32581 + Interview Questions in Mathematics Page 95 InterviewSolution

4701.	A lead pencil consists of a cylinder of wood with solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.
Answer» A lead pencil consists of a cylinder of wood with solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

Discussion

4702.	Tan a +sec a -1/tan a -sec a +1=1+sin a /cos a
Answer» Tan a +sec a -1/tan a -sec a +1=1+sin a /cos a

Discussion

4703.	Find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.
Answer» Find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.

Discussion

4704.	A reservoir in the form of the frustum of a right circular cone contains 44 × 107 litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir. (Take : π = 22/7)
Answer» A reservoir in the form of the frustum of a right circular cone contains $44 \times 10^{7}$ litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir. (Take : $π$ = 22/7)

Discussion

4705.	Mode of the data15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is
Answer» Mode of the data 15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is

Discussion

4706.	Draw a circle of radius 4.2 cm. Draw a pair of tangents to this circle inclined to each other at an angle of 45∘.
Answer» Draw a circle of radius 4.2 cm. Draw a pair of tangents to this circle inclined to each other at an angle of $45^{\circ}$ .

Discussion

4707.	A point P divides the line segment joining the points A(3, −5) and B(−4, 8) such that APPB=k1. If P lies on the line x + y = 0, then find the value of k. [CBSE 2012]
Answer» A point P divides the line segment joining the points A(3, −5) and B(−4, 8) such that $\frac{AP}{PB} = \frac{k}{1} .$ If P lies on the line x + y = 0, then find the value of k. [CBSE 2012]

Discussion

4708.	7. How to find zeros of a cubic polynomial
Answer» 7. How to find zeros of a cubic polynomial

Discussion

4709.	Solve the following systems of equations graphically:x + y = 32x + 5y = 12
Answer» Solve the following systems of equations graphically: x + y = 3 2x + 5y = 12

Discussion

4710.	If two chords AB and CD intersect externally at P and if AB = 4 cm , PB = 5 cm, PD = 3 cm, then find the value of CD.
Answer» If two chords AB and CD intersect externally at P and if AB = 4 cm , PB = 5 cm, PD = 3 cm, then find the value of CD.

Discussion

4711.	Find the co-ordinates of the point M if M is the midpoint of a line segment PQ with P(7, -3) and Q(-6, 2).
Answer» Find the co-ordinates of the point M if M is the midpoint of a line segment PQ with P(7, -3) and Q(-6, 2).

Discussion

4712.	A square lawn has a path of 4m around it . The area of the path is 196m2. Find the side length of the lawn.
Answer» $A s q u a r e l a w n h a s a p a t h o f 4 m a r o u n d i t . T h e a r e a o f t h e p a t h i s 196 m^{2} . F i n d t h e s i d e l e n g t h o f t h e l a w n .$

Discussion

4713.	If A=[0−110], then which one of the following statements is correct
Answer» If $A = [\begin{matrix} 0 & - 1 1 & 0 \end{matrix}],$ then which one of the following statements is correct

Discussion

4714.	Question 7Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Answer» Question 7 Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Discussion

4715.

The following table shows classification of number of workers and the number of hours they work in a software company. Find the median of the number of hours they work. Daily No. of hours 8 - 10 10 - 12 12 - 14 14 - 16 Number of workers 150 500 300 50

Answer»

The following table shows classification of number of workers and the number of hours they work in a software company. Find the median of the number of hours they work.

Daily No. of hours	8 - 10	10 - 12	12 - 14	14 - 16
Number of workers	150	500	300	50

Discussion

4716.	What comes next in the Arithmetic progression: 1400, 1500, 1600, 1700, ...?
Answer» What comes next in the Arithmetic progression: 1400, 1500, 1600, 1700, ...?

Discussion

4717.	A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 kmph. What is the initial speed of the train (in kmph)?25
Answer» A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 kmph. What is the initial speed of the train (in kmph)? 25

Discussion

4718.	Two unbiased dice are thrown. If E be the event that the number appearing on both the dice are prime and F be the event that the sum of the number appearing on both the dice is perfect square, then the probability of occurring of events E and event F is
Answer» Two unbiased dice are thrown. If E be the event that the number appearing on both the dice are prime and F be the event that the sum of the number appearing on both the dice is perfect square, then the probability of occurring of events E and event F is

Discussion

4719.	Question 8 If A and B are (–2, –2) and (2, –4) respectively, find the coordinates of P such that AP=37AB and P lies on the line segment AB.
Answer» Question 8 If A and B are (–2, –2) and (2, –4) respectively, find the coordinates of P such that $A P = \frac{3}{7} A B$ and P lies on the line segment AB.

