32581 + Interview Questions in Mathematics Page 239 InterviewSolution

11901.	There are four bus routes between A and B; and three bus routes between B and C. A man can travel round trip in number of ways by bus from A to C via B. If he does not want to use a bus route more than once, the number of ways he can make round trip, is(a) 72(b) 144(c) 14(d) 19
Answer» There are four bus routes between A and B; and three bus routes between B and C. A man can travel round trip in number of ways by bus from A to C via B. If he does not want to use a bus route more than once, the number of ways he can make round trip, is (a) 72 (b) 144 (c) 14 (d) 19

Discussion

11902.	LCM of a and 2
Answer» LCM of a and 2

Discussion

11903.	Solve the following systems of equations:2x-3y=03x-8y=0
Answer» Solve the following systems of equations: $\sqrt{2} x - \sqrt{3} y = 0 \sqrt{3} x - \sqrt{8} y = 0$

Discussion

11904.	If 15cotA=8, find the values of sinA and secA.
Answer» If $15 \cot A = 8$ , find the values of sinA and secA.

Discussion

11905.	Write down the sequence of differences (subtracting the larger form the smaller) of consecutive perfect squares. Is it and arithmetic sequence?
Answer» Write down the sequence of differences (subtracting the larger form the smaller) of consecutive perfect squares. Is it and arithmetic sequence?

Discussion

11906.	Question 7A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Answer» Question 7 A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

Discussion

11907.	The point at which the two coordinate axes meet is called the __________.
Answer» The point at which the two coordinate axes meet is called the __________.

Discussion

11908.	Find the equations of the sides of the triangle, the coordinates of whose vertices are (1, 4), (2, -3) and (-1, -2).
Answer» Find the equations of the sides of the triangle, the coordinates of whose vertices are (1, 4), (2, -3) and (-1, -2).

Discussion

11909.	Which measure of central tendency can be determine graphically?
Answer» Which measure of central tendency can be determine graphically?

Discussion

11910.	Question 21 (i)A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that she will buy it?
Answer» Question 21 (i) A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that she will buy it?

Discussion

11911.	In the given figure, O is the centre of the circle. Find ∠BAC.
Answer» In the given figure, O is the centre of the circle. Find ∠BAC.

Discussion

11912.	How many balls can be placed in the cylindrical tube if they fit exactly as shown in the figure. The inner curved surface area of the cylinder is 30.8 m2 and the surface area of each ball is 61600 cm2. (Use =227)
Answer» How many balls can be placed in the cylindrical tube if they fit exactly as shown in the figure. The inner curved surface area of the cylinder is $30.8 m^{2}$ and the surface area of each ball is $61600 c m^{2}$ . (Use $= \frac{22}{7}$ )

Discussion

11913.	In the given figure, AE and BC intersect each other at point D. If ∠CDE=900, AB = 5cm, BD = 4cm and CD = 9 cm, find AE.
Answer» In the given figure, AE and BC intersect each other at point D. If $∠ C D E = 90^{0}$ , AB = 5cm, BD = 4cm and CD = 9 cm, find AE.

11913.

In the given figure, AE and BC intersect each other at point D. If ∠CDE=900, AB = 5cm, BD = 4cm and CD = 9 cm, find AE.

Answer»

In the given figure, AE and BC intersect each other at point D. If $∠ C D E = 90^{0}$ , AB = 5cm, BD = 4cm and CD = 9 cm, find AE.

Discussion

11914.	6. A number consists of two digits of which the ten's digit exceeds the unit's digit by 6. The number itself is equal to ten times the sum of digits. Find the number.
Answer» 6. A number consists of two digits of which the ten's digit exceeds the unit's digit by 6. The number itself is equal to ten times the sum of digits. Find the number.

Discussion

11915.	Why we cannot construct a triangle of given sides as 5 cm , 5 cm and 10 cm?
Answer» Why we cannot construct a triangle of given sides as 5 cm , 5 cm and 10 cm?

