32581 + Interview Questions in Mathematics Page 200 InterviewSolution

9951.	The value of sin (45° +θ) - cos (45° - θ) is equal to(a) 2 cos θ (b) 0 (c) 2 sin θ (d) 1
Answer» The value of sin ( $45^{°} + θ) - \cos (45^{°} - θ)$ is equal to (a) 2 cos $θ$ (b) 0 (c) 2 sin $θ$ (d) 1

Discussion

9952.	Question 2 (ii) Choose the correct choice in the following and justify. (ii) 11th term of the A.P −3,−12,2 is A) 28 B) 22 C) -38 D) 44
Answer» Question 2 (ii) Choose the correct choice in the following and justify. (ii) $11^{t h} t e r m o f t h e A . P - 3, \frac{- 1}{2}, 2 i s$ A) 28 B) 22 C) -38 D) 44

Discussion

9953.	Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awanded for each correct answer and 2 marks been deducted for each incorrect answer, the Yash would have scored 50 marks. How many question were there in the test?
Answer» Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awanded for each correct answer and 2 marks been deducted for each incorrect answer, the Yash would have scored 50 marks. How many question were there in the test?

Discussion

9954.	From the equation whose roots are(1) 3 and 5(2) 6 and − 5(3) (4) (5) (6)
Answer» From the equation whose roots are (1) 3 and 5 (2) 6 and − 5 (3) (4) (5) (6)

9954.

From the equation whose roots are(1) 3 and 5(2) 6 and − 5(3) (4) (5) (6)

Answer»

From the equation whose roots are

(1) 3 and 5

(2) 6 and − 5

(3)

(4)

(5)

(6)

Discussion

9955.	Question 12Find the sum of first 40 positive integers divisible by 6.
Answer» Question 12 Find the sum of first 40 positive integers divisible by 6.

Discussion

9956.	Write the value of 3cot2θ-3cosec2θ.
Answer» Write the value of $3 \cot^{2} θ - 3 {cosec}^{2} θ$ .

Discussion

9957.	If the range of discrete data of n observations is zero, then:
Answer» If the range of discrete data of n observations is zero, then:

Discussion

9958.	Question 2 Find coordinates of the points of trisection of the line segment joining points (4, -1) and (-2, -3).
Answer» Question 2 Find coordinates of the points of trisection of the line segment joining points (4, -1) and (-2, -3).

Discussion

9959.	If A = {3, 5},then A x A x A is
Answer» If A = {3, 5},then A x A x A is

Discussion

9960.	In a restaurant, WiFi signal has to be provided only to the deluxe class. Signal reaches each of the customer upto a distance of 21 m from the antenna and the total area for which signal to be provided is 231 m2. What is the angle (in degrees) at which the signal has to be spread over a sector by the antenna?
Answer» In a restaurant, WiFi signal has to be provided only to the deluxe class. Signal reaches each of the customer upto a distance of 21 m from the antenna and the total area for which signal to be provided is 231 $m^{2}$ . What is the angle (in degrees) at which the signal has to be spread over a sector by the antenna?

Discussion

9961.	Corresponding sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio(a) 2 : 3(b) 4 : 9(c) 9 : 4(d) 16 : 81
Answer» Corresponding sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio (a) 2 : 3 (b) 4 : 9 (c) 9 : 4 (d) 16 : 81

Discussion

9962.	Question 9 If the common difference of an AP is 5, then what is a18−a13. A) 5 B) 20 C) 25 D) 30
Answer» Question 9 If the common difference of an AP is 5, then what is $a_{18} - a_{13}$ . A) 5 B) 20 C) 25 D) 30

Discussion

9963.	How do we represent 0.123¯¯¯¯¯¯¯¯456?
Answer» How do we represent $0.123 ¯ ¯¯¯¯¯¯ ¯ 456$ ?

Discussion

9964.	To draw a pair of tangents to a circle which are inclined to each other at an angle of 30∘, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be
Answer» To draw a pair of tangents to a circle which are inclined to each other at an angle of $30^{\circ}$ , it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