Discussion

4720.

From the following information, calculate Proprietary Ratio: Share Capital ₹3,00,000 Reserves and Surplus ₹1,80,000 Non-current Assets ₹13,20,000 Current Assets ₹ 6,00,000

Answer» From the following information, calculate Proprietary Ratio:

Share Capital	₹3,00,000	Reserves and Surplus	₹1,80,000
Non-current Assets	₹13,20,000	Current Assets	₹ 6,00,000

Discussion

4721.	The vertical lines in the figure below are drawn 1 centimetres apart.Prove that their heights are in arithmetic sequence.What is the common difference?
Answer» The vertical lines in the figure below are drawn 1 centimetres apart. Prove that their heights are in arithmetic sequence. What is the common difference?

4721.

The vertical lines in the figure below are drawn 1 centimetres apart.Prove that their heights are in arithmetic sequence.What is the common difference?

Answer»

The vertical lines in the figure below are drawn 1 centimetres apart.

Prove that their heights are in arithmetic sequence.

What is the common difference?

Discussion

4722.	The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median of the data. Monthly consumption (in units)Numbers of customers65−85485−1055105−12513125−14520145−16514165−1858185−2054
Answer» The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median of the data. $\begin{matrix} Monthly consumption (in units) & Numbers of customers 65 - 85 & 4 85 - 105 & 5 105 - 125 & 13 125 - 145 & 20 145 - 165 & 14 165 - 185 & 8 185 - 205 & 4 \end{matrix}$

4722.

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median of the data. Monthly consumption (in units)Numbers of customers65−85485−1055105−12513125−14520145−16514165−1858185−2054

Answer»

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality.
Find the median of the data.

$\begin{matrix} Monthly consumption (in units) & Numbers of customers 65 - 85 & 4 85 - 105 & 5 105 - 125 & 13 125 - 145 & 20 145 - 165 & 14 165 - 185 & 8 185 - 205 & 4 \end{matrix}$

Discussion

4723.	If (-1,-1),(5,-2),(6,1) and (2,3) taken in order are the coordinates of the vertices of a quadrilateral , then the area enclosed is A.45sq. UnitsB.30Sq unitsC. 22.5 sq units D. 20.5 sq units
Answer» If (-1,-1),(5,-2),(6,1) and (2,3) taken in order are the coordinates of the vertices of a quadrilateral , then the area enclosed is A.45sq. Units B.30Sq units C. 22.5 sq units D. 20.5 sq units

Discussion

4724.	The complete set of quantities offered for sale at various prices are called
Answer» The complete set of quantities offered for sale at various prices are called

Discussion

4725.	Two small circles of equal radii are cut from a semicircle as shown in the fig. If MN=28 cm and MN\|\|PQ, find the area of the remaining portion of the semicircle.
Answer» Two small circles of equal radii are cut from a semicircle as shown in the fig. If $M N = 28 c m$ and $M N \| \| P Q$ , find the area of the remaining portion of the semicircle.

Discussion

4726.	ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that CQ=14AC. If PQ produced meets BC at R, prove that R is the midpoint BC.
Answer» ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that $C Q = \frac{1}{4} A C .$ If PQ produced meets BC at R, prove that R is the midpoint BC.

Discussion

4727.	Sketch proper figure and write the answers of the following questions. (i) If A - B - C and l(AC) = 11, l(BC) = 6.5, then l(AB) =?(ii) If R - S - T and l(ST) = 3.7, l(RS) = 2.5, then l(RT) =?(iii) If X - Y - Z and l(XZ) = 3 7, l(XY) =7 , then l(YZ) =?
Answer» Sketch proper figure and write the answers of the following questions. (i) If A - B - C and l(AC) = 11, l(BC) = 6.5, then l(AB) =? (ii) If R - S - T and l(ST) = 3.7, l(RS) = 2.5, then l(RT) =? (iii) If X - Y - Z and l(XZ) = 3 $\sqrt{7}$ , l(XY) = $\sqrt{7}$ , then l(YZ) =?

