32581 + Interview Questions in Mathematics Page 40 InterviewSolution

1951.	Parametric form of the equation of the line 3x-6y-2z-15=0=2x+y-2z-5=0 is
Answer» Parametric form of the equation of the line 3x-6y-2z-15=0=2x+y-2z-5=0 is

Discussion

1952.	Which of the following equations represents a line parallel to x – axis?
Answer» Which of the following equations represents a line parallel to x – axis?

Discussion

1953.	A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field, which is 12 m in diameter and 2.5 m deep. If water flows through the pipe at the rate of 3.6 km/hr, in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate of Rs 0.07 per m3.
Answer» A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field, which is 12 m in diameter and 2.5 m deep. If water flows through the pipe at the rate of 3.6 km/hr, in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate of Rs 0.07 per $m^{3}$ .

Discussion

1954.	A man 2 metre high walks at a uniform speed 5 metre per hour away from a lamp post 6 metre high .The rate at which the length of his shadow increases is
Answer» A man 2 metre high walks at a uniform speed 5 metre per hour away from a lamp post 6 metre high .The rate at which the length of his shadow increases is

Discussion

1955.	Consider the following grammar:S→aSB\|dB→bThe number of reduction steps taken by a bottom-up parser while accepting the string aaadbbb is 7
Answer» Consider the following grammar: $S \to a S B \| d$ $B \to b$ The number of reduction steps taken by a bottom-up parser while accepting the string aaadbbb is 7

Discussion

1956.	An aeroplane leaves an airport and flies due north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after112hours?
Answer» An aeroplane leaves an airport and flies due north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after $1 \frac{1}{2}$ hours?

Discussion

1957.	The circumference of a circle is 22 cm. The area of its quadrant (in cm2) is(a) 772(b)774(c)778(d)7716
Answer» The circumference of a circle is 22 cm. The area of its quadrant (in cm²) is (a) $\frac{77}{2}$ (b) $\frac{77}{4}$ (c) $\frac{77}{8}$ (d) $\frac{77}{16}$

Discussion

1958.	A sector is cut from a circle of radius 21 cm. The angle of the sector is 150∘. Find the length of the arc and the area of the sector.
Answer» A sector is cut from a circle of radius 21 cm. The angle of the sector is $150^{\circ}$ . Find the length of the arc and the area of the sector.

Discussion

1959.	The angle between the minute hand and hour hand of the clock when the time is 05:06 hours is
Answer» The angle between the minute hand and hour hand of the clock when the time is $05 : 06$ hours is

Discussion

1960.	Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16cm×8cm×8cm. when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [use π=3.14]
Answer» Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions $16 c m \times 8 c m \times 8 c m$ . when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. $[u s e π = 3.14]$

Discussion

1961.	Very-Short and Short-Answer QuestionsIf the sum of first p terms of an AP is (ap2 + bp), find its common difference. [CBSE 2010]
Answer» Very-Short and Short-Answer Questions If the sum of first p terms of an AP is (ap²+ bp), find its common difference. [CBSE 2010]

Discussion

1962.	In adjacent figure, PR>PQ and PS bisects ∠QPR. Prove that ∠PSR>∠PSQ.
Answer» In adjacent figure, $P R > P Q$ and $P S$ bisects $∠ Q P R$ . Prove that $∠ P S R > ∠ P S Q$ .

Discussion

1963.	Find the area (in cm2) of the yellow region where the square has a side measuring 14 cm.
Answer» Find the area (in $c m^{2}$ ) of the yellow region where the square has a side measuring 14 cm.

Discussion

1964.	Answer the questions based on the following diagram. [4 MARKS]a) Identify three triangles in the figure.b) Write the names of seven anglesc) Write the names of six line segmentsd) Which two triangles have ∠B as common?
Answer» Answer the questions based on the following diagram. [4 MARKS] a) Identify three triangles in the figure. b) Write the names of seven angles c) Write the names of six line segments d) Which two triangles have $∠ B$ as common?

