24740 + Interview Questions in Mathematics Page 218 InterviewSolution

10851.	If I draw two circles of radius 3 cm and 5cm with common centre and draw a line AB such that it is a chord to both the circles and length of CD is 2√5 cm, then find the distance of the chords from the centre and the length AC.
Answer» If I draw two circles of radius 3 cm and 5cm with common centre and draw a line AB such that it is a chord to both the circles and length of CD is $2 \sqrt{5}$ cm, then find the distance of the chords from the centre and the length AC.

10851.

If I draw two circles of radius 3 cm and 5cm with common centre and draw a line AB such that it is a chord to both the circles and length of CD is 2√5 cm, then find the distance of the chords from the centre and the length AC.

Answer»

If I draw two circles of radius 3 cm and 5cm with common centre and draw a line AB such that it is a chord to both the circles and length of CD is $2 \sqrt{5}$ cm, then find the distance of the chords from the centre and the length AC.

Discussion

10852.	The graph of y = p(x) is given. Assuming p(x) increases from x=10, the number of zeroes of y = p(x) is ___.
Answer» The graph of y = p(x) is given. Assuming p(x) increases from x=10, the number of zeroes of y = p(x) is ___.

Discussion

10853.	limx→1 xm-1xn-1 is(a) 1 (b) mn (c) -mn (d) m2n2
Answer» $\lim_{x \to 1} \frac{x^{m} - 1}{x^{n} - 1} is$ (a) 1 (b) $\frac{m}{n}$ (c) $- \frac{m}{n}$ (d) $\frac{m^{2}}{n^{2}}$

Discussion

10854.

Study the table given below and draw a line graph for it. Side of the square (in cm) 2 3 3.5 5 6 Perimeter (in cm) 8 12 14 20 24 Is the graph drawn, a linear graph?

Answer» Study the table given below and draw a line graph for it.

Side of the square (in cm)	2	3	3.5	5	6
Perimeter (in cm)	8	12	14	20	24

Is the graph drawn, a linear graph?

Discussion

10855.	If sinA=12 and cosB=1√2,then find the value of (A+B).
Answer» $If sin A = \frac{1}{2} and cos B = \frac{1}{\sqrt{2}}$ , then find the value of (A+B).

Discussion

10856.	In the figure, AB \|\| CD and ∠1 and ∠2 are in the ratio 3:2. Determine all angles from 1 to 8.
Answer» In the figure, AB \|\| CD and $∠ 1$ and $∠ 2$ are in the ratio 3:2. Determine all angles from 1 to 8.

Discussion

10857.	The figure given below shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CD =16 cm and EB = 4 cm, then find the radius of the circle.
Answer» The figure given below shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CD =16 cm and EB = 4 cm, then find the radius of the circle.

10857.

The figure given below shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CD =16 cm and EB = 4 cm, then find the radius of the circle.

Answer»

The figure given below shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CD =16 cm and EB = 4 cm, then find the radius of the circle.

Discussion

10858.	In the given figure, the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR=∠QPR.
Answer» In the given figure, the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR=∠QPR.

10858.

In the given figure, the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR=∠QPR.

Answer»

In the given figure, the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR=∠QPR.

Discussion

10859.	Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A∪B
Answer» Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in $A \cup B$

10859.

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A∪B

Answer»

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in $A \cup B$

Discussion

10860.	A cone of radius 3 cm and slant height 5 cm has curved surface area of ___ cm2.
Answer» A cone of radius 3 cm and slant height 5 cm has curved surface area of ___ $c m^{2}$ .

Discussion

10861.	Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
Answer» Find the value of 64x³ − 125z³, if 4x − 5z = 16 and xz = 12.

Discussion

10862.	D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE. Prove that the points B, C, E and D are concyclic.
Answer» D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE. Prove that the points B, C, E and D are concyclic.

10862.

D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE. Prove that the points B, C, E and D are concyclic.

Answer»

D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE.

Prove that the points B, C, E and D are concyclic.

Discussion

10863.	Side BC of a triangle ABC has been produced to a point D such that ∠ACD = 120°. If ∠B = 12 ∠A is equal to(a) 80°(b) 75°(c) 60°(d) 90°
Answer» Side BC of a triangle ABC has been produced to a point D such that ∠ACD = 120°. If ∠B = $\frac{1}{2}$ ∠A is equal to (a) 80° (b) 75° (c) 60° (d) 90°

Discussion

10864.	Question 96Every whole number is a rational number
Answer» Question 96 Every whole number is a rational number

Discussion

10865.	If x100+2x99+k is divisible by (x+1), what is the value of k?
Answer» $If x^{100} + 2 x^{99} + k is divisible by (x + 1), what is the value of k?$

Discussion

10866.	Factorise:x2 + 2xy + y2 – a2 + 2ab – b2
Answer» Factorise: x²+ 2xy + y²– a² + 2ab – b²

Discussion

10867.	If the point (2, -2) lies on the graph of the linear equation 5x + ky = 4, find the value of k.
Answer» If the point (2, -2) lies on the graph of the linear equation 5x + ky = 4, find the value of k.