Discussion

4728.	graphs of quad equations given,we need to find the sign of the quadratic equation ,also how to find sign of quadratic equation when sign of 'a 'is given
Answer» graphs of quad equations given,we need to find the sign of the quadratic equation ,also how to find sign of quadratic equation when sign of 'a 'is given

Discussion

4729.	Question 28Sales tax = Tax % of ___
Answer» Question 28 Sales tax = Tax % of ___

4729.

Question 28Sales tax = Tax % of ___

Answer»

Question 28

Sales tax = Tax % of ___

Discussion

4730.	51. Solve for x 1/a+b+x=1/a+1/b+1/x
Answer» 51. Solve for x 1/a+b+x=1/a+1/b+1/x

Discussion

4731.	Question 2While computing mean of grouped data, we assume that the frequencies are(a) evenly distributed over all the classes(b) centred at the class marks of the classes(c) centred at the upper limits of the classes(d) centred at the lower limits of the classes
Answer» Question 2 While computing mean of grouped data, we assume that the frequencies are (a) evenly distributed over all the classes (b) centred at the class marks of the classes (c) centred at the upper limits of the classes (d) centred at the lower limits of the classes

Discussion

4732.	12. 2 cards are selected randomly from a pack of 52 cards, find the probability that first one is a club and second is not a queen,
Answer» 12. 2 cards are selected randomly from a pack of 52 cards, find the probability that first one is a club and second is not a queen,

Discussion

4733.	If sin [cot-1(x+1)] = cos (tan-1x), then find x
Answer» If sin [cot-1(x+1)] = cos (tan-1x), then find x

Discussion

4734.	Complete the given factor tree of 100.
Answer» Complete the given factor tree of 100.

Discussion

4735.	Sowmya takes 6 days less that the number of days takes by Bhagya to complete a piece of work. If both Sowmaya and Bhagya together can complete the same work in 4 days, in how many days will Bhagya alone complete the work?
Answer» Sowmya takes 6 days less that the number of days takes by Bhagya to complete a piece of work. If both Sowmaya and Bhagya together can complete the same work in 4 days, in how many days will Bhagya alone complete the work?

Discussion

4736.	If cos 9θ = sin θ and 9θ < 900 , then the value of tan 6 θ is
Answer» If cos $9 θ$ = sin $θ$ and $9 θ$ < 90⁰ , then the value of tan $6 θ$ is

Discussion

4737.	Find the roots of the following equations:
Answer» Find the roots of the following equations:

4737.

Find the roots of the following equations:

Answer»

Find the roots of the following equations:

Discussion

4738.	The line segment XY is parallel to side AC of △ABC and it divides the triangle into two parts of equal areas. Find the ratio BXAB.
Answer» The line segment XY is parallel to side AC of $△$ ABC and it divides the triangle into two parts of equal areas. Find the ratio $\frac{B X}{A B}$ .

4738.

The line segment XY is parallel to side AC of △ABC and it divides the triangle into two parts of equal areas. Find the ratio BXAB.

Answer»

The line segment XY is parallel to side AC of $△$ ABC and it divides the triangle into two parts of equal areas. Find the ratio $\frac{B X}{A B}$ .

Discussion

4739.	A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
Answer» A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

Discussion

4740.	If am ≠ bl, then the system of equationsax+by=clx+my=n(a) has a unique solution(b) has no solution(c) has infinitely many solutions(d) may or may not have a solution
Answer» If am ≠ bl, then the system of equations $a x + b y = c l x + m y = n$ (a) has a unique solution (b) has no solution (c) has infinitely many solutions (d) may or may not have a solution

Discussion

4741.	Aparna, Manisha and Sonia are partners sharing profits in the ratio of 3 : 2 : 1. Manisha retired and goodwill of the firm is valued at ₹ 1,80,000. Aparna and Sonia decided to share future profits in the ratio of 3 : 2. Pass necessary Journal entries.
Answer» Aparna, Manisha and Sonia are partners sharing profits in the ratio of 3 : 2 : 1. Manisha retired and goodwill of the firm is valued at ₹ 1,80,000. Aparna and Sonia decided to share future profits in the ratio of 3 : 2. Pass necessary Journal entries.

