32581 + Interview Questions in Mathematics Page 93 InterviewSolution

4601.	Construct two tangents to a circle of radius 4.5 cm from a point 2.5 cm away from the circle.
Answer» Construct two tangents to a circle of radius 4.5 cm from a point 2.5 cm away from the circle.

Discussion

4602.	Which angle is known as theta, what is tan theta and how to find it
Answer» Which angle is known as theta, what is tan theta and how to find it

Discussion

4603.	The tops of two towers of height x and y, standing on level ground, subtend angles of 30º and 60º respectively at the centre of the line joining their feet, then find x : y. [CBSE 2015]
Answer» The tops of two towers of height x and y, standing on level ground, subtend angles of 30º and 60º respectively at the centre of the line joining their feet, then find x : y. [CBSE 2015]

Discussion

4604.	Question 3A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.
Answer» Question 3 A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.

Discussion

4605.	The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.
Answer» The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.

Discussion

4606.	If a vertex of a triangle is (1, 1) and the mid-points of the two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is _____.
Answer» If a vertex of a triangle is (1, 1) and the mid-points of the two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is _____.

Discussion

4607.	The product of two consecutive integers is 182. Find the integers.
Answer» The product of two consecutive integers is 182. Find the integers.

Discussion

4608.	The area of an equilateral triangle is 493 cm2 . Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles. [Take π = 1.73] [CBSE 2009]
Answer» The area of an equilateral triangle is $49 \sqrt{3}$ cm² . Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles. [Take π = 1.73] [CBSE 2009]

Discussion

4609.	Find the argument in second quadrant?
Answer» Find the argument in second quadrant?

Discussion

4610.	Question 2 (ii)Find the capacity in litres of a conical vessel with:(ii) height 12 cm, slant height 12 cm.[Assume π=227]
Answer» Question 2 (ii) Find the capacity in litres of a conical vessel with: (ii) height 12 cm, slant height 12 cm. $[A s s u m e π = \frac{22}{7}]$

Discussion

4611.	Draw a circle of radius 4 cm. Construct the two tangents to the circle from a P which is at the distance of 7 cm from centre. Measure the length of the tangents
Answer» Draw a circle of radius 4 cm. Construct the two tangents to the circle from a P which is at the distance of 7 cm from centre. Measure the length of the tangents

4611.

Draw a circle of radius 4 cm. Construct the two tangents to the circle from a P which is at the distance of 7 cm from centre. Measure the length of the tangents

Answer»

Draw a circle of radius 4 cm. Construct the two tangents to the circle from a P which is at the distance of 7 cm from centre. Measure the length of the tangents

Discussion

4612.	If x : y = 1 : 1, then 3x+4y5x+6y=(a) 711(b) 1711(c) 1723(d) 45
Answer» If x : y = 1 : 1, then $\frac{3 x + 4 y}{5 x + 6 y} =$ (a) $\frac{7}{11}$ (b) $\frac{17}{11}$ (c) $\frac{17}{23}$ (d) $\frac{4}{5}$

Discussion

4613.	If ∠A and ∠B are acute angles such that tanA = tanB, the prove that ∠A=∠B.
Answer» If $∠ A$ and $∠ B$ are acute angles such that tanA = tanB, the prove that $∠ A = ∠ B$ .

Discussion

4614.	Let A=[2432],B=[13−25],C=[−2534], then find(i) A+B(ii) A−B(iii) 3A−C(iv) AB(v) BA
Answer» Let $A = [\begin{matrix} 2 & 4 3 & 2 \end{matrix}], B = [\begin{matrix} 1 & 3 - 2 & 5 \end{matrix}], C = [\begin{matrix} - 2 & 5 3 & 4 \end{matrix}],$ then find $(i)$ $A + B$ $(i i)$ $A - B$ $(i i i)$ $3 A - C$ $(i v)$ $A B$ $(v)$ $B A$

Discussion

4615.	If cosecθ−cotθ=12,0<θ<π2, then cosθ is equal to
Answer» If $c o s e c θ - c o t θ = \frac{1}{2}, 0 < θ < \frac{π}{2}$ , then $c o s θ$ is equal to

Discussion

4616.	Radius of a sector of a circle is 7 cm. If measure of arc of the sector is -(1) 30° (2) 210° (3 ) three right angles;find the area of the sector in each case.
Answer» Radius of a sector of a circle is 7 cm. If measure of arc of the sector is - (1) 30^° (2) 210^° (3 ) three right angles; find the area of the sector in each case.

