32581 + Interview Questions in Mathematics Page 68 InterviewSolution

3351.	The ratio of the base-radii of two cones is 3 : 5 and their heights are in the ratio 2 : 3. What is the ratio of their volumes?
Answer» The ratio of the base-radii of two cones is 3 : 5 and their heights are in the ratio 2 : 3. What is the ratio of their volumes?

Discussion

3352.	Question 20(i) Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is 7?
Answer» Question 20(i) Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is 7?

Discussion

3353.	If the centroid of the triangle formed by the points (3, −5), (−7, 4), (10, −k) is at the point (k −1), then k =(a) 3(b) 1(c) 2(d) 4
Answer» If the centroid of the triangle formed by the points (3, −5), (−7, 4), (10, −k) is at the point (k −1), then k = (a) 3 (b) 1 (c) 2 (d) 4

Discussion

3354.	In a ∆ABC, D and E are points on AB and AC respectively such that DE \|\| BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm, find BD and CE.
Answer» In a ∆ABC, D and E are points on AB and AC respectively such that DE \|\| BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm, find BD and CE.

Discussion

3355.	Find the values of x, y if the distances of the point (x, y) from (-3, 0) as well as from (3, 0) are 4.
Answer» Find the values of x, y if the distances of the point (x, y) from (-3, 0) as well as from (3, 0) are 4.

Discussion

3356.	Which of the following are not quadratic polynomials?(i) 3+4x–7x2(ii) 8x2–15(iii) 6x – 15(iv) 4x3–3x (v) x2–x+1
Answer» Which of the following are not quadratic polynomials? (i) $3 + 4 x - 7 x^{2}$ (ii) $8 x^{2} - 15$ (iii) 6x – 15 (iv) $4 x^{3} - 3 x$ (v) $x^{2} - x + 1$

3356.

Which of the following are not quadratic polynomials?(i) 3+4x–7x2(ii) 8x2–15(iii) 6x – 15(iv) 4x3–3x (v) x2–x+1

Answer»

Which of the following are not quadratic polynomials?

(i) $3 + 4 x - 7 x^{2}$

(ii) $8 x^{2} - 15$

(iii) 6x – 15

(iv) $4 x^{3} - 3 x$

(v) $x^{2} - x + 1$

Discussion

3357.	sec 30ocosec 60o=? (a) 2√3 (b) √32 (c) √3 (d) 1
Answer» $\frac{s e c 30^{o}}{c o s e c 60^{o}}$ =? (a) $\frac{2}{\sqrt{3}}$ (b) $\frac{\sqrt{3}}{2}$ (c) $\sqrt{3}$ (d) 1

3357.

sec 30ocosec 60o=? (a) 2√3 (b) √32 (c) √3 (d) 1

Answer»

$\frac{s e c 30^{o}}{c o s e c 60^{o}}$ =?

(a) $\frac{2}{\sqrt{3}}$ (b) $\frac{\sqrt{3}}{2}$ (c) $\sqrt{3}$ (d) 1

Discussion

3358.	The length of the shadow of a tower standing on level plane is found to be 2x metres longer when the sun' s altitude is 30∘ than when it was 45∘. Prove that the height of tower is x(√3+1) metres.
Answer» The length of the shadow of a tower standing on level plane is found to be 2x metres longer when the sun' s altitude is $30^{\circ}$ than when it was $45^{\circ}$ . Prove that the height of tower is $x (\sqrt{3} + 1)$ metres.

Discussion

3359.	from the top of a building 15m high, the angle of elevation of the top of the tower is to be 30 degree. From the bottom of the buildung the angle of elevation of the tower is found to be 45 degree. The height of the tower is
Answer» from the top of a building 15m high, the angle of elevation of the top of the tower is to be 30 degree. From the bottom of the buildung the angle of elevation of the tower is found to be 45 degree. The height of the tower is

Discussion

3360.	A small indoor greenhouse is made entirely of glass panes held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. How much of tape is needed for all the 12 edges?
Answer» A small indoor greenhouse is made entirely of glass panes held together with tape. It is $30 c m$ long, $25 c m$ wide and $25 c m$ high. How much of tape is needed for all the 12 edges?