Discussion

9965.	If H.C.F. of 65 and 117 is expressible in the form of 65 m - 117, then the value of m is :
Answer» If H.C.F. of 65 and 117 is expressible in the form of 65 m - 117, then the value of m is :

Discussion

9966.	Find the area of the shaded region (in cm2) as shown in figure of the two concentric circles with centre O and radius 7 cm and 14 cm respectively. Given ∠AOC = 40∘. (use π = 227)
Answer» Find the area of the shaded region (in $c m^{2}$ ) as shown in figure of the two concentric circles with centre O and radius 7 $c m$ and 14 $c m$ respectively. Given $∠$ AOC = $40^{\circ}$ . (use $π$ = $\frac{22}{7}$ )

Discussion

9967.	Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact
Answer» Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact

Discussion

9968.	Find the area of the triangle PQR with Q(3, 2) and the mid-points of the sides through Q being (2, −1) and (1, 2). [CBSE 2015]
Answer» Find the area of the triangle PQR with Q(3, 2) and the mid-points of the sides through Q being (2, −1) and (1, 2). [CBSE 2015]

Discussion

9969.	Which bar model shows the correct length of the strip?
Answer» Which bar model shows the correct length of the strip?

Discussion

9970.	If the sum of n terms of an AP is 3n2+5n then which of its terms is 164?
Answer» If the sum of n terms of an AP is 3n²+5n then which of its terms is 164?

Discussion

9971.	Find the principal value of cosec x=-1
Answer» Find the principal value of cosec x=-1

Discussion

9972.	FUNCTIONS If f(x) is a polynomial satisfying f(x).f(y) = f(x) + f(y) + f(xy) - 2, for all x,y belong to R and f(2) = 5, then show that f(x) is an even function.
Answer» FUNCTIONS If f(x) is a polynomial satisfying f(x).f(y) = f(x) + f(y) + f(xy) - 2, for all x,y belong to R and f(2) = 5, then show that f(x) is an even function.

Discussion

9973.	Explain estimation method (For perfect cubes). In advance thanks
Answer» Explain estimation method (For perfect cubes). In advance thanks

Discussion

9974.	Question 1 (iii)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(iii)……−318−5
Answer» Question 1 (iii) 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. $\begin{matrix} a & d & n & a_{n} (i i i) & \dots \dots & - 3 & 18 & - 5 \end{matrix}$

Discussion

9975.	Question 3The value of the expression cosec(75∘+θ)−sec(15∘−θ)−tan(55∘+θ)+cot(35∘−θ) is(A) -1(B) 0(C) 1(D) 32
Answer» Question 3 The value of the expression $c o s e c (75^{\circ} + θ) - s e c (15^{\circ} - θ) - t a n (55^{\circ} + θ) + c o t (35^{\circ} - θ)$ is (A) -1 (B) 0 (C) 1 (D) $\frac{3}{2}$

Discussion

9976.	The height of a cone is 8 cm and its base radius is 6 cm. Find the curved surface area the cone. (Use π = 3.14).
Answer» The height of a cone is 8 cm and its base radius is 6 cm. Find the curved surface area the cone. (Use $π$ = 3.14).

Discussion

9977.	Vijay inherited huge wealth from his father and by establishing a soft drinks company, he squared his wealth. He started a company that manufactures airplane toys and incurred huge losses amounting to k (>0) times the wealth he inherited from his father. His total assets now stand at the debt of 4 crores. For what value of k is the above scenario possible?
Answer» Vijay inherited huge wealth from his father and by establishing a soft drinks company, he squared his wealth. He started a company that manufactures airplane toys and incurred huge losses amounting to k (>0) times the wealth he inherited from his father. His total assets now stand at the debt of 4 crores. For what value of k is the above scenario possible?

Discussion

9978.	Question 5A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Answer» Question 5 A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Discussion

9979.	Find the distance of the point P (4, 3) from the origin?
Answer» Find the distance of the point P (4, 3) from the origin?