Discussion

4617.	A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Answer» A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Discussion

4618.	Equation of the circle passing through (2,3) and centre at the origin is _______ .
Answer» Equation of the circle passing through $(2, 3)$ and centre at the origin is _______ .

Discussion

4619.	From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the lighthouse be h metres and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is h(tan α+tan β)tan α tan β metres.
Answer» From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be $α$ and $β$ . If the height of the lighthouse be h metres and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is $\frac{h (t a n α + t a n β)}{t a n α t a n β}$ metres.

Discussion

4620.

Calculate the Mean Deviation using mean and Standard Deviation for the following distribution.ClassesFrequencies20 – 40340 – 80680 – 10020100 – 12012120 – 1409Total50

Answer»

Calculate the Mean Deviation using mean and Standard Deviation for the following distribution.

Classes	Frequencies
20 – 40	3
40 – 80	6
80 – 100	20
100 – 120	12
120 – 140	9
Total	50

Discussion

4621.	ABC is an isosceles triangle with AC = BC. If AB2 = 2 AC2, prove that ABC is a right triangle.
Answer» ABC is an isosceles triangle with AC = BC. If AB² = 2 AC², prove that ABC is a right triangle.

Discussion

4622.	In the figure a chord AB on the circle. If the angle made by AB on the Circumference of the circle is ∠ACB=55∘. What is the angle ∠AOB(in degrees)?
Answer» In the figure a chord AB on the circle. If the angle made by AB on the Circumference of the circle is $∠ A C B = 55^{\circ}$ . What is the angle $∠ A O B$ (in degrees)?

4622.

In the figure a chord AB on the circle. If the angle made by AB on the Circumference of the circle is ∠ACB=55∘. What is the angle ∠AOB(in degrees)?

Answer»

In the figure a chord AB on the circle. If the angle made by AB on the Circumference of the circle is $∠ A C B = 55^{\circ}$ . What is the angle $∠ A O B$ (in degrees)?

Discussion

4623.	Divide first polynomial by second polynomial and write the answer in the form ‘Dividend = Divisor × Quotient + Remainder’.(i) x3 - 64 ; x - 4 (ii) 5x5 + 4x4 - 3x3 + 2x2 + 2 ; x2 - x
Answer» Divide first polynomial by second polynomial and write the answer in the form ‘Dividend = Divisor $\times$ Quotient + Remainder’. (i) $x^{3} - 64; x - 4$ (ii) $5 x^{5} + 4 x^{4} - 3 x^{3} + 2 x^{2} + 2; x^{2} - x$

Discussion

4624.	A cone and cylinder are carved of two solid cubes of side a. Find the ratio of the volumes of the cone and cylinder.
Answer» A cone and cylinder are carved of two solid cubes of side $a$ . Find the ratio of the volumes of the cone and cylinder.

Discussion

4625.	I have doubt how to find angles in alternate segments
Answer» I have doubt how to find angles in alternate segments

Discussion

4626.	In the given figure, APB and AQO are semicircles and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. [CBSE 2015]
Answer» In the given figure, APB and AQO are semicircles and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. [CBSE 2015]

Discussion

4627.	Mr. Tiwari receives ₹6455 at the end of one year at the rate of 14% per annum in a recurring deposit account. What is his monthly installment (in ₹)?500
Answer» Mr. Tiwari receives ₹6455 at the end of one year at the rate of 14% per annum in a recurring deposit account. What is his monthly installment (in ₹)? 500

Discussion

4628.	Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
Answer» Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?