Discussion

10868.	Which property of a rectangle do we use to construct a rectangle given one diagonal and angle between diagonals?
Answer» Which property of a rectangle do we use to construct a rectangle given one diagonal and angle between diagonals?

Discussion

10869.	Find the Zeros of the polynomial 1.7x-2 2.14+9x
Answer» Find the Zeros of the polynomial 1.7x-2 2.14+9x

10869.

Find the Zeros of the polynomial 1.7x-2 2.14+9x

Answer»

Find the Zeros of the polynomial

1.7x-2

2.14+9x

Discussion

10870.	Factorise (5x6−7x3−6)
Answer» Factorise $(5 x^{6} - 7 x^{3} - 6)$

Discussion

10871.	Question 2 (i)Consider the following parallelograms. Find the values of the unknowns x,y,z(i)
Answer» Question 2 (i) Consider the following parallelograms. Find the values of the unknowns x,y,z (i)

Discussion

10872.	How many values of 'x' are possible such that x is a whole number less than 50 and √x is an integer.8
Answer» How many values of 'x' are possible such that x is a whole number less than 50 and $\sqrt{x}$ is an integer. 8

Discussion

10873.

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes: Outcome 3 heads 2 heads 1 head No Head Frequency 23 72 77 28 Find the experimental probability of getting(i) 2 Heads(ii) at least 2 Heads

Answer» Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome	3 heads	2 heads	1 head	No Head
Frequency	23	72	77	28

Find the experimental probability of getting

(i) 2 Heads

(ii) at least 2 Heads

Discussion

10874.	The medians of a triangle ABC is intersect at G. Then
Answer» The medians of a triangle ABC is intersect at G. Then

Discussion

10875.	Which of the following is not an irrational number?
Answer» Which of the following is not an irrational number?

Discussion

10876.	Explain the meaning of each of the following terms:(i) Variate(ii) Class interval(iii) Class size(iv) Class mark(v) Class limit(vi) True class limits(vii) Frequency of a class(viii) Cumulative frequency of a class
Answer» Explain the meaning of each of the following terms: (i) Variate (ii) Class interval (iii) Class size (iv) Class mark (v) Class limit (vi) True class limits (vii) Frequency of a class (viii) Cumulative frequency of a class

Discussion

10877.	The function f:A→B defined by f(x)=−x2+6x−8 is a bijection if
Answer» The function $f : A \to B$ defined by $f (x) = - x^{2} + 6 x - 8$ is a bijection if

Discussion

10878.	If a→ and b→ are two unit vectors such that a→+b→ is also a unit vector, then a⇀-b⇀ ______________________.
Answer» If $\vec{a} and \vec{b}$ are two unit vectors such that $\|\vec{a} + \vec{b}\|$ is also a unit vector, then $\|\overset{⇀}{a} - \overset{⇀}{b}\|______________________.$

Discussion

10879.	A point lies on. x axis at a distance of 9 units from y axis what are its coordinates
Answer» A point lies on. x axis at a distance of 9 units from y axis what are its coordinates

Discussion

10880.	Question 04.A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
Answer» Question 04. A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

Discussion

10881.	Find the value of 0.111.... + 0.333.....
Answer» Find the value of 0.111.... + 0.333.....

Discussion

10882.	XY and X'Y' are two parallel †an gents to a circle with center O and another †an gent AB with point of contact C intersecting XY at A and X'Y' at B.Prove that\angle AOB=90^°
Answer» XY and X'Y' are two parallel †an gents to a circle with center O and another †an gent AB with point of contact C intersecting XY at A and X'Y' at B.Prove that\angle AOB=90^°

Discussion

10883.	Angles of a quadrilateral are given as 85∘, 95∘, x∘, (x+10)∘. Find the value of x.
Answer» Angles of a quadrilateral are given as $85^{\circ}, 95^{\circ}, x^{\circ}, (x + 10)^{\circ}$ . Find the value of $x$ .