Discussion

9980.	Question 1(c) Find the following product: (- 21) × (- 30)
Answer» Question 1(c) Find the following product: (- 21) $\times$ (- 30)

Discussion

9981.	Q. 3\|x\| + 5\|y\|=8 , 7\|x\| - 3 \|y\| =48 , then find the value of x+y .
Answer» Q. 3\|x\| + 5\|y\|=8 , 7\|x\| - 3 \|y\| =48 , then find the value of x+y .

Discussion

9982.	Solve the inequality 18−3(2x−5)>12;x ϵ W
Answer» Solve the inequality $18 - 3 (2 x - 5) > 12; x ϵ W$

Discussion

9983.	Write the following numbers in the form of rational indices.(1) Square root of 5th power of 121(2) Cube of 4th root of 324(3) 5th root of square of 264(4) Cube of cube root of 3
Answer» Write the following numbers in the form of rational indices. (1) Square root of 5th power of 121 (2) Cube of 4th root of 324 (3) 5th root of square of 264 (4) Cube of cube root of 3

Discussion

9984.	The L-shaped ABCDEF is reflected about x=−1 to L-shaped A′B′C′D′E′F′. The mirror images of the points A(−3,3) & B(−3,2) are & respectively.
Answer» The L-shaped ABCDEF is reflected about $x = - 1$ to L-shaped $A^{'} B^{'} C^{'} D^{'} E^{'} F^{'}$ . The mirror images of the points $A (- 3, 3) & B (- 3, 2)$ are & respectively.

Discussion

9985.	Two years ago, a father was five times as old as his son. Two year later, his age will be 8 more than three times the age of the son. Find the present ages of father and son.
Answer» Two years ago, a father was five times as old as his son. Two year later, his age will be 8 more than three times the age of the son. Find the present ages of father and son.

Discussion

9986.	The height of a tower is 100 m. When the angle of elevation of the sun changes from 30° to 45°, the shadow of the tower becomes x metres less. The value of x is(a) 100 m(b) 1003 m(c) 1003 -1 m(d) 1003m
Answer» The height of a tower is 100 m. When the angle of elevation of the sun changes from 30° to 45°, the shadow of the tower becomes x metres less. The value of x is (a) 100 m (b) $100 \sqrt{3} m$ (c) $100 (\sqrt{3} - 1) m$ (d) $\frac{100}{3} m$

Discussion

9987.	If the equation x2+2(k+2)x+9k=0 has real equal roots, then values of k are
Answer» If the equation $x^{2} + 2 (k + 2) x + 9 k = 0$ has real equal roots, then values of $k$ are

Discussion

9988.	Two parallel lines touch a circle at points A and B respectively. The area of the circle is 25π cm2, then find the distance between the lines.
Answer» Two parallel lines touch a circle at points A and B respectively. The area of the circle is 25 $π$ ${c m}^{2}$ , then find the distance between the lines.

Discussion

9989.	If the zeroes of the cubic polynomial f(x)=kx^3-8x^2+5 are à-b,à andà+b are the zeroes of the polynomial.
Answer» If the zeroes of the cubic polynomial f(x)=kx^3-8x^2+5 are à-b,à andà+b are the zeroes of the polynomial.

Discussion

9990.	Prove the following trigonometric identities.1-cos θsin θ=sin θ1+cos θ
Answer» Prove the following trigonometric identities. $\frac{1 - \cos θ}{\sin θ} = \frac{\sin θ}{1 + \cos θ}$

Discussion

9991.	If A and B are the angles in the first quadrant TanA=1/7 and SinB=1/root10 then find value of A+2B
Answer» If A and B are the angles in the first quadrant TanA=1/7 and SinB=1/root10 then find value of A+2B

Discussion

9992.	The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per m2.
Answer» The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per $m^{2}$ .

9992.

The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per m2.

Answer»

The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per $m^{2}$ .

