24740 + Interview Questions in Mathematics Page 207 InterviewSolution

10301.	Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of onto functions from A into B is
Answer» Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of onto functions from A into B is

Discussion

10302.	A circle with centre O and radius 7 cm is circumscribing a square ABCD of side 8 cm. Find the area of the shaded region. [Take π=227]
Answer» A circle with centre $O$ and radius $7 c m$ is circumscribing a square $A B C D$ of side $8 c m$ . Find the area of the shaded region. [Take $π = \frac{22}{7}$ ]

10302.

A circle with centre O and radius 7 cm is circumscribing a square ABCD of side 8 cm. Find the area of the shaded region. [Take π=227]

Answer»

A circle with centre $O$ and radius $7 c m$ is circumscribing a square $A B C D$ of side $8 c m$ .

Find the area of the shaded region. [Take $π = \frac{22}{7}$ ]

Discussion

10303.	Locate \sqrt{13 on the number line.
Answer» Locate \sqrt{13 on the number line.

Discussion

10304.	The string of a kite is 100m long and it makes an angle of 60∘ with the horizontal. Find the height of the kite from the ground, assuming that there is no slack in the string.
Answer» The string of a kite is 100m long and it makes an angle of $60^{\circ}$ with the horizontal. Find the height of the kite from the ground, assuming that there is no slack in the string.

10304.

The string of a kite is 100m long and it makes an angle of 60∘ with the horizontal. Find the height of the kite from the ground, assuming that there is no slack in the string.

Answer»

The string of a kite is 100m long and it makes an angle of $60^{\circ}$ with the horizontal. Find the height of the kite from the ground, assuming that there is no slack in the string.

Discussion

10305.	Question 9 (i)A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be red?
Answer» Question 9 (i) A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be red?

Discussion

10306.	In each pair of triangles in the following figures, parts bearing indentical marks are congruent. State the test and correspondence of vertices by which triangles in each pair are congruent.(i) (ii) (iii) (iv)(v)
Answer» In each pair of triangles in the following figures, parts bearing indentical marks are congruent. State the test and correspondence of vertices by which triangles in each pair are congruent. (i) (ii) (iii) (iv) (v)

Discussion

10307.	If both x−2 and x−12 are factors of px2+5x+r , then .
Answer» If both $x - 2$ and $x - \frac{1}{2}$ are factors of $p x^{2} + 5 x + r$ , then .

Discussion

10308.	The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively and the angle between the first two sides is a right angle. Find its area.
Answer» The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively and the angle between the first two sides is a right angle. Find its area.

Discussion

10309.	s=\sqrt{3n+2}+\sqrt{3n} , n∈ N, then s is 1. always rational 2. rational for 2 values of n 3. always irrational 4.rational for a unique value of N
Answer» s=\sqrt{3n+2}+\sqrt{3n} , n∈ N, then s is 1. always rational 2. rational for 2 values of n 3. always irrational 4.rational for a unique value of N

Discussion

10310.	Prove that root 3 add root 3 is an irrational number.
Answer» Prove that root 3 add root 3 is an irrational number.

Discussion

10311.	How many circles can be drawn through two points?
Answer» How many circles can be drawn through two points?

Discussion

10312.	Question 9 (v)In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:APCQ is a parallelogram
Answer» Question 9 (v) In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that: APCQ is a parallelogram

Discussion

10313.	In the following figures, are the centre of the circle and the circumcentre of the triangle the same?
Answer» In the following figures, are the centre of the circle and the circumcentre of the triangle the same?

10313.

In the following figures, are the centre of the circle and the circumcentre of the triangle the same?

Answer»

In the following figures, are the centre of the circle and the circumcentre of the triangle the same?