Discussion

4742.	O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ∆OCD is an isosceles triangle.
Answer» O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ∆OCD is an isosceles triangle.

Discussion

4743.	If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, then find the common difference.2
Answer» If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, then find the common difference. 2

Discussion

4744.	(i) Points P and Q trisect the line segment joining the points A(–2, 0) and B(0, 8) such that P is near to A. Find the coordinates of P and Q.(ii) The line segment joining the points (3, −4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, −2) and (5/3, q) respectively. Find the values of p and q.
Answer» (i) Points P and Q trisect the line segment joining the points A(–2, 0) and B(0, 8) such that P is near to A. Find the coordinates of P and Q. (ii) The line segment joining the points (3, −4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, −2) and (5/3, q) respectively. Find the values of p and q.

Discussion

4745.	The vector component of ^i+^j+^k perpendicular to the direction of 2^i−^j+2^k is
Answer» The vector component of $^i +^j +^k$ perpendicular to the direction of $2^i -^j + 2^k$ is

Discussion

4746.	If the 10th term of an A.P. is 21 and the sum of its first 10 terms is 120, find its nth term.
Answer» If the 10^th term of an A.P. is 21 and the sum of its first 10 terms is 120, find its n^thterm.

Discussion

4747.	The angle of elevation of the top of a building from the foot of thetower is 30^° and the angle of elevation of the top of the tower from the foot of the building is 60^° . If the tower is 30m high, then the height of the building is
Answer» The angle of elevation of the top of a building from the foot of thetower is 30^° and the angle of elevation of the top of the tower from the foot of the building is 60^° . If the tower is 30m high, then the height of the building is

Discussion

4748.	Let S ={x : x is a positive multiple of 3 less than 100} P = {x : x is a prime number less than 20} Then, n(S) + n(P) = ____________.
Answer» Let S ={x : x is a positive multiple of 3 less than 100} P = {x : x is a prime number less than 20} Then, n(S) + n(P) = ____________.

Discussion

4749.	Consider the experiment of rolling a die. Let A be the event ‘getting a prime number’, B be the event ‘getting an odd number’. Write the set representing the events(i) A or B.(ii) A and B.(iii) A but not B.(iv) ′not A′.
Answer» Consider the experiment of rolling a die. Let $A$ be the event ‘getting a prime number’, $B$ be the event ‘getting an odd number’. Write the set representing the events $(i)$ $A or B$ . $(i i)$ $A and B$ . $(i i i)$ $A but not B$ . $(i v)$ $^{'} not A^{'}$ .

Discussion

4750.	Sum of series tan−1√35+tan−1(√39)+tan−1(√315)+tan−1(√323)................. upto infinite terms is equal to
Answer» Sum of series $t a n^{- 1} \frac{\sqrt{3}}{5} + {tan}^{- 1} (\frac{\sqrt{3}}{9}) + {tan}^{- 1} (\frac{\sqrt{3}}{15}) + {tan}^{- 1} (\frac{\sqrt{3}}{23})$ ................. upto infinite terms is equal to

Discussion

Explore topic-wise InterviewSolutions in .

A lead pencil consists of a cylinder of wood with solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

Tan a +sec a -1/tan a -sec a +1=1+sin a /cos a

Find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.

Mode of the data15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is

Draw a circle of radius 4.2 cm. Draw a pair of tangents to this circle inclined to each other at an angle of 45∘.

A point P divides the line segment joining the points A(3, −5) and B(−4, 8) such that APPB=k1. If P lies on the line x + y = 0, then find the value of k. [CBSE 2012]

7. How to find zeros of a cubic polynomial

Solve the following systems of equations graphically:x + y = 32x + 5y = 12

If two chords AB and CD intersect externally at P and if AB = 4 cm , PB = 5 cm, PD = 3 cm, then find the value of CD.

Find the co-ordinates of the point M if M is the midpoint of a line segment PQ with P(7, -3) and Q(-6, 2).

A square lawn has a path of 4m around it . The area of the path is 196m2. Find the side length of the lawn.

If A=[0−110], then which one of the following statements is correct

Question 7Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

The following table shows classification of number of workers and the number of hours they work in a software company. Find the median of the number of hours they work. Daily No. of hours 8 - 10 10 - 12 12 - 14 14 - 16 Number of workers 150 500 300 50

What comes next in the Arithmetic progression: 1400, 1500, 1600, 1700, ...?

