32581 + Interview Questions in Mathematics Page 266 InterviewSolution

13251.	212. What is the minimum value of F needed so thatblock begins to move upward on frictionless inclineplane as shown(1) Mg tan(2) Mg cotMg sin0(1+ sin0)(4) Mg sin
Answer» 212. What is the minimum value of F needed so thatblock begins to move upward on frictionless inclineplane as shown(1) Mg tan(2) Mg cotMg sin0(1+ sin0)(4) Mg sin

Discussion

13252.	Find the value of cos(/15).cos(2/15).cos(3/15)cos(4/15)cos(5/15)cs(6/15)cos(7/15)
Answer» Find the value of cos(/15).cos(2/15).cos(3/15)cos(4/15)cos(5/15)cs(6/15)cos(7/15)

Discussion

13253.	Find the mean using step-deviation. Class IntervalFrequency35−4520045−5525055−655065−757075−8540
Answer» Find the mean using step-deviation. $\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y 35 - 45 & 200 45 - 55 & 250 55 - 65 & 50 65 - 75 & 70 75 - 85 & 40 \end{matrix}$

Discussion

13254.	Question 3Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.
Answer» Question 3 Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

Discussion

13255.	The value of x such that 32x-2×3x+2+81=0 is
Answer» The value of $x$ such that $3^{2 x} - 2 \times 3^{x + 2} + 81 = 0$ is

Discussion

13256.	24. Sum of two number is 8 also the sum of their reciprocal is 8 by 15 find the numbers
Answer» 24. Sum of two number is 8 also the sum of their reciprocal is 8 by 15 find the numbers

Discussion

13257.	If θ1, θ2, θ3........,θn are in A.P., whose common difference is d, then, sec θ1 sec θ2+sec θ2 sec θ3+..........+sec θn−1 sec θn=
Answer» If θ1, θ2, θ3........,θn are in A.P., whose common difference is d, then, sec θ1 sec θ2+sec θ2 sec θ3+..........+sec θn−1 sec θn=

Discussion

13258.	sin (55° - A) - cos (35° + A) = ___.
Answer» sin (55° - A) - cos (35° + A) = ___.

Discussion

13259.	F:R to R . F(x)=x^3+x-1. Find the solution of f(x)^-1
Answer» F:R to R . F(x)=x^3+x-1. Find the solution of f(x)^-1

Discussion

13260.

Write the median class of the following distribution: [CBSE 2009] Class 0−10 10−20 20−30 30−40 40−50 50−60 60−70 Frequency 4 4 8 10 12 8 4

Answer» Write the median class of the following distribution: [CBSE 2009]

Class	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	4	4	8	10	12	8	4

Discussion

13261.	When five pens were bought together, the total price was reduced by three rupees and only seventeen rupees had to be paid. Had they been bought one by one, how much would have been the price of each pen?
Answer» When five pens were bought together, the total price was reduced by three rupees and only seventeen rupees had to be paid. Had they been bought one by one, how much would have been the price of each pen?

Discussion

13262.	The equation of a straight line passing through the origin and perpendicular to the straight line 2x + 3y - 7 = 0 is
Answer» The equation of a straight line passing through the origin and perpendicular to the straight line 2x + 3y - 7 = 0 is

Discussion

13263.	Sangam Ltd. invited applications for 10,000 Equity Shares of ₹ 100 each issued at par. The amount was payable on application. The issue was oversubscribed by 2,000 shares and allotment was made on pro rata basis. Pass necessary Journal entries.
Answer» Sangam Ltd. invited applications for 10,000 Equity Shares of ₹ 100 each issued at par. The amount was payable on application. The issue was oversubscribed by 2,000 shares and allotment was made on pro rata basis. Pass necessary Journal entries.

Discussion

13264.	Solve the following systems of equations: 44x+y+30x−y=10 55x+y+40x−y=13
Answer» Solve the following systems of equations: $\frac{44}{x + y} + \frac{30}{x - y} = 10$ $\frac{55}{x + y} + \frac{40}{x - y} = 13$

13264.