Discussion

11916.	The largest 4 digit number exactly divisible by 88 is:
Answer» The largest 4 digit number exactly divisible by 88 is:

Discussion

11917.	During a practice match, a softball pitcher throws a ball whose height at any instant from ground level is given by the equation h = −16t2 + 24t + 1 , where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet from the ground level?
Answer» During a practice match, a softball pitcher throws a ball whose height at any instant from ground level is given by the equation h = $- 16 t^{2}$ + 24t + 1 , where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet from the ground level?

Discussion

11918.	Find the ratio in which C (, 1) divides the join of A (–4, 4) and B (6, –1) and hence find the value of .
Answer» Find the ratio in which C (, 1) divides the join of A (–4, 4) and B (6, –1) and hence find the value of .

Discussion

11919.	When the rate of sales tax is decreased from 9% to 7% for a radio, Rahul has to pay Rs 632 less for it. What is the listed price of the radio? [4 MARKS]
Answer» When the rate of sales tax is decreased from $9 %$ to $7 %$ for a radio, Rahul has to pay Rs 632 less for it. What is the listed price of the radio? [4 MARKS]

Discussion

11920.	Finding torsional angle in cyclic compound
Answer» Finding torsional angle in cyclic compound

Discussion

11921.	If π∑i=1i = n(n+1)2, then π∑i=1(3i−2) =
Answer» If $π \sum i = 1 i$ = $\frac{n (n + 1)}{2}$ , then $π \sum i = 1 (3 i - 2)$ =

Discussion

11922.	All edges of a square pyramid are of equal lengths. If the length of the base edge is 20 cm, what is the slant height?
Answer» All edges of a square pyramid are of equal lengths. If the length of the base edge is $20 c m$ , what is the slant height?

Discussion

11923.	Find the values of p and q for which the following system of linear equations has infinite number of solutions: 2x + 3y = 9 (p + q) x + (2p - q) y = 3 (p +q + 1)
Answer» Find the values of p and q for which the following system of linear equations has infinite number of solutions: 2x + 3y = 9 (p + q) x + (2p - q) y = 3 (p +q + 1)

11923.

Find the values of p and q for which the following system of linear equations has infinite number of solutions: 2x + 3y = 9 (p + q) x + (2p - q) y = 3 (p +q + 1)

Answer»

Find the values of p and q for which the following system of linear equations has infinite number of solutions:

2x + 3y = 9

(p + q) x + (2p - q) y = 3 (p +q + 1)

Discussion

11924.	Question 4Is it true to say that area of segment of a circle is less than the areas of its corresponding sector? Why?
Answer» Question 4 Is it true to say that area of segment of a circle is less than the areas of its corresponding sector? Why?

Discussion

11925.	The product of the zeros of x3 + 4x2 + x − 6 is(a) −4(b) 4(c) 6(d) −6
Answer» The product of the zeros of x³ + 4x² + x − 6 is (a) −4 (b) 4 (c) 6 (d) −6

Discussion

11926.	A hemispherical bowl fits exactly on the open surface of a cone with height 5 cm and radius 3.5 cm.What is the volume of the solid formed?
Answer» A hemispherical bowl fits exactly on the open surface of a cone with height 5 cm and radius 3.5 cm.What is the volume of the solid formed?

Discussion

11927.	If 1 is a zero of the polynomial P(x), then:
Answer» If 1 is a zero of the polynomial P(x), then:

Discussion

11928.	1. Lis le texte ci-dessus et réponds aux questions suivantes : A. Quelles sont les deux fonctions des vêtements ? B. Comment peut-on différencier entre les différents types de vêtements ? C. Qui influence notre choix de vêtements? i. pendant l'enfance? ii. à l'école?2. Coche la bonne réponse : A. Si vous ne vous habillez pas à la mode i. on vous aime beaucoup ii. on ne vous aime pas du tout iii. on vous aime peu B. «La vie quotidienne» signifie i. la vie en famille ii. la vie scolaire iii. la vie de tous les jours C. «Avoir envie de» signifie i. désirer ii. espérer iii. détester D. Dans le texte, «les mêmes vêtements» signifie : i. les vêtements différents. ii. les vêtements de la même couleur. iii. les vêtements que tout le monde porte.
Answer» 1. Lis le texte ci-dessus et réponds aux questions suivantes : A. Quelles sont les deux fonctions des vêtements ? B. Comment peut-on différencier entre les différents types de vêtements ? C. Qui influence notre choix de vêtements? i. pendant l'enfance? ii. à l'école? 2. Coche la bonne réponse : A. Si vous ne vous habillez pas à la mode i. on vous aime beaucoup ii. on ne vous aime pas du tout iii. on vous aime peu B. «La vie quotidienne» signifie i. la vie en famille ii. la vie scolaire iii. la vie de tous les jours C. «Avoir envie de» signifie i. désirer ii. espérer iii. détester D. Dans le texte, «les mêmes vêtements» signifie : i. les vêtements différents. ii. les vêtements de la même couleur. iii. les vêtements que tout le monde porte.