A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 kmph. What is the initial speed of the train (in kmph)?25

Two unbiased dice are thrown. If E be the event that the number appearing on both the dice are prime and F be the event that the sum of the number appearing on both the dice is perfect square, then the probability of occurring of events E and event F is

Question 8 If A and B are (–2, –2) and (2, –4) respectively, find the coordinates of P such that AP=37AB and P lies on the line segment AB.

From the following information, calculate Proprietary Ratio: Share Capital ₹3,00,000 Reserves and Surplus ₹1,80,000 Non-current Assets ₹13,20,000 Current Assets ₹ 6,00,000

The vertical lines in the figure below are drawn 1 centimetres apart.Prove that their heights are in arithmetic sequence.What is the common difference?

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median of the data. Monthly consumption (in units)Numbers of customers65−85485−1055105−12513125−14520145−16514165−1858185−2054

If (-1,-1),(5,-2),(6,1) and (2,3) taken in order are the coordinates of the vertices of a quadrilateral , then the area enclosed is A.45sq. UnitsB.30Sq unitsC. 22.5 sq units D. 20.5 sq units

The complete set of quantities offered for sale at various prices are called

Two small circles of equal radii are cut from a semicircle as shown in the fig. If MN=28 cm and MN||PQ, find the area of the remaining portion of the semicircle.

ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that CQ=14AC. If PQ produced meets BC at R, prove that R is the midpoint BC.

Sketch proper figure and write the answers of the following questions. (i) If A - B - C and l(AC) = 11, l(BC) = 6.5, then l(AB) =?(ii) If R - S - T and l(ST) = 3.7, l(RS) = 2.5, then l(RT) =?(iii) If X - Y - Z and l(XZ) = 3 7, l(XY) =7 , then l(YZ) =?

graphs of quad equations given,we need to find the sign of the quadratic equation ,also how to find sign of quadratic equation when sign of 'a 'is given

Question 28Sales tax = Tax % of ___

51. Solve for x 1/a+b+x=1/a+1/b+1/x

Question 2While computing mean of grouped data, we assume that the frequencies are(a) evenly distributed over all the classes(b) centred at the class marks of the classes(c) centred at the upper limits of the classes(d) centred at the lower limits of the classes

12. 2 cards are selected randomly from a pack of 52 cards, find the probability that first one is a club and second is not a queen,

If sin [cot-1(x+1)] = cos (tan-1x), then find x

Complete the given factor tree of 100.

Sowmya takes 6 days less that the number of days takes by Bhagya to complete a piece of work. If both Sowmaya and Bhagya together can complete the same work in 4 days, in how many days will Bhagya alone complete the work?

If cos 9θ = sin θ and 9θ < 900 , then the value of tan 6 θ is

Find the roots of the following equations:

The line segment XY is parallel to side AC of △ABC and it divides the triangle into two parts of equal areas. Find the ratio BXAB.

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

If am ≠ bl, then the system of equationsax+by=clx+my=n(a) has a unique solution(b) has no solution(c) has infinitely many solutions(d) may or may not have a solution

Aparna, Manisha and Sonia are partners sharing profits in the ratio of 3 : 2 : 1. Manisha retired and goodwill of the firm is valued at ₹ 1,80,000. Aparna and Sonia decided to share future profits in the ratio of 3 : 2. Pass necessary Journal entries.

O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ∆OCD is an isosceles triangle.

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, then find the common difference.2

The vector component of ^i+^j+^k perpendicular to the direction of 2^i−^j+2^k is

If the 10th term of an A.P. is 21 and the sum of its first 10 terms is 120, find its nth term.

The angle of elevation of the top of a building from the foot of thetower is 30^° and the angle of elevation of the top of the tower from the foot of the building is 60^° . If the tower is 30m high, then the height of the building is

Let S ={x : x is a positive multiple of 3 less than 100} P = {x : x is a prime number less than 20} Then, n(S) + n(P) = ____________.

Consider the experiment of rolling a die. Let A be the event ‘getting a prime number’, B be the event ‘getting an odd number’. Write the set representing the events(i) A or B.(ii) A and B.(iii) A but not B.(iv) ′not A′.

Sum of series tan−1√35+tan−1(√39)+tan−1(√315)+tan−1(√323)................. upto infinite terms is equal to