Discussion

4629.	For what value of k the following system of equations will be inconsistent?4x+6y=112x+ky=7
Answer» For what value of k the following system of equations will be inconsistent? $4 x + 6 y = 11 2 x + k y = 7$

Discussion

4630.	Question - 2 (i) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (i) a = 10, d = 10
Answer» Question - 2 (i) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (i) a = 10, d = 10

Discussion

4631.	Which point on y-axis is equidistant from (2, 3) and (-4, 1) ?
Answer» Which point on y-axis is equidistant from (2, 3) and (-4, 1) ?

Discussion

4632.	If the first term of an A.P. is –5 and the common difference is 2, then the sum of first 6 terms is(a) 0(b) 5(c) 6(d) 15
Answer» If the first term of an A.P. is –5 and the common difference is 2, then the sum of first 6 terms is (a) 0 (b) 5 (c) 6 (d) 15

Discussion

4633.	Question 9If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.
Answer» Question 9 If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Discussion

4634.	Question 1 (ii)Find the square roots of each of the following numbers by Division method:4489
Answer» Question 1 (ii) Find the square roots of each of the following numbers by Division method: 4489

4634.

Question 1 (ii)Find the square roots of each of the following numbers by Division method:4489

Answer»

Question 1 (ii)

Find the square roots of each of the following numbers by Division method:

4489

Discussion

4635.	If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p+q terms will be
Answer» If the sum of p terms of an A.P. is $q$ and the sum of $q$ terms is $p,$ then the sum of $p + q$ terms will be

Discussion

4636.	Let A=⎛⎜⎝100210321⎞⎟⎠ , If μ1 and μ2 are column matrices such that Aμ1=⎛⎜⎝100⎞⎟⎠ and Aμ2=⎛⎜⎝010⎞⎟⎠, then μ1+μ2 is equal to:
Answer» Let $A = ⎛ ⎜ ⎝ \begin{matrix} 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 \end{matrix} ⎞ ⎟ ⎠$ , If $μ_{1}$ and $μ_{2}$ are column matrices such that $A μ_{1} = ⎛ ⎜ ⎝ \begin{matrix} 100 \end{matrix} ⎞ ⎟ ⎠$ and $A μ_{2} = ⎛ ⎜ ⎝ \begin{matrix} 010 \end{matrix} ⎞ ⎟ ⎠$ , then $μ_{1} + μ_{2}$ is equal to:

Discussion

4637.	A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train. [CBSE 2013]
Answer» A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train. [CBSE 2013]

Discussion

4638.	Question 8Write ‘True’ or ‘False’ and justify your answer in the followingAn open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder
Answer» Question 8 Write ‘True’ or ‘False’ and justify your answer in the following An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder

Discussion

4639.	A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:(i) Minor segment(ii) Major sector[Use π = 3.14]
Answer» A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) Minor segment (ii) Major sector [Use π = 3.14]

4639.

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:(i) Minor segment(ii) Major sector[Use π = 3.14]

Answer»

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:

(i) Minor segment

(ii) Major sector

[Use π = 3.14]

Discussion

4640.	A, B and C are partners in a firm sharing profits in the ratio of 3 : 2 : 1. They earned a profit of ₹ 30,000 during the year ended 31st March, 2019. Distribute profit among A, B and C if:(a) C's share of profit is guaranteed to be ₹ 6,000 Minimum.(b) Minimum profit payable to C amounting to ₹ 6,000 is guaranteed by A.(c) Guaranteed minimum profit of ₹ 6,000 payable to C is guaranteed by B.(d) Any deficiency after making payment of guaranteed ₹ 6,000 will be borne by A and B in the ratio of 3 : 1.
Answer» A, B and C are partners in a firm sharing profits in the ratio of 3 : 2 : 1. They earned a profit of ₹ 30,000 during the year ended 31st March, 2019. Distribute profit among A, B and C if: (a) C's share of profit is guaranteed to be ₹ 6,000 Minimum. (b) Minimum profit payable to C amounting to ₹ 6,000 is guaranteed by A. (c) Guaranteed minimum profit of ₹ 6,000 payable to C is guaranteed by B. (d) Any deficiency after making payment of guaranteed ₹ 6,000 will be borne by A and B in the ratio of 3 : 1.