Discussion

11929.	AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find the angle ∠APB in degrees.__
Answer» AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find the angle $∠$ APB in degrees. __

Discussion

11930.	Which of the following equations is written in standard form?
Answer» Which of the following equations is written in standard form?

Discussion

11931.	Question 14 (ii)One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a face card.
Answer» Question 14 (ii) One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a face card.

Discussion

11932.	The common ratio of the G.P series 9, 27, 81 is _____.
Answer» The common ratio of the G.P series 9, 27, 81 is _____.

Discussion

11933.	Question 4A conical tent is 10 m high and the radius of its base is 24 m. Find(i) Slant height of the tent.(ii) Cost of the canvas required to make the tent, if the cost of 1m2 canvas is Rs 70. [Assume π=227]
Answer» Question 4 A conical tent is 10 m high and the radius of its base is 24 m. Find (i) Slant height of the tent. (ii) Cost of the canvas required to make the tent, if the cost of $1 m^{2}$ canvas is Rs 70. $[A s s u m e π = \frac{22}{7}]$

Discussion

11934.	(i) If the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p.(ii) Find the value of k so that the area of triangle ABC with A(k + 1, 1), B(4, –3) and C(7, –k) is 6 square units.
Answer» (i) If the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p. (ii) Find the value of k so that the area of triangle ABC with A(k + 1, 1), B(4, –3) and C(7, –k) is 6 square units.

Discussion

11935.	Question 3In the following figure, if LM \|\| CB and LN \|\| CD, prove that AMAB=ANAD.
Answer» Question 3 In the following figure, if LM \|\| CB and LN \|\| CD, prove that $\frac{A M}{A B} = \frac{A N}{A D}$ .

Discussion

11936.	A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whole ice cream is to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice cream cone.
Answer» A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whole ice cream is to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice cream cone.

Discussion

11937.	Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3?
Answer» Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3?

Discussion

11938.	If tan θ=2021, show that 1-sin θ+cos θ1+sin θ+cos θ=37.
Answer» If $\tan θ = \frac{20}{21}$ , show that $\frac{1 - \sin θ + \cos θ}{1 + \sin θ + \cos θ} = \frac{3}{7}$ .

Discussion

11939.	The ratio of lateral surface area to the total surface area of a cylinder with base diameter 1.6 m and height 20 cm is(a) 1 : 7(b) 1 : 5(c) 7 : 1(d) 8 : 1
Answer» The ratio of lateral surface area to the total surface area of a cylinder with base diameter 1.6 m and height 20 cm is (a) 1 : 7 (b) 1 : 5 (c) 7 : 1 (d) 8 : 1

Discussion

11940.	62. The numbers a,b,c are the digits of a three digit number which satisfies 49a+7b+c=286. What is the value of 190a+10b+c?
Answer» 62. The numbers a,b,c are the digits of a three digit number which satisfies 49a+7b+c=286. What is the value of 190a+10b+c?

Discussion

11941.	The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is(a) 8 cm(b) 104 cm(c) 12 cm(d) 125 cm
Answer» The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is (a) 8 cm (b) $\sqrt{104}$ cm (c) 12 cm (d) $\sqrt{125}$ cm

Discussion

11942.	Taking the set of natural numbers as a universal set, write down the complement of the following set: xi) \{x:x∈ N and 2x+1>10\
Answer» Taking the set of natural numbers as a universal set, write down the complement of the following set: xi) \{x:x∈ N and 2x+1>10\

Discussion

11943.	What first degree polynomial added to 3x3 − 2x2 gives a polynomial for which both x − 1 and x + 1 are factors?
Answer» What first degree polynomial added to 3x³ − 2x² gives a polynomial for which both x − 1 and x + 1 are factors?

