bx−ay)=3b−2a

Answer»

Solve each of the following systems of equations by the method of cross-multiplication:

$6 (a x + b y) = 3 a + 2 b$

$6 (b x - a y) = 3 b - 2 a$

Discussion

50.	A tower is on a horizontal plane. The angles of elevation of top of the tower from two points on a line passing through the foot of the tower at distances 49m and 36m are 41∘ m and 49∘. The height of the tower is :
Answer» A tower is on a horizontal plane. The angles of elevation of top of the tower from two points on a line passing through the foot of the tower at distances 49m and 36m are $41^{\circ} m a n d 49^{\circ}$ . The height of the tower is :

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The angle of elevation of a cloud from a point 60 m above a lake is 300 and the angle of depression of the reflection of the cloud in the lake is 600. Find the height of the cloud.

Finding the square root of the polynomial 9x4−6x3+7x2−2x+1.

What must be subtracted from 8x4+14x3−2x2+7x−8 so that the resulting polynomial is exactly divisible by 4x2+3x−2 [4 MARKS]

Which term of the A.P 10,8,6,… will be the first negative term?

Solve the following inequation: 2x−3&lt;x+2≤2x+5 [4 MARKS]

Question 6 The ratio of the 11th term to the 18th term of an AP is 2:3. Find the ratio of the 5th term to the 21st term and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

Find the next two terms of the A.P.:- -10, -6,-2…

If A and B are two matrices such that AB=B and BA=A, then A2+B2=

Which of the following cannot form a right-angled triangle, whose three sides are given below?

If ax2+bx+c=0 is a quadratic equation, then a CANNOT be

Question 8 Which term of an AP : 21, 42, 63, 84, …. is 210? A) 9th B) 10th C) 11th D) 12th

If the L.C.M. of 9x2+6x+1,3x2+7x+2 and 2x2+3x−2 is (x+a)(2x−b)(3x+c)2. Find value of a−b−c=

write down the first 4 term of the sequences whose general terms are 1 ) Tn=2n + 3 2)Tn=3raise to not n +1 3)T1=2,Tn

Question 7 (ii) Solve the following pair of linear equations. (ii) ax + by = c bx + ay = 1 + c

Out of the given equations, is not a quadratic equation.

Question 4 (iv) Choose the correct option. Justify your choice. (iv) 1+tan2A1+cot2A (A) sec2A (B) -1 (C) cot2A (D) tan2A

Find the radius of the circle.

Question 1 (iv) 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. adnan(iv)−18.92.5……3.6

Find the mean using step-deviation. Class IntervalFrequency0−1016010−2020020−3032030−4048040−5030050−60140 [4 MARKS]

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

Question 1(iii) Find the roots of the following quadratic equations by factorisation: (iii) √2x2+7x+5√2=0

(1+tanA tanB)2+(tanA − tanB)2sec2A sec2B= ___

tan2 θ+cot2 θ+2=

The sides of ΔABC are 6 cm, 8 cm and 10 cm. Find the sides of the larger triangle which is similar to ΔABC if the ratio of corresponding sides is 2.

Factorise x2–5x+6 by using the Factor Theorem.

The circles x2+y2−6x+6y+17=0 and x2+y2−6x−2y+1=0, a common exterior tangent is drawn thus forming a curvilinear triangle.The radius of the circle inscribed in this triangle is

D and E are points on the sides AB and AC respectively of a △ABC such that DE || BC and DE divides △ABC into two parts that are equal in area. Find BDAB.

ABCD is a square with side a. With centres A, B, C and D four circles are drawn such that each circle touches externally two of the remaining three circles. Let δ be the area of the region in the interior of the square and exterior of the circles. Then the maximum value of δ is:

Osho was instructed to make a hexagonal pyramid during math lab. To construct such a pyramid he would require one hexagonal base and ___ isosceles triangles.

In the figure below, two tangents are drawn from a point P to a circle meeting it at points A and C. If ∠AOC=120∘, what is the value of ∠APC?

(2,0) is a point on the line joining the points (2x2,4x) and (2y2,4y). Then,

What is the solution for the following pair of linear equations? 12x−1y=−1 1x+12y=8 (Given: x≠0 and y≠0)

Tick the correct answer in the following. Area of a sector of angle p∘ of a circle with radius R is: 1. p∘180∘×2πR 2. p∘360∘×πR2 3. p∘360∘×2πR 4. p∘720∘×2πR2

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a spade card.

Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, ∠A=70o, PR=9cm, ∠P=70o and PQ=4.5cm. Show that ΔABC∼ΔPQR and state the similarity criterion.

In figure, ∠BAC=90∘ and segment AD⊥BC. Prove that AD2=BD×DC. [3 MARKS]

Represent 57 in decimal form. [2 MARKS]

Which of the following is correct about the nature of the roots of x2−3x+2=0?

In the equation ax+by+c=0, the line is parallel to x axis when a = .

Find the area of the shaded region in Fig. 2, where areas drawn with centres A, B, C and D intersed in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π=3.14]

The 14th term of an AP is twice its 8th. If its 6th term is -8, then find the sum of its first 20 terms.

The curved surface area of a hemisphere is 308 m2. Find the volume and the total surface area of the hemisphere.

Find the difference between the sum of first 100 natural numbers and the sum of even numbers from 1 to 100.

A chord PQ of length 12 cm subtends an angle of 120∘ at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.

In the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region [ Use π = 3.14.]

A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be filled into cylindrical-shaped bottles each of diameter 5 cm and height 6 cm. Find the number of bottles necessary to empty the bowl.

Solve each of the following systems of equations by the method of cross-multiplication: 6(ax+by)=3a+2b 6(bx−ay)=3b−2a

A tower is on a horizontal plane. The angles of elevation of top of the tower from two points on a line passing through the foot of the tower at distances 49m and 36m are 41∘ m and 49∘. The height of the tower is :

Solve the following inequation: 2x−3<x+2≤2x+5 [4 MARKS]