Solve the following systems of equations: 44x+y+30x−y=10 55x+y+40x−y=13

Answer»

Solve the following systems of equations:

$\frac{44}{x + y} + \frac{30}{x - y} = 10$

$\frac{55}{x + y} + \frac{40}{x - y} = 13$

Discussion

13265.	Factorize z2+3√3z−12
Answer» Factorize $z^{2} + 3 \sqrt{3} z - 12$

Discussion

13266.	Which of the following pairs of equations is inconsistent?
Answer» Which of the following pairs of equations is inconsistent?

Discussion

13267.	The HCF of 95 and 152, is(a) 57(b) 1(c) 19(d) 38
Answer» The HCF of 95 and 152, is (a) 57 (b) 1 (c) 19 (d) 38

Discussion

13268.	If A=[0110], then which of the following is/are equal to A2020
Answer» If $A = [\begin{matrix} 0 & 1 1 & 0 \end{matrix}]$ , then which of the following is/are equal to $A^{2020}$

Discussion

13269.	If an AP the first term is 22 and nth term is -11 . If the sum to first n terms is 66 , then the value of n is
Answer» If an AP the first term is 22 and nth term is -11 . If the sum to first n terms is 66 , then the value of n is

Discussion

13270.	Find HCF of 81 and 237 and express it as a linear combination of 81 and 237 i.e., HCF (81,237)= 81x + 237y for some x and y. Please explain.
Answer» Find HCF of 81 and 237 and express it as a linear combination of 81 and 237 i.e., HCF (81,237)= 81x + 237y for some x and y. Please explain.

Discussion

13271.	Solve for x and y: xa+yb=a+b , xa2+yb2=2.
Answer» Solve for x and y: $\frac{x}{a} + \frac{y}{b} = a + b$ , $\frac{x}{a^{2}} + \frac{y}{b^{2}} = 2$ .

13271.

Solve for x and y: xa+yb=a+b , xa2+yb2=2.

Answer»

Solve for x and y:

$\frac{x}{a} + \frac{y}{b} = a + b$ ,

$\frac{x}{a^{2}} + \frac{y}{b^{2}} = 2$ .

Discussion

13272.	A spherical balloon of radius 4 cm subtends an angle 60º at the eye of an observer. If the angle of elevation of its centre is 45º, then the height of the centre of the balloon is
Answer» A spherical balloon of radius 4 cm subtends an angle 60º at the eye of an observer. If the angle of elevation of its centre is 45º, then the height of the centre of the balloon is

Discussion

13273.	If the numerator of a fraction is multipled by 2 and the denominator is reduced by 5 the fraction becomes 6/5/ And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. Find the fraction.
Answer» If the numerator of a fraction is multipled by 2 and the denominator is reduced by 5 the fraction becomes 6/5/ And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. Find the fraction.

Discussion

13274.	Simplify:35+38÷64
Answer» Simplify: $\frac{3}{5} + \frac{3}{8} \div \frac{6}{4}$

Discussion

13275.	A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?
Answer» A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?

Discussion

13276.	In this multiplication question, the five letters represent five different digits. What are the actual figures? There is no zero.
Answer» In this multiplication question, the five letters represent five different digits. What are the actual figures? There is no zero.

13276.

In this multiplication question, the five letters represent five different digits. What are the actual figures? There is no zero.

Answer»

In this multiplication question, the five letters represent five different digits. What are the actual figures?

There is no zero.

Discussion

13277.	If the sum of n terms of AP is 2n2+5 then prove that an is equal to 4n+3 ?
Answer» If the sum of n terms of AP is 2n²+5 then prove that a_n is equal to 4n+3 ?

Discussion

13278.	A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs 7 per 100 cm2.
Answer» A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs 7 per 100 cm².

Discussion

13279.	9. In Δ ABC , E is mid point of median AD such that BE is produced meets AC at F. If AC =10.5 cm, then AF=
Answer» 9. In Δ ABC , E is mid point of median AD such that BE is produced meets AC at F. If AC =10.5 cm, then AF=

Discussion

13280.	A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is black or king.
Answer» A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is black or king.