Discussion

3361.	F, G, H, I, J are the reflected points of A(3, 1), B(0, 5), C(4, 8), D(8, 5) and E(5, 1) respectively about Y = 0. The perimeter of the figure formed by ABCDEJIHGF is ___.
Answer» F, G, H, I, J are the reflected points of A(3, 1), B(0, 5), C(4, 8), D(8, 5) and E(5, 1) respectively about Y = 0. The perimeter of the figure formed by ABCDEJIHGF is ___.

Discussion

3362.	Solve the following quadratic equations by factorization:x+1x-1-x-1x+1=56, x≠1, -1
Answer» Solve the following quadratic equations by factorization: $\frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} = \frac{5}{6}, x \neq 1, - 1$

Discussion

3363.	If a+b=25 and a2+b2=225, then find ab.
Answer» If $a + b = 25$ and $a^{2} + b^{2} = 225$ , then find ab.

Discussion

3364.	Find the hcf of 445&84 using Euclid's division lemma
Answer» Find the hcf of 445&84 using Euclid's division lemma

Discussion

3365.	if two sources have a randomly varying phase difference \varnothing(t),the resul†an t intensity will be given by
Answer» if two sources have a randomly varying phase difference \varnothing(t),the resul†an t intensity will be given by

Discussion

3366.	The radius of a circle is 17.0 cm and the length of perpendicular drawn from its centre to a chord is 8.0 cm. Calculate the length of the chord.
Answer» The radius of a circle is 17.0 cm and the length of perpendicular drawn from its centre to a chord is 8.0 cm. Calculate the length of the chord.

Discussion

3367.	Question 18If a card is selected from a deck of 52 cards, then the probability of its being a red face card is(a) 326(b) 313(c) 213(d) 12
Answer» Question 18 If a card is selected from a deck of 52 cards, then the probability of its being a red face card is (a) $\frac{3}{26}$ (b) $\frac{3}{13}$ (c) $\frac{2}{13}$ (d) $\frac{1}{2}$

Discussion

3368.	Solve the equ. (x - 1)² - 5(x - 1) - 6 = 0
Answer» Solve the equ. (x - 1)² - 5(x - 1) - 6 = 0

Discussion

3369.	One person reaches the bus stop in between 10:05 to 10:15 and bus reaches bus stop in between10:00 to 10:10 then what will be probability of person to catch the bus?
Answer» One person reaches the bus stop in between 10:05 to 10:15 and bus reaches bus stop in between10:00 to 10:10 then what will be probability of person to catch the bus?

Discussion

3370.	A well of diameter 4 m is dug 14 m deep the earth taken out is spread evenly all around the well to form embankment .find the width of enbakment.
Answer» A well of diameter 4 m is dug 14 m deep the earth taken out is spread evenly all around the well to form embankment .find the width of enbakment.

Discussion

3371.	In △ABC, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Which of the following is true?
Answer» In $△ A B C$ , B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Which of the following is true?

3371.

In △ABC, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Which of the following is true?

Answer»

In $△ A B C$ , B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Which of the following is true?

Discussion

3372.	Question 1 (iv)Which of the following form an AP? Justify your answer.11, 22, 33, ….
Answer» Question 1 (iv) Which of the following form an AP? Justify your answer. 11, 22, 33, ….

Discussion

3373.	What are the consecutive numbers
Answer» What are the consecutive numbers

Discussion

3374.	The sum of a number and its reciprocal is 2120. The number is(a) 54 or 45(b) 43 or 34(c) 56 or 65(d) 16 or 6
Answer» The sum of a number and its reciprocal is $2 \frac{1}{20} .$ The number is (a) $\frac{5}{4} or \frac{4}{5}$ (b) $\frac{4}{3} or \frac{3}{4}$ (c) $\frac{5}{6} or \frac{6}{5}$ (d) $\frac{1}{6} or 6$

Discussion

3375.	The point P(x, y) divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1. The value of x + y is0
Answer» The point P(x, y) divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1. The value of x + y is 0

Discussion

3376.	tangents are drawn to the circle x2+y2=16 at the points where it is met by the circle x2+y2-5x+3y-2=0 the point of intersection of these tangents
Answer» tangents are drawn to the circle x2+y2=16 at the points where it is met by the circle x2+y2-5x+3y-2=0 the point of intersection of these tangents

Discussion

3377.	What would be the perimeter of a triangle with sides (a - d), a and (a + d)?
Answer» What would be the perimeter of a triangle with sides (a - d), a and (a + d)?