Discussion

1965.	The midpoint of the line joining the points (1, 2) and (5, 6) is
Answer» The midpoint of the line joining the points (1, 2) and (5, 6) is

Discussion

1966.	Select the correct approach for solving a pair of linear equations in 2 variables by elimination method. (i) Add or subtract one equation from the other so that one variable gets eliminated. (ii) Multiply both the equations by any non-zero constant to make the coefficients of one variable (either x or y) numerically equal. (iii) Solve the equation in one variable (x or y) to get its value. (iv) Substitute the value of x (or y) in either of the original equations to get the value of the other variable.
Answer» Select the correct approach for solving a pair of linear equations in 2 variables by elimination method. (i) Add or subtract one equation from the other so that one variable gets eliminated. (ii) Multiply both the equations by any non-zero constant to make the coefficients of one variable (either x or y) numerically equal. (iii) Solve the equation in one variable (x or y) to get its value. (iv) Substitute the value of x (or y) in either of the original equations to get the value of the other variable.

Discussion

1967.	Question 15Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(AOD) = ar(BOC). Prove that ABCD is a trapezium.
Answer» Question 15 Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(AOD) = ar(BOC). Prove that ABCD is a trapezium.

Discussion

1968.	In a school, students thought of planting saplings in and around the school to reduce air pollution. It was decided that the number of saplings, that each section of each class will plant, will be the same as the class, in which they are studying, e.g, a section of Class I will plant 1 tree, a section of class II will plant two saplings and so on till Class XII. There are three sections of each class. How many saplings will be planted by the students?
Answer» In a school, students thought of planting saplings in and around the school to reduce air pollution. It was decided that the number of saplings, that each section of each class will plant, will be the same as the class, in which they are studying, e.g, a section of Class I will plant 1 tree, a section of class II will plant two saplings and so on till Class XII. There are three sections of each class. How many saplings will be planted by the students?

Discussion

1969.	Find the roots of the equation 5x2−6x−2=0 by the method of completing the square. [3 MARKS]
Answer» Find the roots of the equation $5 x^{2} - 6 x - 2 = 0$ by the method of completing the square. [3 MARKS]

Discussion

1970.	If the sum of first 10 natural numbers is S1 and that of first 10 whole numbers is S2. Then S1−S2 is
Answer» If the sum of first 10 natural numbers is $S_{1}$ and that of first 10 whole numbers is $S_{2} .$ Then $S_{1} - S_{2}$ is

Discussion

1971.	In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are, of lengths 4 cm and 3 cm respectively. If the area of △ABC = 21 cm2 then find the lengths of sides of AB and AC. [CBSE 2011]
Answer» In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are, of lengths 4 cm and 3 cm respectively. If the area of △ABC = 21 cm² then find the lengths of sides of AB and AC. [CBSE 2011]

Discussion

1972.	If 'd' is the ICT of 30,72,find the value of 'x' and 'y' satisfying d=30x+72y(PLEASE ANSWER THIS QUESTION IN SIMPLE STEP BY STEP WAY)
Answer» If 'd' is the ICT of 30,72,find the value of 'x' and 'y' satisfying d=30x+72y(PLEASE ANSWER THIS QUESTION IN SIMPLE STEP BY STEP WAY)

Discussion

1973.	Make the correct alternative in the following question:If 10n+3×4n+2+λ is divisible by 9 for all n ∈ N, then the least positive integral value of λ is(a) 5 (b) 3 (c) 7 (d) 1
Answer» Make the correct alternative in the following question: If $10^{n} + 3 \times 4^{n + 2} + λ$ is divisible by 9 for all n $\in$ N, then the least positive integral value of $λ$ is (a) 5 (b) 3 (c) 7 (d) 1

Discussion

1974.	Question 75Find the length of the largest pole that can be placed in a room of dimensions 12m×4m×3m.
Answer» Question 75 Find the length of the largest pole that can be placed in a room of dimensions $12 m \times 4 m \times 3 m$ .

1974.

Question 75Find the length of the largest pole that can be placed in a room of dimensions 12m×4m×3m.

Answer»

Question 75

Find the length of the largest pole that can be placed in a room of dimensions $12 m \times 4 m \times 3 m$ .

Discussion

1975.	An archery target has three regions formed by three concentric circles as shown in figure15.8. If the diameters of the concentric circles are in the ratios 1 : 2 : 3 , then find the ratio of the areas of three regions .
Answer» An archery target has three regions formed by three concentric circles as shown in figure15.8. If the diameters of the concentric circles are in the ratios 1 : 2 : 3 , then find the ratio of the areas of three regions .