Discussion

13281.	Water flows through a horizontal pipe of varying area of cross section at the rate 15 cubic meter per minute. Find the radius of the pipe where water flows with a velocity 3 meter per second
Answer» Water flows through a horizontal pipe of varying area of cross section at the rate 15 cubic meter per minute. Find the radius of the pipe where water flows with a velocity 3 meter per second

Discussion

13282.	The sum of the squares of two consecutive positive odd numbers is 514. Find the numbers.
Answer» The sum of the squares of two consecutive positive odd numbers is 514. Find the numbers.

Discussion

13283.	If the figure formed by joining the points A(0, 0) , B(0,a),C(2 , 0) and D(2, a) is square, then a can be
Answer» If the figure formed by joining the points A(0, 0) , B(0,a),C(2 , 0) and D(2, a) is square, then a can be

Discussion

13284.	Find the point on X–axis which is equidistant from P(2,–5) and Q(–2,9).
Answer» Find the point on X–axis which is equidistant from P(2,–5) and Q(–2,9).

Discussion

13285.	If the cost of a bike is 'x' and it is twice the cost of the scooter which is y; express it in the form of ax+by−c=0
Answer» If the cost of a bike is 'x' and it is twice the cost of the scooter which is y; express it in the form of $a x + b y - c = 0$

Discussion

13286.	2.The sum of first p,q,r terms of an AP are a,b,c respectively. Then show that a(q-r)/p +b(r-p)/q + c(p-q)/r =0
Answer» 2.The sum of first p,q,r terms of an AP are a,b,c respectively. Then show that a(q-r)/p +b(r-p)/q + c(p-q)/r =0

Discussion

13287.	Prove that is irrational.
Answer» Prove that is irrational.

Discussion

13288.	ABC and ABD are two triangle on the same base AB .if line segment CD is bisected by AB at O show that ar(ABC)=ar(ABD)
Answer» ABC and ABD are two triangle on the same base AB .if line segment CD is bisected by AB at O show that ar(ABC)=ar(ABD)

Discussion

13289.	Question 2Write down the decimal expansions of(i) 133125(ii) 178(iii) 151600(iv) 232352(v) 615(vi) 3550
Answer» Question 2 Write down the decimal expansions of (i) $\frac{13}{3125}$ (ii) $\frac{17}{8}$ (iii) $\frac{15}{1600}$ (iv) $\frac{23}{2^{3} 5^{2}}$ (v) $\frac{6}{15}$ (vi) $\frac{35}{50}$

Discussion

13290.	Using factor theorem, factorize the polynomial x3−6x2+11x−6.
Answer» Using factor theorem, factorize the polynomial $x^{3} - 6 x^{2} + 11 x - 6$ .

Discussion

13291.	You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of 60∘ with each other. Refer to the figure and select the option which would lead us to the required construction. 'd' is the distance OE.
Answer» You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of $60^{\circ}$ with each other. Refer to the figure and select the option which would lead us to the required construction. 'd' is the distance OE.

Discussion

13292.	A shopkeeper buys some books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought. OR The sum of two numbers is 9 and the sum of their reciprocals is 12 . Find the numbers
Answer» A shopkeeper buys some books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought. OR The sum of two numbers is 9 and the sum of their reciprocals is $\frac{1}{2}$ . Find the numbers

Discussion

13293.	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° than when it was 45°. Prove that the height of tower is x ( $\sqrt{3} + 1$ ) metres.

Discussion

13294.	A train travels 360km at a uniform speed. If the speed had been 5km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Answer» A train travels 360km at a uniform speed. If the speed had been 5km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Discussion

13295.	The Following data shows the goals scored by 19 clubs in a Premiere League Season :Goals ScoredNo. of Clubs0−10210−20320−30230−40440−50350−605Find the Median number of Goals scored in the season.
Answer» The Following data shows the goals scored by 19 clubs in a Premiere League Season : $\begin{matrix} Goals Scored & No. of Clubs 0 - 10 & 2 10 - 20 & 3 20 - 30 & 2 30 - 40 & 4 40 - 50 & 3 50 - 60 & 5 \end{matrix}$ Find the Median number of Goals scored in the season.

13295.