Discussion

3378.	(a) Atul had 64 cards; he gave 55 cards to Hamda. What fraction of the cards is left with Atul? If Hamda loses 6 cards what fraction of cards in left with her?(b) Saleema purchased 214 kg apples and 134 kg oranges. What is the total weight of fruits purchased by her?
Answer» (a) Atul had 64 cards; he gave 55 cards to Hamda. What fraction of the cards is left with Atul? If Hamda loses 6 cards what fraction of cards in left with her? (b) Saleema purchased $2 \frac{1}{4}$ kg apples and $1 \frac{3}{4}$ kg oranges. What is the total weight of fruits purchased by her?

Discussion

3379.	Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
Answer» Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

Discussion

3380.	34. The height of the cone of maximum volume inscribed in a sphere of radius R is a)R/3. b)2R/3 c)4R/3 d)4R/3
Answer» 34. The height of the cone of maximum volume inscribed in a sphere of radius R is a)R/3. b)2R/3 c)4R/3 d)4R/3

Discussion

3381.	Five years ago Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu? [3 MARKS]
Answer» Five years ago Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu? [3 MARKS]

Discussion

3382.	Which of the following are correct:
Answer» Which of the following are correct:

Discussion

3383.

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised in the table given below. Find the mode of the data: Number of cars: 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80 Frequency: 7 14 13 12 20 11 15 8

Answer» A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised in the table given below. Find the mode of the data:

Number of cars:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	7	14	13	12	20	11	15	8

Discussion

3384.	Show graphically that the following given systems of equations is inconsistent i.e. has no solution:x-2y=63x-6y=0
Answer» Show graphically that the following given systems of equations is inconsistent i.e. has no solution: $x - 2 y = 6 3 x - 6 y = 0$

Discussion

3385.	A boy of height 60 cm is walking away from the base of a building at a speed of 2.2 m/s. If the height of the building is 7.2 m, then find the length of his shadow after 5 seconds.
Answer» A boy of height 60 cm is walking away from the base of a building at a speed of 2.2 m/s. If the height of the building is 7.2 m, then find the length of his shadow after 5 seconds.

Discussion

3386.	Find the number of positive integers less than101 that can not be written as the difference oftwo squares of integers.
Answer» Find the number of positive integers less than 101 that can not be written as the difference of two squares of integers.

Discussion

3387.	If in the given figure radius of smaller and larger circles be 4 and 5 cm. Find the length of chord AB.
Answer» If in the given figure radius of smaller and larger circles be 4 and 5 cm. Find the length of chord AB.

3387.

If in the given figure radius of smaller and larger circles be 4 and 5 cm. Find the length of chord AB.

Answer»

If in the given figure radius of smaller and larger circles be 4 and 5 cm. Find the length of chord AB.

Discussion

3388.	If a and b are distinct real numbers, show that the quadratic equation 2(a2+b2)x2+2(a+b)x+1=0 has no real roots.
Answer» If a and b are distinct real numbers, show that the quadratic equation $2 (a^{2} + b^{2}) x^{2} + 2 (a + b) x + 1 = 0$ has no real roots.

Discussion

3389.	In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then ∠AOB= ___
Answer» In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then $∠ A O B =$ ___

3389.

In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then ∠AOB= ___

Answer»

In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then $∠ A O B =$ ___

Discussion

3390.	If A=[−8524] satisfies the equation x2+4x−p=0,then p =
Answer» If $A = [\begin{matrix} - 8 & 5 2 & 4 \end{matrix}]$ satisfies the equation $x^{2} + 4 x - p = 0, t h e n p =$

Discussion

3391.	If a=pl.qm.rn and b=px.qy.rz where p,q,r are primes and p<q<r and l,m,n,x,y,z are all natural numbers. Given HCF = p2.q3.r and LCM = p3.q4.r3, which one of the following is NOT true?
Answer» If $a = p^{l} . q^{m} . r^{n}$ and $b = p^{x} . q^{y} . r^{z}$ where p,q,r are primes and p<q<r and l,m,n,x,y,z are all natural numbers. Given HCF = $p^{2}$ . $q^{3} . r$ and LCM = $p^{3}$ . $q^{4}$ . $r^{3}$ , which one of the following is NOT true?