Discussion

1976.	10. The topic relation between zeroes and coefficients of a polynomial
Answer» 10. The topic relation between zeroes and coefficients of a polynomial

Discussion

1977.	30. The sum of the pair of opposite angles of a cyclic quadrilateral is 180 degree
Answer» 30. The sum of the pair of opposite angles of a cyclic quadrilateral is 180 degree

Discussion

1978.	Prove the following trigonometric identities.(i) cotA+tanBcotB+tanA=cotA tanB(ii) tanA+tanBcotA+cotB=tanA tanB
Answer» Prove the following trigonometric identities. (i) $\frac{\cot A + \tan B}{\cot B + \tan A} = \cot A \tan B$ (ii) $\frac{\tan A + \tan B}{\cot A + \cot B} = \tan A \tan B$

Discussion

1979.	What is the distance of the point (-6,8) from the origin?
Answer» What is the distance of the point (-6,8) from the origin?

Discussion

1980.	If the difference of the root of the equation x square minus px plus q equal to 0 and x square minus qx plus p equal to 0 be the same then p plus q equal to
Answer» If the difference of the root of the equation x square minus px plus q equal to 0 and x square minus qx plus p equal to 0 be the same then p plus q equal to

Discussion

1981.	Two cubes, each of edge length 12 cm are joined end to end. Find the surface area of the resulting cuboid.
Answer» Two cubes, each of edge length 12 cm are joined end to end. Find the surface area of the resulting cuboid.

Discussion

1982.	The rationalising factor for the irrational number, 5−√7 is .
Answer» The rationalising factor for the irrational number, $5 - \sqrt{7}$ is .

Discussion

1983.	Solve for x and y: x-y=3x3+y2=6
Answer» Solve for x and y: $x - y = 3 \frac{x}{3} + \frac{y}{2} = 6$

Discussion

1984.	Question 4 (i) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (i) 2, 4, 8, 16, …
Answer» Question 4 (i) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (i) 2, 4, 8, 16, …

Discussion

1985.	If the area of a circle is 154 cm2, then its perimeter is __________.
Answer» If the area of a circle is 154 cm², then its perimeter is __________.

Discussion

1986.	The arithmetic mean and mode of a data are 24 and 12 respectively, then its median is(a) 25(b) 18(c) 20(d) 22
Answer» The arithmetic mean and mode of a data are 24 and 12 respectively, then its median is (a) 25 (b) 18 (c) 20 (d) 22

Discussion

1987.	Solve the following system of equations8x+7y=2xy6x+y=10xy (x is not equal to 0, y is not equal to 0)
Answer» Solve the following system of equations 8x+7y=2xy 6x+y=10xy (x is not equal to 0, y is not equal to 0)

Discussion

1988.	The triangles ΔABC and ΔPQC are similar by which similarity criteria?
Answer» The triangles $Δ A B C$ and $Δ P Q C$ are similar by which similarity criteria?

Discussion

1989.	In Figure 2. a right triangle ABC. circumscribes a circle of radius r. If AB and BC are of length 8 cm and 6 cm respectively. find the value of r.
Answer» In Figure 2. a right triangle ABC. circumscribes a circle of radius r. If AB and BC are of length 8 cm and 6 cm respectively. find the value of r.

Discussion

1990.	(i) A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h.(ii) A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle of elevation of the top of the light house from 60° to 30°. Find the speed of the boat in metres per minute. (Use 3 = 1.732)
Answer» (i) A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h. (ii) A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle of elevation of the top of the light house from 60° to 30°. Find the speed of the boat in metres per minute. (Use $\sqrt{3}$ = 1.732)

Discussion

1991.	Two consecutive positive integers, sum of whose squares is 365 are ___ and ___ .
Answer» Two consecutive positive integers, sum of whose squares is 365 are ___ and ___ .