Discussion

9993.	51.In triangle ABC, BM and CN is perpendicular from Band C respectively on any line passing through A .If L is the midpoint of BC, prove that ML=NL
Answer» 51.In triangle ABC, BM and CN is perpendicular from Band C respectively on any line passing through A .If L is the midpoint of BC, prove that ML=NL

Discussion

9994.	Let A = {1, 2, 3, 4} and R be the relation on A defined by {(a, b): a, b ∈ A, a×b is an even number}, then the range of R is __________________.
Answer» Let A = {1, 2, 3, 4} and R be the relation on A defined by {(a, b): a, b ∈ A, a×b is an even number}, then the range of R is __________________.

Discussion

9995.	In the given figure, ABCD is a trapezium of area 24.5 cm2 , If AD \|\| BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle, then find the area of the shaded region. [CBSE 2014]
Answer» In the given figure, ABCD is a trapezium of area 24.5 cm² , If AD \|\| BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle, then find the area of the shaded region. [CBSE 2014]

Discussion

9996.	What is the duplicate ratio of 9:17
Answer» What is the duplicate ratio of 9:17

Discussion

9997.	Which polynomial should be added in 3x³-2x²+3 to get the polynomial 3x²+4?
Answer» Which polynomial should be added in 3x³-2x²+3 to get the polynomial 3x²+4?

Discussion

9998.	An arc AB forms ∠AOB at the centre of the circle. If I draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will ___________ the ∠AOB.
Answer» An arc AB forms $∠ A O B$ at the centre of the circle. If I draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will ___________ the $∠ A O B$ .

Discussion

9999.	Solve the following quadratic equations by factorization:3x2-22x-23=0
Answer» Solve the following quadratic equations by factorization: $\sqrt{3} x^{2} - 2 \sqrt{2} x - 2 \sqrt{3} = 0$

Discussion

10000.

The following table shows the information regarding the milk collected from farmers on a milk collection centre and the content of fat in the milk, measured by a lactometer. Find the mode of fat content. Content of fat (%) 2 - 3 3 - 4 4 - 5 5 - 6 6 - 7 Milk collected (Litre) 30 70 80 60 20

Answer» The following table shows the information regarding the milk collected from farmers on a milk collection centre and the content of fat in the milk, measured by a lactometer. Find the mode of fat content.

Content of fat (%)	2 - 3	3 - 4	4 - 5	5 - 6	6 - 7
Milk collected (Litre)	30	70	80	60	20

Discussion

Explore topic-wise InterviewSolutions in .

The value of sin (45° +θ) - cos (45° - θ) is equal to(a) 2 cos θ (b) 0 (c) 2 sin θ (d) 1

Question 2 (ii) Choose the correct choice in the following and justify. (ii) 11th term of the A.P −3,−12,2 is A) 28 B) 22 C) -38 D) ​​​​​​​ 44

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awanded for each correct answer and 2 marks been deducted for each incorrect answer, the Yash would have scored 50 marks. How many question were there in the test?

From the equation whose roots are(1) 3 and 5(2) 6 and − 5(3) (4) (5) (6)

Question 12Find the sum of first 40 positive integers divisible by 6.

Write the value of 3cot2θ-3cosec2θ.

If the range of discrete data of n observations is zero, then:

Question 2 Find coordinates of the points of trisection of the line segment joining points (4, -1) and (-2, -3).

If A = {3, 5},then A x A x A is

Corresponding sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio(a) 2 : 3(b) 4 : 9(c) 9 : 4(d) 16 : 81

Question 9 If the common difference of an AP is 5, then what is a18−a13. A) 5 B) 20 C) 25 D) 30

How do we represent 0.123¯¯¯¯¯¯¯¯456?

To draw a pair of tangents to a circle which are inclined to each other at an angle of 30∘, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

If H.C.F. of 65 and 117 is expressible in the form of 65 m - 117, then the value of m is :

Find the area of the shaded region (in cm2) as shown in figure of the two concentric circles with centre O and radius 7 cm and 14 cm respectively. Given ∠AOC = 40∘. (use π = 227)

Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact

Find the area of the triangle PQR with Q(3, 2) and the mid-points of the sides through Q being (2, −1) and (1, 2). [CBSE 2015]

Which bar model shows the correct length of the strip?