Discussion

3392.	25. What is polynomial
Answer» 25. What is polynomial

Discussion

3393.	Solve by elimination method 2x-3y=8 and 4x+6y=7
Answer» Solve by elimination method 2x-3y=8 and 4x+6y=7

Discussion

3394.	Prove that one out of every three consecutive integers is a multiple of three. (3 Marks)
Answer» Prove that one out of every three consecutive integers is a multiple of three. (3 Marks)

3394.

Prove that one out of every three consecutive integers is a multiple of three. (3 Marks)

Answer»

Prove that one out of every three consecutive integers is a multiple of three.

(3 Marks)

Discussion

3395.	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

3396.	A circular swimming pool consists of a straight rope connecting 2 points on the boundary of the pool. What will the region between the rope and the boundary be called?
Answer» A circular swimming pool consists of a straight rope connecting 2 points on the boundary of the pool. What will the region between the rope and the boundary be called?

3396.

A circular swimming pool consists of a straight rope connecting 2 points on the boundary of the pool. What will the region between the rope and the boundary be called?

Answer»

A circular swimming pool consists of a straight rope connecting 2 points on the boundary of the pool. What will the region between the rope and the boundary be called?

Discussion

3397.	Given that 2 is a zero of the cubic polynomial 6x3 + 2x2 - 10x - 42 , find its other two zeroes .
Answer» Given that $\sqrt{2}$ is a zero of the cubic polynomial $6 x^{3} + \sqrt{2} x^{2} - 10 x - 4 \sqrt{2}$ , find its other two zeroes .

Discussion

3398.	In the given figure, RQ is a tangent to the circle with centre O. If SQ = 6 cm and QR = 4 cm, then OR is equal to [CBSE 2014](a) 2.5 cm(b) 3 cm(c) 5 cm(d) 8 cm
Answer» In the given figure, RQ is a tangent to the circle with centre O. If SQ = 6 cm and QR = 4 cm, then OR is equal to [CBSE 2014] (a) 2.5 cm (b) 3 cm (c) 5 cm (d) 8 cm

Discussion

3399.	Write the sum of the series 2+4+6+8+...+2n.
Answer» Write the sum of the series 2+4+6+8+...+2n.

Discussion

3400.	Which of the following operations would make the expression x2+8x√3 a perfect square?
Answer» Which of the following operations would make the expression $x^{2} + \frac{8 x}{\sqrt{3}}$ a perfect square?

Discussion

Explore topic-wise InterviewSolutions in .

The ratio of the base-radii of two cones is 3 : 5 and their heights are in the ratio 2 : 3. What is the ratio of their volumes?

Question 20(i) Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is 7?

If the centroid of the triangle formed by the points (3, −5), (−7, 4), (10, −k) is at the point (k −1), then k =(a) 3(b) 1(c) 2(d) 4

In a ∆ABC, D and E are points on AB and AC respectively such that DE || BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm, find BD and CE.

Find the values of x, y if the distances of the point (x, y) from (-3, 0) as well as from (3, 0) are 4.

Which of the following are not quadratic polynomials?(i) 3+4x–7x2(ii) 8x2–15(iii) 6x – 15(iv) 4x3–3x (v) x2–x+1

sec 30ocosec 60o=? (a) 2√3 (b) √32 (c) √3 (d) 1

The length of the shadow of a tower standing on level plane is found to be 2x metres longer when the sun' s altitude is 30∘ than when it was 45∘. Prove that the height of tower is x(√3+1) metres.

from the top of a building 15m high, the angle of elevation of the top of the tower is to be 30 degree. From the bottom of the buildung the angle of elevation of the tower is found to be 45 degree. The height of the tower is

A small indoor greenhouse is made entirely of glass panes held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. How much of tape is needed for all the 12 edges?

F, G, H, I, J are the reflected points of A(3, 1), B(0, 5), C(4, 8), D(8, 5) and E(5, 1) respectively about Y = 0. The perimeter of the figure formed by ABCDEJIHGF is ___.