Discussion

1992.	If a, b, c, d are in proportion , then prove that (i) 11a2 + 9ac11b2 + 9bd= a2 + 3acb2 + 3bd(ii) a2 + 5c2b2 + 5d2= ab(iii) a2 + ab + b2a2 - ab + b2= c2 +cd+ d2c2 -cd+ d2
Answer» If a, b, c, d are in proportion , then prove that (i) $\frac{11 a^{2} + 9 a c}{11 b^{2} + 9 b d} = \frac{a^{2} + 3 a c}{b^{2} + 3 b d}$ (ii) $\sqrt{\frac{a^{2} + 5 c^{2}}{b^{2} + 5 d^{2}}} = \frac{a}{b}$ (iii) $\frac{a^{2} + a b + b^{2}}{a^{2} - a b + b^{2}} = \frac{c^{2} + c d + d^{2}}{c^{2} - c d + d^{2}}$

Discussion

1993.	Directions:- Study the following information carefully to answer the question given below. Eight friends A, B, C, D, E, F, G and H are sitting around a circle facing the centre, but not necessarily in the same order. • D sits third to left of A. A is an immediate neighbour of both F and H. • Only one person sits between C and F. • B is not an immediate neighbour of D. • Only one person sits between B and G. What is the position of C with respect to the position of E?
Answer» Directions:- Study the following information carefully to answer the question given below. Eight friends A, B, C, D, E, F, G and H are sitting around a circle facing the centre, but not necessarily in the same order. • D sits third to left of A. A is an immediate neighbour of both F and H. • Only one person sits between C and F. • B is not an immediate neighbour of D. • Only one person sits between B and G. What is the position of C with respect to the position of E?

Discussion

1994.	In the given figure PA = 3 cm and PT = 4 cm, the value of PB is equal to
Answer» In the given figure PA = 3 cm and PT = 4 cm, the value of PB is equal to

Discussion

1995.	ABD is a triangle right angled at A and AC⊥BD. Find x.
Answer» $A B D$ is a triangle right angled at $A$ and $A C ⊥ B D$ . Find $x$ .

Discussion

1996.	Question 7 (iv) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The number of bacteria in a certain food item after each second, when they double in every second.
Answer» Question 7 (iv) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The number of bacteria in a certain food item after each second, when they double in every second.

Discussion

1997.	if the 5th term of an A.p is zero, then show that its 33rd term is 4 times its12th term
Answer» if the 5th term of an A.p is zero, then show that its 33rd term is 4 times its12th term

Discussion

1998.	Question 14A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the the slant height of the conical portion is 5 cm, find the total surface area and volume of the rocket [Use π=3.14]
Answer» Question 14 A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the the slant height of the conical portion is 5 cm, find the total surface area and volume of the rocket [Use $π = 3.14]$

Discussion

1999.	Gloria is walking along the path joining (−2, 3) and (2, −2), while Suresh is walking along the path joining (0, 5) and (4, 0). Represent this situation graphically.
Answer» Gloria is walking along the path joining (−2, 3) and (2, −2), while Suresh is walking along the path joining (0, 5) and (4, 0). Represent this situation graphically.

Discussion

2000.	Samaira heard 3 bells toll together at 10:00 AM. The first bell tolls after every 5 second, the second tolls after every 9 seconds and the third tolls after every 10 seconds. When will they toll together again?
Answer» Samaira heard 3 bells toll together at 10:00 AM. The first bell tolls after every 5 second, the second tolls after every 9 seconds and the third tolls after every 10 seconds. When will they toll together again?

Discussion

Explore topic-wise InterviewSolutions in .

Parametric form of the equation of the line 3x-6y-2z-15=0=2x+y-2z-5=0 is

Which of the following equations represents a line parallel to x – axis?

A man 2 metre high walks at a uniform speed 5 metre per hour away from a lamp post 6 metre high .The rate at which the length of his shadow increases is

Consider the following grammar:S→aSB|dB→bThe number of reduction steps taken by a bottom-up parser while accepting the string aaadbbb is 7

An aeroplane leaves an airport and flies due north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after112hours?

The circumference of a circle is 22 cm. The area of its quadrant (in cm2) is(a) 772(b)774(c)778(d)7716

A sector is cut from a circle of radius 21 cm. The angle of the sector is 150∘. Find the length of the arc and the area of the sector.