If the sum of n terms of an AP is 3n2+5n then which of its terms is 164?

Find the principal value of cosec x=-1

FUNCTIONS If f(x) is a polynomial satisfying f(x).f(y) = f(x) + f(y) + f(xy) - 2, for all x,y belong to R and f(2) = 5, then show that f(x) is an even function.

Explain estimation method (For perfect cubes). In advance thanks

Question 1 (iii)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(iii)……−318−5

Question 3The value of the expression cosec(75∘+θ)−sec(15∘−θ)−tan(55∘+θ)+cot(35∘−θ) is(A) -1(B) 0(C) 1(D) 32

The height of a cone is 8 cm and its base radius is 6 cm. Find the curved surface area the cone. (Use π = 3.14).

Question 5A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Find the distance of the point P (4, 3) from the origin?

Question 1(c) Find the following product: (- 21) × (- 30)

Q. 3|x| + 5|y|=8 , 7|x| - 3 |y| =48 , then find the value of x+y .

Solve the inequality 18−3(2x−5)&gt;12;x ϵ W

Write the following numbers in the form of rational indices.(1) Square root of 5th power of 121(2) Cube of 4th root of 324(3) 5th root of square of 264(4) Cube of cube root of 3

The L-shaped ABCDEF is reflected about x=−1 to L-shaped A′B′C′D′E′F′. The mirror images of the points A(−3,3) &amp; B(−3,2) are & respectively.

Two years ago, a father was five times as old as his son. Two year later, his age will be 8 more than three times the age of the son. Find the present ages of father and son.

The height of a tower is 100 m. When the angle of elevation of the sun changes from 30° to 45°, the shadow of the tower becomes x metres less. The value of x is(a) 100 m(b) 1003 m(c) 1003 -1 m(d) 1003m

If the equation x2+2(k+2)x+9k=0 has real equal roots, then values of k are

Two parallel lines touch a circle at points A and B respectively. The area of the circle is 25π cm2, then find the distance between the lines.

If the zeroes of the cubic polynomial f(x)=kx^3-8x^2+5 are à-b,à andà+b are the zeroes of the polynomial.

Prove the following trigonometric identities.1-cos θsin θ=sin θ1+cos θ

If A and B are the angles in the first quadrant TanA=1/7 and SinB=1/root10 then find value of A+2B

The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per m2.

51.In triangle ABC, BM and CN is perpendicular from Band C respectively on any line passing through A .If L is the midpoint of BC, prove that ML=NL

Let A = {1, 2, 3, 4} and R be the relation on A defined by {(a, b): a, b ∈ A, a×b is an even number}, then the range of R is __________________.

In the given figure, ABCD is a trapezium of area 24.5 cm2 , If AD || BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle, then find the area of the shaded region. [CBSE 2014]

What is the duplicate ratio of 9:17

Which polynomial should be added in 3x³-2x²+3 to get the polynomial 3x²+4?

An arc AB forms ∠AOB at the centre of the circle. If I draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will ___________ the ∠AOB.

Solve the following quadratic equations by factorization:3x2-22x-23=0

The following table shows the information regarding the milk collected from farmers on a milk collection centre and the content of fat in the milk, measured by a lactometer. Find the mode of fat content. Content of fat (%) 2 - 3 3 - 4 4 - 5 5 - 6 6 - 7 Milk collected (Litre) 30 70 80 60 20

Question 2 (ii) Choose the correct choice in the following and justify. (ii) 11th term of the A.P −3,−12,2 is A) 28 B) 22 C) -38 D) 44

Solve the inequality 18−3(2x−5)>12;x ϵ W

The L-shaped ABCDEF is reflected about x=−1 to L-shaped A′B′C′D′E′F′. The mirror images of the points A(−3,3) & B(−3,2) are & respectively.