Solve the following quadratic equations by factorization:x+1x-1-x-1x+1=56, x≠1, -1

If a+b=25 and a2+b2=225, then find ab.

Find the hcf of 445&84 using Euclid's division lemma

if two sources have a randomly varying phase difference \varnothing(t),the resul†an t intensity will be given by

The radius of a circle is 17.0 cm and the length of perpendicular drawn from its centre to a chord is 8.0 cm. Calculate the length of the chord.

Question 18If a card is selected from a deck of 52 cards, then the probability of its being a red face card is(a) 326(b) 313(c) 213(d) 12

Solve the equ. (x - 1)² - 5(x - 1) - 6 = 0

One person reaches the bus stop in between 10:05 to 10:15 and bus reaches bus stop in between10:00 to 10:10 then what will be probability of person to catch the bus?

A well of diameter 4 m is dug 14 m deep the earth taken out is spread evenly all around the well to form embankment .find the width of enbakment.

In △ABC, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Which of the following is true?

Question 1 (iv)Which of the following form an AP? Justify your answer.11, 22, 33, ….

What are the consecutive numbers

The sum of a number and its reciprocal is 2120. The number is(a) 54 or 45(b) 43 or 34(c) 56 or 65(d) 16 or 6

The point P(x, y) divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1. The value of x + y is0

tangents are drawn to the circle x2+y2=16 at the points where it is met by the circle x2+y2-5x+3y-2=0 the point of intersection of these tangents

What would be the perimeter of a triangle with sides (a - d), a and (a + d)?

(a) Atul had 64 cards; he gave 55 cards to Hamda. What fraction of the cards is left with Atul? If Hamda loses 6 cards what fraction of cards in left with her?(b) Saleema purchased 214 kg apples and 134 kg oranges. What is the total weight of fruits purchased by her?

Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

34. The height of the cone of maximum volume inscribed in a sphere of radius R is a)R/3. b)2R/3 c)4R/3 d)4R/3

Five years ago Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu? [3 MARKS]

Which of the following are correct:

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised in the table given below. Find the mode of the data: Number of cars: 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80 Frequency: 7 14 13 12 20 11 15 8

Show graphically that the following given systems of equations is inconsistent i.e. has no solution:x-2y=63x-6y=0

A boy of height 60 cm is walking away from the base of a building at a speed of 2.2 m/s. If the height of the building is 7.2 m, then find the length of his shadow after 5 seconds.

Find the number of positive integers less than101 that can not be written as the difference oftwo squares of integers.

If in the given figure radius of smaller and larger circles be 4 and 5 cm. Find the length of chord AB.

If a and b are distinct real numbers, show that the quadratic equation 2(a2+b2)x2+2(a+b)x+1=0 has no real roots.

In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then ∠AOB= ___

If A=[−8524] satisfies the equation x2+4x−p=0,then p =

If a=pl.qm.rn and b=px.qy.rz where p,q,r are primes and p&lt;q&lt;r and l,m,n,x,y,z are all natural numbers. Given HCF = p2.q3.r and LCM = p3.q4.r3, which one of the following is NOT true?

25. What is polynomial

Solve by elimination method 2x-3y=8 and 4x+6y=7

Prove that one out of every three consecutive integers is a multiple of three. (3 Marks)

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

A circular swimming pool consists of a straight rope connecting 2 points on the boundary of the pool. What will the region between the rope and the boundary be called?

Given that 2 is a zero of the cubic polynomial 6x3 + 2x2 - 10x - 42 , find its other two zeroes .

In the given figure, RQ is a tangent to the circle with centre O. If SQ = 6 cm and QR = 4 cm, then OR is equal to [CBSE 2014](a) 2.5 cm(b) 3 cm(c) 5 cm(d) 8 cm

Write the sum of the series 2+4+6+8+...+2n.

Which of the following operations would make the expression x2+8x√3 a perfect square?

If a=pl.qm.rn and b=px.qy.rz where p,q,r are primes and p<q<r and l,m,n,x,y,z are all natural numbers. Given HCF = p2.q3.r and LCM = p3.q4.r3, which one of the following is NOT true?