The angle between the minute hand and hour hand of the clock when the time is 05:06 hours is

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16cm×8cm×8cm. when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [use π=3.14]

Very-Short and Short-Answer QuestionsIf the sum of first p terms of an AP is (ap2 + bp), find its common difference. [CBSE 2010]

In adjacent figure, PR&gt;PQ and PS bisects ∠QPR. Prove that ∠PSR&gt;∠PSQ.

Find the area (in cm2) of the yellow region where the square has a side measuring 14 cm.

Answer the questions based on the following diagram. [4 MARKS]a) Identify three triangles in the figure.b) Write the names of seven anglesc) Write the names of six line segmentsd) Which two triangles have ∠B as common?

The midpoint of the line joining the points (1, 2) and (5, 6) is

Question 15Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(AOD) = ar(BOC). Prove that ABCD is a trapezium.

Find the roots of the equation 5x2−6x−2=0 by the method of completing the square. [3 MARKS]

If the sum of first 10 natural numbers is S1 and that of first 10 whole numbers is S2. Then S1−S2 is

If 'd' is the ICT of 30,72,find the value of 'x' and 'y' satisfying d=30x+72y(PLEASE ANSWER THIS QUESTION IN SIMPLE STEP BY STEP WAY)

Make the correct alternative in the following question:If 10n+3×4n+2+λ is divisible by 9 for all n ∈ N, then the least positive integral value of λ is(a) 5 (b) 3 (c) 7 (d) 1

Question 75Find the length of the largest pole that can be placed in a room of dimensions 12m×4m×3m.

An archery target has three regions formed by three concentric circles as shown in figure15.8. If the diameters of the concentric circles are in the ratios 1 : 2 : 3 , then find the ratio of the areas of three regions .

10. The topic relation between zeroes and coefficients of a polynomial

30. The sum of the pair of opposite angles of a cyclic quadrilateral is 180 degree

Prove the following trigonometric identities.(i) cotA+tanBcotB+tanA=cotA tanB(ii) tanA+tanBcotA+cotB=tanA tanB

What is the distance of the point (-6,8) from the origin?

If the difference of the root of the equation x square minus px plus q equal to 0 and x square minus qx plus p equal to 0 be the same then p plus q equal to

Two cubes, each of edge length 12 cm are joined end to end. Find the surface area of the resulting cuboid.

The rationalising factor for the irrational number, 5−√7 is .

Solve for x and y: x-y=3x3+y2=6

Question 4 (i) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (i) 2, 4, 8, 16, …

If the area of a circle is 154 cm2, then its perimeter is __________.

The arithmetic mean and mode of a data are 24 and 12 respectively, then its median is(a) 25(b) 18(c) 20(d) 22

Solve the following system of equations8x+7y=2xy6x+y=10xy (x is not equal to 0, y is not equal to 0)

The triangles ΔABC and ΔPQC are similar by which similarity criteria?

In Figure 2. a right triangle ABC. circumscribes a circle of radius r. If AB and BC are of length 8 cm and 6 cm respectively. find the value of r.

Two consecutive positive integers, sum of whose squares is 365 are ___ and ___ .

If a, b, c, d are in proportion , then prove that (i) 11a2 + 9ac11b2 + 9bd= a2 + 3acb2 + 3bd(ii) a2 + 5c2b2 + 5d2= ab(iii) a2 + ab + b2a2 - ab + b2= c2 +cd+ d2c2 -cd+ d2

In the given figure PA = 3 cm and PT = 4 cm, the value of PB is equal to

ABD is a triangle right angled at A and AC⊥BD. Find x.

Question 7 (iv) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The number of bacteria in a certain food item after each second, when they double in every second.

if the 5th term of an A.p is zero, then show that its 33rd term is 4 times its12th term

Gloria is walking along the path joining (−2, 3) and (2, −2), while Suresh is walking along the path joining (0, 5) and (4, 0). Represent this situation graphically.

Samaira heard 3 bells toll together at 10:00 AM. The first bell tolls after every 5 second, the second tolls after every 9 seconds and the third tolls after every 10 seconds. When will they toll together again?

In adjacent figure, PR>PQ and PS bisects ∠QPR. Prove that ∠PSR>∠PSQ.

Two consecutive positive integers, sum of whose squares is 365 are _ and _ .