The Following data shows the goals scored by 19 clubs in a Premiere League Season :Goals ScoredNo. of Clubs0−10210−20320−30230−40440−50350−605Find the Median number of Goals scored in the season.

Answer»

The Following data shows the goals scored by 19 clubs in a Premiere League Season :

$\begin{matrix} Goals Scored & No. of Clubs 0 - 10 & 2 10 - 20 & 3 20 - 30 & 2 30 - 40 & 4 40 - 50 & 3 50 - 60 & 5 \end{matrix}$

Find the Median number of Goals scored in the season.

Discussion

13296.	The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.ScoresNo. of shooters0−101010−201220−301530−40840−502050−602460−70770−801180−903090−10018Using the table find the Modal Class.
Answer» The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition. $\begin{matrix} Scores & No. of shooters 0 - 10 & 10 10 - 20 & 12 20 - 30 & 15 30 - 40 & 8 40 - 50 & 20 50 - 60 & 24 60 - 70 & 7 70 - 80 & 11 80 - 90 & 30 90 - 100 & 18 \end{matrix}$ Using the table find the Modal Class.

13296.

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.ScoresNo. of shooters0−101010−201220−301530−40840−502050−602460−70770−801180−903090−10018Using the table find the Modal Class.

Answer»

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{matrix} Scores & No. of shooters 0 - 10 & 10 10 - 20 & 12 20 - 30 & 15 30 - 40 & 8 40 - 50 & 20 50 - 60 & 24 60 - 70 & 7 70 - 80 & 11 80 - 90 & 30 90 - 100 & 18 \end{matrix}$

Using the table find the Modal Class.

Discussion

13297.	Find the mean of the first five whole numbers.
Answer» Find the mean of the first five whole numbers.

Discussion

13298.	Construct a frequency distribution table for the following distributions: Marks (less than) \| 0 \| 10 \| 20 \| 30 \| 40 \| 50 Cumulative frequency \| 0 \| 7 \| 28 \| 54 \| 71 \| 84
Answer» Construct a frequency distribution table for the following distributions: Marks (less than) \| 0 \| 10 \| 20 \| 30 \| 40 \| 50 Cumulative frequency \| 0 \| 7 \| 28 \| 54 \| 71 \| 84

13298.

Construct a frequency distribution table for the following distributions: Marks (less than) | 0 | 10 | 20 | 30 | 40 | 50 Cumulative frequency | 0 | 7 | 28 | 54 | 71 | 84

Answer»

Construct a frequency distribution table for the following distributions:

Marks (less than) | 0 | 10 | 20 | 30 | 40 | 50

Cumulative frequency | 0 | 7 | 28 | 54 | 71 | 84

Discussion

13299.	Question 177 A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.
Answer» Question 177 A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.

Discussion

13300.	If the polynomial (x4+2x3+8x2+12x+18) is divided by another polynomial (x2+5), the remainder comes out to be (px+q), find the values of p and q.
Answer» If the polynomial $(x^{4} + 2 x^{3} + 8 x^{2} + 12 x + 18)$ is divided by another polynomial $(x^{2} + 5)$ , the remainder comes out to be $(p x + q)$ , find the values of p and q.

Discussion

Explore topic-wise InterviewSolutions in .

212. What is the minimum value of F needed so thatblock begins to move upward on frictionless inclineplane as shown(1) Mg tan(2) Mg cotMg sin0(1+ sin0)(4) Mg sin

Find the value of cos(/15).cos(2/15).cos(3/15)cos(4/15)cos(5/15)cs(6/15)cos(7/15)

Find the mean using step-deviation. Class IntervalFrequency35−4520045−5525055−655065−757075−8540

Question 3Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

The value of x such that 32x-2×3x+2+81=0 is

24. Sum of two number is 8 also the sum of their reciprocal is 8 by 15 find the numbers

If θ1, θ2, θ3........,θn are in A.P., whose common difference is d, then, sec θ1 sec θ2+sec θ2 sec θ3+..........+sec θn−1 sec θn=

sin (55° - A) - cos (35° + A) = ___.