Discussion

11944.	If the areas of two similar triangles are equal, prove that they are congruent.
Answer» If the areas of two similar triangles are equal, prove that they are congruent.

Discussion

11945.	Question 1 (i)Do the following pair of linear equations have no solution? Justify your answer.2x + 4y = 3 and 12y + 6x = 6
Answer» Question 1 (i) Do the following pair of linear equations have no solution? Justify your answer. 2x + 4y = 3 and 12y + 6x = 6

Discussion

11946.	Identify the cubic polynomials among the following. 1. 2x3+3x2+2x+1 2. x3+2x+3 3. √3x+5 4. y+√2
Answer» Identify the cubic polynomials among the following. 1. $2 x^{3} + 3 x^{2} + 2 x + 1$ 2. $x^{3} + 2 x + 3$ 3. $\sqrt{3} x + 5$ 4. $y + \sqrt{2}$

11946.

Identify the cubic polynomials among the following. 1. 2x3+3x2+2x+1 2. x3+2x+3 3. √3x+5 4. y+√2

Answer»

Identify the cubic polynomials among the following.

1. $2 x^{3} + 3 x^{2} + 2 x + 1$

2. $x^{3} + 2 x + 3$

3. $\sqrt{3} x + 5$

4. $y + \sqrt{2}$

Discussion

11947.	Solve each of the following quadratic equations:1x+1+2x+2=5x+4, x≠-1, -2, -4 [CBSE 2013C]
Answer» Solve each of the following quadratic equations: $\frac{1}{x + 1} + \frac{2}{x + 2} = \frac{5}{x + 4}, x \neq - 1, - 2, - 4$ [CBSE 2013C]

Discussion

11948.	If a ladder 20 m long makes an angle of elevation of 30° with the top of the wall, then the height of the wall is ___ m.
Answer» If a ladder 20 m long makes an angle of elevation of 30° with the top of the wall, then the height of the wall is ___ m.

11948.

If a ladder 20 m long makes an angle of elevation of 30° with the top of the wall, then the height of the wall is ___ m.

Answer»

If a ladder 20 m long makes an angle of elevation of 30° with the top of the wall, then the height of the wall is ___ m.

Discussion

11949.	Question 7In which quadrant or on which axis each of the following points lies?(-3, 5), (4, -1), (2, 0), (2, 2), (-3, -6)
Answer» Question 7 In which quadrant or on which axis each of the following points lies? (-3, 5), (4, -1), (2, 0), (2, 2), (-3, -6)

Discussion

11950.	a †an gent is drawn to each of the circle x^2+y^2=4 and x^2+y^2=8. if the two †an gents are mutually perpendicular, the locus of their points of intersection is a circle, then centre of circle s
Answer» a †an gent is drawn to each of the circle x^2+y^2=4 and x^2+y^2=8. if the two †an gents are mutually perpendicular, the locus of their points of intersection is a circle, then centre of circle s

Discussion

Explore topic-wise InterviewSolutions in .

There are four bus routes between A and B; and three bus routes between B and C. A man can travel round trip in number of ways by bus from A to C via B. If he does not want to use a bus route more than once, the number of ways he can make round trip, is(a) 72(b) 144(c) 14(d) 19

LCM of a and 2

Solve the following systems of equations:2x-3y=03x-8y=0

If 15cotA=8, find the values of sinA and secA.

Write down the sequence of differences (subtracting the larger form the smaller) of consecutive perfect squares. Is it and arithmetic sequence?

The point at which the two coordinate axes meet is called the __________.

Find the equations of the sides of the triangle, the coordinates of whose vertices are (1, 4), (2, -3) and (-1, -2).

Which measure of central tendency can be determine graphically?

Question 21 (i)A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that she will buy it?

In the given figure, O is the centre of the circle. Find ∠BAC.