Discussion

4641.	The probability of an event occurring is 0.7. The probability of that event not occuring is __.
Answer» The probability of an event occurring is 0.7. The probability of that event not occuring is __.

Discussion

4642.	6. A sphere,cone and cylinder has same height and radius. Then find the ratios of its curve surface area.
Answer» 6. A sphere,cone and cylinder has same height and radius. Then find the ratios of its curve surface area.

Discussion

4643.	38. The mean and median of 100 observations are 50 & 52 respectively. The value of the largest observation is 100. It was later found that the observation is 110 not 100. Find the true mean and median.
Answer» 38. The mean and median of 100 observations are 50 & 52 respectively. The value of the largest observation is 100. It was later found that the observation is 110 not 100. Find the true mean and median.

Discussion

4644.	If x + √y = 2 + √7 where, x is a rational number and y is an irrational number. Then the value of y = ___
Answer» If $x + \sqrt{y} = 2 + \sqrt{7}$ where, x is a rational number and y is an irrational number. Then the value of y = ___

Discussion

4645.	You are given a figure (x) by four figures 1, 2, 3 and 4 such that (x) is embedded in one of them. Trace the correct alternative.
Answer» You are given a figure (x) by four figures 1, 2, 3 and 4 such that (x) is embedded in one of them. Trace the correct alternative.

Discussion

4646.	If the sum of the squares of first n natural numbers exceeds their sum by 330, then n = _______________.
Answer» If the sum of the squares of first n natural numbers exceeds their sum by 330, then n = _______________.

Discussion

4647.	The difference between the third and first term of a sequence defined by a tn= n^3/4n+1
Answer» The difference between the third and first term of a sequence defined by a tn= n^3/4n+1

Discussion

4648.	Very-Short-Answer QuestionsIf one root of the quadratic equation 3x2-10x+k=0 is reciprocal of the other, find the value of k. [CBSE 2014]
Answer» Very-Short-Answer Questions If one root of the quadratic equation $3 x^{2} - 10 x + k = 0$ is reciprocal of the other, find the value of k. [CBSE 2014]

Discussion

4649.	Prove that the points (2, 3), (-4, -6) and (1,32) do not form a triangle.
Answer» Prove that the points (2, 3), (-4, -6) and $(1, \frac{3}{2})$ do not form a triangle.

Discussion

4650.	Question 4In a cylinder, the radius is doubled and height is halved, then the curved surface area will be:A) HalvedB) DoubledC) SameD) Four times
Answer» Question 4 In a cylinder, the radius is doubled and height is halved, then the curved surface area will be: A) Halved B) Doubled C) Same D) Four times

Discussion

Explore topic-wise InterviewSolutions in .

Construct two tangents to a circle of radius 4.5 cm from a point 2.5 cm away from the circle.

Which angle is known as theta, what is tan theta and how to find it

The tops of two towers of height x and y, standing on level ground, subtend angles of 30º and 60º respectively at the centre of the line joining their feet, then find x : y. [CBSE 2015]

Question 3A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.

If a vertex of a triangle is (1, 1) and the mid-points of the two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is _____.

The product of two consecutive integers is 182. Find the integers.

The area of an equilateral triangle is 493 cm2 . Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles. [Take π = 1.73] [CBSE 2009]

Find the argument in second quadrant?