Discussion

10314.	The paint in a certain container is sufficient to paint on area equal to 9.375m2. How many bricks of dimension 22.5 cm×10 cm×7.5 cm can be painted out of this container?
Answer» The paint in a certain container is sufficient to paint on area equal to 9.375 $m^{2}$ . How many bricks of dimension 22.5 $c m \times 10 c m \times 7.5 c m can be painted out of this container?$

Discussion

10315.	Your challenge is to mark the points between the rays PA and PB (both included) which lie at a certain distance, say 'd', from a point P, as shown. PC = d. How many such points exist?
Answer» Your challenge is to mark the points between the rays PA and PB (both included) which lie at a certain distance, say 'd', from a point P, as shown. PC = d. How many such points exist?

Discussion

10316.	If the side of a cube is increased by x%, then find the percentage increment of its volume.
Answer» If the side of a cube is increased by x%, then find the percentage increment of its volume.

Discussion

10317.	Let \|A1\|=3,\|A2\|=5, and \|A1+A2\|=5. A1 is same as −→A1 and A2 is same as −→A2. The value of (2A1+3A2).(3A1−2A2) is: (report the magnitude).
Answer» Let $\| \begin{matrix} A_{1} \end{matrix} \| = 3, \| \begin{matrix} A_{2} \end{matrix} \| = 5,$ and $\| \begin{matrix} A_{1} + A_{2} \end{matrix} \| = 5$ . $A_{1}$ is same as $_{1}$ and $A_{2}$ is same as $_{2}$ . The value of $(2 A_{1} + 3 A_{2}) . (3 A_{1} - 2 A_{2})$ is: (report the magnitude).

Discussion

10318.	Polynomials are everywhere. It is found in the slope of a hill, the curve of a bridge or the continuity of a mountain range. Based on the given information, answer the following question. If the path traced by the hills is represented by the graph y=p(x) below, find the number of zeroes.
Answer» Polynomials are everywhere. It is found in the slope of a hill, the curve of a bridge or the continuity of a mountain range. Based on the given information, answer the following question. If the path traced by the hills is represented by the graph $y = p (x)$ below, find the number of zeroes.

Discussion

10319.	Find the length of each side of a rhombus whose diagonals are 24 cm and 10 cm long.
Answer» Find the length of each side of a rhombus whose diagonals are 24 cm and 10 cm long.

Discussion

10320.	Simplify (3√64)−12
Answer» Simplify $({\sqrt[3]{64})}^{\frac{- 1}{2}}$

Discussion

10321.	Question 78(iv)Observe the toothpick pattern given belowWould it make sense to join the points on this graph? Explain.
Answer» Question 78(iv) Observe the toothpick pattern given below Would it make sense to join the points on this graph? Explain.

Discussion

10322.	Question 5A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
Answer» Question 5 A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

Discussion

10323.	P is the mid-point of the side CD of a parallelogram ABCD. A line through C parallel to PA intersects AB at Q and DA produced at R. Then:
Answer» P is the mid-point of the side CD of a parallelogram ABCD. A line through C parallel to PA intersects AB at Q and DA produced at R. Then:

Discussion

10324.	In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.
Answer» In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.

10324.

In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.

Answer»

In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.

Discussion

10325.	Write each of the following in decimal form and say what kind of decimal expansion each has. (i) 58 (ii) 725 (iii) 311 (iv)513 (v) 1124 (vi)261400 (vii) 231625 (viii)2512
Answer» Write each of the following in decimal form and say what kind of decimal expansion each has. (i) $\frac{5}{8}$ (ii) $\frac{7}{25}$ (iii) $\frac{3}{11}$ (iv) $\frac{5}{13}$ (v) $\frac{11}{24}$ (vi) $\frac{261}{400}$ (vii) $\frac{231}{625}$ (viii) $2 \frac{5}{12}$

Discussion

10326.	The figure shows a circle with centre O, in which the diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm. Find the radius of the circle.
Answer» The figure shows a circle with centre O, in which the diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm. Find the radius of the circle.

10326.

The figure shows a circle with centre O, in which the diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm. Find the radius of the circle.

Answer»

The figure shows a circle with centre O, in which the diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm. Find the radius of the circle.

Discussion

10327.	From the options given below, choose the option which has all the measurements you'll require to construct a quadrilateral ABCD.
Answer» From the options given below, choose the option which has all the measurements you'll require to construct a quadrilateral ABCD.