F:R to R . F(x)=x^3+x-1. Find the solution of f(x)^-1

Write the median class of the following distribution: [CBSE 2009] Class 0−10 10−20 20−30 30−40 40−50 50−60 60−70 Frequency 4 4 8 10 12 8 4

When five pens were bought together, the total price was reduced by three rupees and only seventeen rupees had to be paid. Had they been bought one by one, how much would have been the price of each pen?

The equation of a straight line passing through the origin and perpendicular to the straight line 2x + 3y - 7 = 0 is

Sangam Ltd. invited applications for 10,000 Equity Shares of ₹ 100 each issued at par. The amount was payable on application. The issue was oversubscribed by 2,000 shares and allotment was made on pro rata basis. Pass necessary Journal entries.

Solve the following systems of equations: 44x+y+30x−y=10 55x+y+40x−y=13

Factorize z2+3√3z−12

Which of the following pairs of equations is inconsistent?

The HCF of 95 and 152, is(a) 57(b) 1(c) 19(d) 38

If A=[0110], then which of the following is/are equal to A2020

If an AP the first term is 22 and nth term is -11 . If the sum to first n terms is 66 , then the value of n is

Find HCF of 81 and 237 and express it as a linear combination of 81 and 237 i.e., HCF (81,237)= 81x + 237y for some x and y. Please explain.

Solve for x and y: xa+yb=a+b , xa2+yb2=2.

A spherical balloon of radius 4 cm subtends an angle 60º at the eye of an observer. If the angle of elevation of its centre is 45º, then the height of the centre of the balloon is

If the numerator of a fraction is multipled by 2 and the denominator is reduced by 5 the fraction becomes 6/5/ And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. Find the fraction.

Simplify:35+38÷64

A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?

In this multiplication question, the five letters represent five different digits. What are the actual figures? There is no zero.

If the sum of n terms of AP is 2n2+5 then prove that an is equal to 4n+3 ?

A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs 7 per 100 cm2.

9. In Δ ABC , E is mid point of median AD such that BE is produced meets AC at F. If AC =10.5 cm, then AF=

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

Water flows through a horizontal pipe of varying area of cross section at the rate 15 cubic meter per minute. Find the radius of the pipe where water flows with a velocity 3 meter per second

The sum of the squares of two consecutive positive odd numbers is 514. Find the numbers.

If the figure formed by joining the points A(0, 0) , B(0,a),C(2 , 0) and D(2, a) is square, then a can be

Find the point on X–axis which is equidistant from P(2,–5) and Q(–2,9).

If the cost of a bike is 'x' and it is twice the cost of the scooter which is y; express it in the form of ax+by−c=0

2.The sum of first p,q,r terms of an AP are a,b,c respectively. Then show that a(q-r)/p +b(r-p)/q + c(p-q)/r =0

Prove that is irrational.

ABC and ABD are two triangle on the same base AB .if line segment CD is bisected by AB at O show that ar(ABC)=ar(ABD)

Question 2Write down the decimal expansions of(i) 133125(ii) 178(iii) 151600(iv) 232352(v) 615(vi) 3550

Using factor theorem, factorize the polynomial x3−6x2+11x−6.

You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of 60∘ with each other. Refer to the figure and select the option which would lead us to the required construction. 'd' is the distance OE.

A shopkeeper buys some books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought. OR The sum of two numbers is 9 and the sum of their reciprocals is 12 . Find the numbers

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.

A train travels 360km at a uniform speed. If the speed had been 5km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

The Following data shows the goals scored by 19 clubs in a Premiere League Season :Goals ScoredNo. of Clubs0−10210−20320−30230−40440−50350−605Find the Median number of Goals scored in the season.

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.ScoresNo. of shooters0−101010−201220−301530−40840−502050−602460−70770−801180−903090−10018Using the table find the Modal Class.

Find the mean of the first five whole numbers.

Construct a frequency distribution table for the following distributions: Marks (less than) | 0 | 10 | 20 | 30 | 40 | 50 Cumulative frequency | 0 | 7 | 28 | 54 | 71 | 84

Question 177 A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.

If the polynomial (x4+2x3+8x2+12x+18) is divided by another polynomial (x2+5), the remainder comes out to be (px+q), find the values of p and q.