Question 2 (ii)Find the capacity in litres of a conical vessel with:(ii) height 12 cm, slant height 12 cm.[Assume π=227]

Draw a circle of radius 4 cm. Construct the two tangents to the circle from a P which is at the distance of 7 cm from centre. Measure the length of the tangents

If x : y = 1 : 1, then 3x+4y5x+6y=(a) 711(b) 1711(c) 1723(d) 45

If ∠A and ∠B are acute angles such that tanA = tanB, the prove that ∠A=∠B.

Let A=[2432],B=[13−25],C=[−2534], then find(i) A+B(ii) A−B(iii) 3A−C(iv) AB(v) BA

If cosecθ−cotθ=12,0&lt;θ&lt;π2, then cosθ is equal to

Radius of a sector of a circle is 7 cm. If measure of arc of the sector is -(1) 30° (2) 210° (3 ) three right angles;find the area of the sector in each case.

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Equation of the circle passing through (2,3) and centre at the origin is _______ .

Calculate the Mean Deviation using mean and Standard Deviation for the following distribution.ClassesFrequencies20 – 40340 – 80680 – 10020100 – 12012120 – 1409Total50

ABC is an isosceles triangle with AC = BC. If AB2 = 2 AC2, prove that ABC is a right triangle.

In the figure a chord AB on the circle. If the angle made by AB on the Circumference of the circle is ∠ACB=55∘. What is the angle ∠AOB(in degrees)?

Divide first polynomial by second polynomial and write the answer in the form ‘Dividend = Divisor × Quotient + Remainder’.(i) x3 - 64 ; x - 4 (ii) 5x5 + 4x4 - 3x3 + 2x2 + 2 ; x2 - x

A cone and cylinder are carved of two solid cubes of side a. Find the ratio of the volumes of the cone and cylinder.

I have doubt how to find angles in alternate segments

In the given figure, APB and AQO are semicircles and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. [CBSE 2015]

Mr. Tiwari receives ₹6455 at the end of one year at the rate of 14% per annum in a recurring deposit account. What is his monthly installment (in ₹)?500

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?

For what value of k the following system of equations will be inconsistent?4x+6y=112x+ky=7

Question - 2 (i) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (i) a = 10, d = 10

Which point on y-axis is equidistant from (2, 3) and (-4, 1) ?

If the first term of an A.P. is –5 and the common difference is 2, then the sum of first 6 terms is(a) 0(b) 5(c) 6(d) 15

Question 9If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Question 1 (ii)Find the square roots of each of the following numbers by Division method:4489

If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p+q terms will be

Let A=⎛⎜⎝100210321⎞⎟⎠ , If μ1 and μ2 are column matrices such that Aμ1=⎛⎜⎝100⎞⎟⎠ and Aμ2=⎛⎜⎝010⎞⎟⎠, then μ1+μ2 is equal to:

A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train. [CBSE 2013]

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:(i) Minor segment(ii) Major sector[Use π = 3.14]

The probability of an event occurring is 0.7. The probability of that event not occuring is __.

6. A sphere,cone and cylinder has same height and radius. Then find the ratios of its curve surface area.

38. The mean and median of 100 observations are 50 & 52 respectively. The value of the largest observation is 100. It was later found that the observation is 110 not 100. Find the true mean and median.

If x + √y = 2 + √7 where, x is a rational number and y is an irrational number. Then the value of y = ___

You are given a figure (x) by four figures 1, 2, 3 and 4 such that (x) is embedded in one of them. Trace the correct alternative.

If the sum of the squares of first n natural numbers exceeds their sum by 330, then n = _______________.

The difference between the third and first term of a sequence defined by a tn= n^3/4n+1

Very-Short-Answer QuestionsIf one root of the quadratic equation 3x2-10x+k=0 is reciprocal of the other, find the value of k. [CBSE 2014]

Prove that the points (2, 3), (-4, -6) and (1,32) do not form a triangle.

Question 4In a cylinder, the radius is doubled and height is halved, then the curved surface area will be:A) HalvedB) DoubledC) SameD) Four times

If cosecθ−cotθ=12,0<θ<π2, then cosθ is equal to