Discussion

10328.	Find the length of the side of a cube whose total surface area is 1536 cm2.
Answer» Find the length of the side of a cube whose total surface area is $1536 c m^{2}$ .

Discussion

10329.	Question 1 (v) Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.
Answer» Question 1 (v) Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Discussion

10330.

Given below is a table which shows the year wise strength of a school. Represent this data by a bar graph. Year 2011-12 2012-13 2013-14 2014-15 2015-16 No. of students 800 975 1100 1400 1625

Answer» Given below is a table which shows the year wise strength of a school. Represent this data by a bar graph.

Year	2011-12	2012-13	2013-14	2014-15	2015-16
No. of students	800	975	1100	1400	1625

Discussion

10331.	Look at the graph given below:The equation of the graph is .
Answer» Look at the graph given below: The equation of the graph is .

Discussion

10332.	Fill in the blanks so as to make the following statements true:(i) If one angle of a linear pair is acute, then its other angle will be ........(ii) A ray stands on a line, then the sum of the two adjacent angles so formed is ..........(iii) If the sum of two adjacent angles is 180°, then the ........ arms of the two angles are opposite rays.
Answer» Fill in the blanks so as to make the following statements true: (i) If one angle of a linear pair is acute, then its other angle will be ........ (ii) A ray stands on a line, then the sum of the two adjacent angles so formed is .......... (iii) If the sum of two adjacent angles is 180°, then the ........ arms of the two angles are opposite rays.

Discussion

10333.	516−314 =_____
Answer» $5 \frac{1}{6} - 3 \frac{1}{4}$ =_____

Discussion

10334.	In PQR right angled at Q, QR=3 cm and PR -PQ =1 cm. determine thw values of sin R, cosR and tan R.
Answer» In PQR right angled at Q, QR=3 cm and PR -PQ =1 cm. determine thw values of sin R, cosR and tan R.

Discussion

10335.	PQRS and ABRS are parallelograms and X is any point on side BR. Then, ar(parallelogram PQRS) is equal to
Answer» PQRS and ABRS are parallelograms and X is any point on side BR. Then, ar(parallelogram PQRS) is equal to

10335.

PQRS and ABRS are parallelograms and X is any point on side BR. Then, ar(parallelogram PQRS) is equal to

Answer»

PQRS and ABRS are parallelograms and X is any point on side BR. Then, ar(parallelogram PQRS) is equal to

Discussion

10336.	Evaluate the following using suitable identities: (102)3
Answer» Evaluate the following using suitable identities: ${(102)}^{3}$

Discussion

10337.	If PQRS is a parallelogram, then what are the remaining angles?
Answer» If PQRS is a parallelogram, then what are the remaining angles?

Discussion

10338.	How many plastic boxes of size 9 cm, 6 cm,5 cm can be packed inside a cardboard box of size 36 cm, 24 cm, 20 cm?
Answer» How many plastic boxes of size $9 c m, 6 c m, 5 c m$ can be packed inside a cardboard box of size $36 c m, 24 c m, 20 c m$ ?

Discussion

10339.	80. From a point p normal is drawn to curve 3x2+6y2=18which is perpendicular to line x+y=8cordinate of p
Answer» 80. From a point p normal is drawn to curve 3x2+6y2=18which is perpendicular to line x+y=8cordinate of p

Discussion

10340.	Which of the following yields maximum interest for 2 years?(a) ₹1500 at 8% per annum(b) ₹1000 at 11% per annum(c) ₹2000 at 5% per annum(d) ₹900 at 20% per annum
Answer» Which of the following yields maximum interest for 2 years? (a) ₹1500 at 8% per annum (b) ₹1000 at 11% per annum (c) ₹2000 at 5% per annum (d) ₹900 at 20% per annum

Discussion

10341.	Question 8 AB is a diameter and AC is a chord of a circle with centre O such that ∠BAC=30∘. The tangent at c intersects extended AB at a point D. Prove that BC = BD.
Answer» Question 8 AB is a diameter and AC is a chord of a circle with centre O such that $∠ B A C = 30^{\circ}$ . The tangent at c intersects extended AB at a point D. Prove that BC = BD.