How many balls can be placed in the cylindrical tube if they fit exactly as shown in the figure. The inner curved surface area of the cylinder is 30.8 m2 and the surface area of each ball is 61600 cm2. (Use =227)

In the given figure, AE and BC intersect each other at point D. If ∠CDE=900, AB = 5cm, BD = 4cm and CD = 9 cm, find AE.

6. A number consists of two digits of which the ten's digit exceeds the unit's digit by 6. The number itself is equal to ten times the sum of digits. Find the number.

Why we cannot construct a triangle of given sides as 5 cm , 5 cm and 10 cm?

The largest 4 digit number exactly divisible by 88 is:

During a practice match, a softball pitcher throws a ball whose height at any instant from ground level is given by the equation h = −16t2 + 24t + 1 , where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet from the ground level?

Find the ratio in which C (, 1) divides the join of A (–4, 4) and B (6, –1) and hence find the value of .

When the rate of sales tax is decreased from 9% to 7% for a radio, Rahul has to pay Rs 632 less for it. What is the listed price of the radio? [4 MARKS]

Finding torsional angle in cyclic compound

If π∑i=1i = n(n+1)2, then π∑i=1(3i−2) =

All edges of a square pyramid are of equal lengths. If the length of the base edge is 20 cm, what is the slant height?

Find the values of p and q for which the following system of linear equations has infinite number of solutions: 2x + 3y = 9 (p + q) x + (2p - q) y = 3 (p +q + 1)

Question 4Is it true to say that area of segment of a circle is less than the areas of its corresponding sector? Why?

The product of the zeros of x3 + 4x2 + x − 6 is(a) −4(b) 4(c) 6(d) −6

A hemispherical bowl fits exactly on the open surface of a cone with height 5 cm and radius 3.5 cm.What is the volume of the solid formed?

If 1 is a zero of the polynomial P(x), then:

AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find the angle ∠APB in degrees.__

Which of the following equations is written in standard form?

Question 14 (ii)One card is drawn from a well–shuffled deck of 52 cards. Find the probability of getting a face card.

The common ratio of the G.P series 9, 27, 81 is _____.

Question 4A conical tent is 10 m high and the radius of its base is 24 m. Find(i) Slant height of the tent.(ii) Cost of the canvas required to make the tent, if the cost of 1m2 canvas is Rs 70. [Assume π=227]

(i) If the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p.(ii) Find the value of k so that the area of triangle ABC with A(k + 1, 1), B(4, –3) and C(7, –k) is 6 square units.

Question 3In the following figure, if LM || CB and LN || CD, prove that AMAB=ANAD.

A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whole ice cream is to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice cream cone.

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3?

If tan θ=2021, show that 1-sin θ+cos θ1+sin θ+cos θ=37.

The ratio of lateral surface area to the total surface area of a cylinder with base diameter 1.6 m and height 20 cm is(a) 1 : 7(b) 1 : 5(c) 7 : 1(d) 8 : 1

62. The numbers a,b,c are the digits of a three digit number which satisfies 49a+7b+c=286. What is the value of 190a+10b+c?

The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is(a) 8 cm(b) 104 cm(c) 12 cm(d) 125 cm

Taking the set of natural numbers as a universal set, write down the complement of the following set: xi) \{x:x∈ N and 2x+1>10\

What first degree polynomial added to 3x3 − 2x2 gives a polynomial for which both x − 1 and x + 1 are factors?

If the areas of two similar triangles are equal, prove that they are congruent.

Question 1 (i)Do the following pair of linear equations have no solution? Justify your answer.2x + 4y = 3 and 12y + 6x = 6

Identify the cubic polynomials among the following. 1. 2x3+3x2+2x+1 2. x3+2x+3 3. √3x+5 4. y+√2

Solve each of the following quadratic equations:1x+1+2x+2=5x+4, x≠-1, -2, -4 [CBSE 2013C]

If a ladder 20 m long makes an angle of elevation of 30° with the top of the wall, then the height of the wall is ___ m.

Question 7In which quadrant or on which axis each of the following points lies?(-3, 5), (4, -1), (2, 0), (2, 2), (-3, -6)

a †an gent is drawn to each of the circle x^2+y^2=4 and x^2+y^2=8. if the two †an gents are mutually perpendicular, the locus of their points of intersection is a circle, then centre of circle s