Discussion

10342.	38. Determine if the points (1,5), (2,3) and (-2,-11) are collinear.
Answer» 38. Determine if the points (1,5), (2,3) and (-2,-11) are collinear.

Discussion

10343.	Give rectifying Journal entries for the following errors:(i) Sales of goods to Madan ₹ 6,000 were entered in the Sales Book as ₹ 600.(ii) Credit purchase of ₹ 1,500 from Ajay has been wrongly passed through the Sales Book.(iii) Repairs to building ₹ 300 were debited to Building Account.(iv) ₹ 2,050 paid to Rohit is posted to the debit of Mohit’s Account as ₹ 5,020.(v) Purchases Return Book is overcasted by ₹ 400.
Answer» Give rectifying Journal entries for the following errors: (i) Sales of goods to Madan ₹ 6,000 were entered in the Sales Book as ₹ 600. (ii) Credit purchase of ₹ 1,500 from Ajay has been wrongly passed through the Sales Book. (iii) Repairs to building ₹ 300 were debited to Building Account. (iv) ₹ 2,050 paid to Rohit is posted to the debit of Mohit’s Account as ₹ 5,020. (v) Purchases Return Book is overcasted by ₹ 400.

Discussion

10344.	While constructing a triangle, which of the following set of lengths can be the sides of a triangle?
Answer» While constructing a triangle, which of the following set of lengths can be the sides of a triangle?

Discussion

10345.	If the polynomials az3 + 4z2 + 3z − 4 and z3 − 4z + a leave the same remainder when divided by z − 3, find a.
Answer» If the polynomials az³ + 4z² + 3z − 4 and z³ − 4z + a leave the same remainder when divided by z − 3, find a.

Discussion

10346.	Note Use π=227, unless stated otherwise.The curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.
Answer» Note Use $π = \frac{22}{7}$ , unless stated otherwise. The curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.

Discussion

10347.	3. Let f(x) be a polynomial of 5 degree with leading coefficient unity such that f(1)=5 f(2)=4 f(3)=3 f(4)=2 f(5)=1. Then f(6) is equal to:
Answer» 3. Let f(x) be a polynomial of 5 degree with leading coefficient unity such that f(1)=5 f(2)=4 f(3)=3 f(4)=2 f(5)=1. Then f(6) is equal to:

Discussion

10348.	A drain cover is made from a square metal plate of side 40 cm and has 336 holes of radius 1 cm each drilled in it. Find the area in cm2 of the remaining square plate.(Take π =227)
Answer» A drain cover is made from a square metal plate of side 40 cm and has 336 holes of radius 1 cm each drilled in it. Find the area in ${cm}^{2}$ of the remaining square plate. (Take $π$ = $\frac{22}{7}$ )

Discussion

10349.	In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:AQ = CP
Answer» In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that: AQ = CP

Discussion

10350.	(7a+2) (7a+2b) factories by(X+a)(X+b) identity
Answer» (7a+2) (7a+2b) factories by(X+a)(X+b) identity

Discussion

Explore topic-wise InterviewSolutions in .

Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of onto functions from A into B is

A circle with centre O and radius 7 cm is circumscribing a square ABCD of side 8 cm. Find the area of the shaded region. [Take π=227]

Locate \sqrt{13 on the number line.

The string of a kite is 100m long and it makes an angle of 60∘ with the horizontal. Find the height of the kite from the ground, assuming that there is no slack in the string.

Question 9 (i)A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be red?

In each pair of triangles in the following figures, parts bearing indentical marks are congruent. State the test and correspondence of vertices by which triangles in each pair are congruent.(i) (ii) (iii) (iv)(v)

If both x−2 and x−12 are factors of px2+5x+r , then .

The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively and the angle between the first two sides is a right angle. Find its area.

s=\sqrt{3n+2}+\sqrt{3n} , n∈ N, then s is 1. always rational 2. rational for 2 values of n 3. always irrational 4.rational for a unique value of N

Prove that root 3 add root 3 is an irrational number.

How many circles can be drawn through two points?

Question 9 (v)In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:APCQ is a parallelogram

In the following figures, are the centre of the circle and the circumcentre of the triangle the same?

The paint in a certain container is sufficient to paint on area equal to 9.375m2. How many bricks of dimension 22.5 cm×10 cm×7.5 cm can be painted out of this container?

Your challenge is to mark the points between the rays PA and PB (both included) which lie at a certain distance, say 'd', from a point P, as shown. PC = d. How many such points exist?

If the side of a cube is increased by x%, then find the percentage increment of its volume.

Let |A1|=3,|A2|=5, and |A1+A2|=5. A1 is same as −→A1 and A2 is same as −→A2. The value of (2A1+3A2).(3A1−2A2) is: (report the magnitude).

Polynomials are everywhere. It is found in the slope of a hill, the curve of a bridge or the continuity of a mountain range. Based on the given information, answer the following question. If the path traced by the hills is represented by the graph y=p(x) below, find the number of zeroes.

Find the length of each side of a rhombus whose diagonals are 24 cm and 10 cm long.

Simplify (3√64)−12

Question 78(iv)Observe the toothpick pattern given belowWould it make sense to join the points on this graph? Explain.

P is the mid-point of the side CD of a parallelogram ABCD. A line through C parallel to PA intersects AB at Q and DA produced at R. Then:

In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.

Write each of the following in decimal form and say what kind of decimal expansion each has. (i) 58 (ii) 725 (iii) 311 (iv)513 (v) 1124 (vi)261400 (vii) 231625 (viii)2512

The figure shows a circle with centre O, in which the diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm. Find the radius of the circle.

From the options given below, choose the option which has all the measurements you'll require to construct a quadrilateral ABCD.

Find the length of the side of a cube whose total surface area is 1536 cm2.

Question 1 (v) Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Given below is a table which shows the year wise strength of a school. Represent this data by a bar graph. Year 2011-12 2012-13 2013-14 2014-15 2015-16 No. of students 800 975 1100 1400 1625

Look at the graph given below:The equation of the graph is .

516−314 =_____

In PQR right angled at Q, QR=3 cm and PR -PQ =1 cm. determine thw values of sin R, cosR and tan R.

PQRS and ABRS are parallelograms and X is any point on side BR. Then, ar(parallelogram PQRS) is equal to

Evaluate the following using suitable identities: (102)3

If PQRS is a parallelogram, then what are the remaining angles?

How many plastic boxes of size 9 cm, 6 cm,5 cm can be packed inside a cardboard box of size 36 cm, 24 cm, 20 cm?

80. From a point p normal is drawn to curve 3x2+6y2=18which is perpendicular to line x+y=8cordinate of p

Which of the following yields maximum interest for 2 years?(a) ₹1500 at 8% per annum(b) ₹1000 at 11% per annum(c) ₹2000 at 5% per annum(d) ₹900 at 20% per annum

Question 8 AB is a diameter and AC is a chord of a circle with centre O such that ∠BAC=30∘. The tangent at c intersects extended AB at a point D. Prove that BC = BD.

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

While constructing a triangle, which of the following set of lengths can be the sides of a triangle?

If the polynomials az3 + 4z2 + 3z − 4 and z3 − 4z + a leave the same remainder when divided by z − 3, find a.

Note Use π=227, unless stated otherwise.The curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.

3. Let f(x) be a polynomial of 5 degree with leading coefficient unity such that f(1)=5 f(2)=4 f(3)=3 f(4)=2 f(5)=1. Then f(6) is equal to:

A drain cover is made from a square metal plate of side 40 cm and has 336 holes of radius 1 cm each drilled in it. Find the area in cm2 of the remaining square plate.(Take π =227)

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:AQ = CP

(7a+2) (7a+2b) factories by(X+a)(X+b) identity