Discussion

10884.	Factorise:6x2 – 11x – 35
Answer» Factorise: 6x² – 11x – 35

Discussion

10885.	E and F are points on diagonal AC of parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.
Answer» E and F are points on diagonal AC of parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

Discussion

10886.	Express 8−4 as a power with the base 2.
Answer» Express $8^{- 4}$ as a power with the base 2.

Discussion

10887.	Question 13Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.
Answer» Question 13 Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Discussion

10888.	If x=3+2√2, then the value of (√x−1√x) = _____. 2
Answer» If $x = 3 + 2 \sqrt{2}$ , then the value of $(\sqrt{x} - \frac{1}{\sqrt{x}})$ = _____. 2

Discussion

10889.	Question 4The number of polynomials having zeroes as –2 and 5 is(A) 1(B) 2(C) 3(D) more than 3
Answer» Question 4 The number of polynomials having zeroes as –2 and 5 is (A) 1 (B) 2 (C) 3 (D) more than 3

Discussion

10890.	10 If the supplement of an angle is two third of itself, then its supplement is
Answer» 10 If the supplement of an angle is two third of itself, then its supplement is

Discussion

10891.	Using ruler and compasses only, construct a Δ ABC from the following data:AB + BC + CA = 12 cm, ∠B = 45° and ∠C = 60°.
Answer» Using ruler and compasses only, construct a Δ ABC from the following data: AB + BC + CA = 12 cm, ∠B = 45° and ∠C = 60°.

Discussion

10892.	Measure the angles given below using the Protractor and write downthe measure.
Answer» Measure the angles given below using the Protractor and write down the measure.

10892.

Measure the angles given below using the Protractor and write downthe measure.

Answer»

Measure the angles given below using the Protractor and write down
the measure.

Discussion

10893.	Irrational number between 1.011243... and 1.012243... is
Answer» Irrational number between 1.011243... and 1.012243... is

Discussion

10894.	In the given figure, circles with centres X and Y touch internally at point Z . Seg BZ is a chord of bigger circle and it itersects smaller circle at point A. Prove that, seg AX \|\| seg BY.
Answer» In the given figure, circles with centres X and Y touch internally at point Z . Seg BZ is a chord of bigger circle and it itersects smaller circle at point A. Prove that, seg AX \|\| seg BY.

Discussion

10895.	Let ABC be an equilateral triangle. The bisector of ∠BAC meets the circumcircle of ABC in D. Suppose DB + DC = 4. The diameter of the circumcircle of triangle ABC is
Answer» Let ABC be an equilateral triangle. The bisector of ∠BAC meets the circumcircle of ABC in D. Suppose DB + DC = 4. The diameter of the circumcircle of triangle ABC is

Discussion

10896.	If roots of the equation x4−8x3+bx2+cx+16=0 are positive, then
Answer» If roots of the equation $x^{4} - 8 x^{3} + b x^{2} + c x + 16 = 0$ are positive, then

Discussion

10897.	If 3a+2b+4c=0, then show that the equation ax+by+c=0 represents a family of concurrent straight lines and find the point of concurrency.
Answer» If 3a+2b+4c=0, then show that the equation ax+by+c=0 represents a family of concurrent straight lines and find the point of concurrency.

Discussion

10898.	Find three different irrational no between the rational numbers 5/7 & 9/11
Answer» Find three different irrational no between the rational numbers 5/7 & 9/11

Discussion

10899.	14 If the line y-3x+3=0 cuts the parabola y=x+2 at A and B.If P(3,0) then PA.PB is
Answer» 14 If the line y-3x+3=0 cuts the parabola y=x+2 at A and B.If P(3,0) then PA.PB is

Discussion

10900.	The base of a prism is a right angled triangle with dimensions as follows:Base = 15 cmAltitude = 8 cmIf the height of the prism is 20 cm, find the total surface area of the prism.
Answer» The base of a prism is a right angled triangle with dimensions as follows: Base = 15 cm Altitude = 8 cm If the height of the prism is 20 cm, find the total surface area of the prism.

Discussion

Explore topic-wise InterviewSolutions in .

If I draw two circles of radius 3 cm and 5cm with common centre and draw a line AB such that it is a chord to both the circles and length of CD is 2√5 cm, then find the distance of the chords from the centre and the length AC.

The graph of y = p(x) is given. Assuming p(x) increases from x=10, the number of zeroes of y = p(x) is ___.

limx→1 xm-1xn-1 is​(a) 1 (b) mn (c) -mn (d) m2n2

Study the table given below and draw a line graph for it. Side of the square (in cm) 2 3 3.5 5 6 Perimeter (in cm) 8 12 14 20 24 Is the graph drawn, a linear graph?

If sinA=12 and cosB=1√2,then find the value of (A+B).

In the figure, AB || CD and ∠1 and ∠2 are in the ratio 3:2. Determine all angles from 1 to 8.

The figure given below shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CD =16 cm and EB = 4 cm, then find the radius of the circle.

In the given figure, the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR=∠QPR.

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A∪B

A cone of radius 3 cm and slant height 5 cm has curved surface area of ___ cm2.

Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.

D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE. Prove that the points B, C, E and D are concyclic.

Side BC of a triangle ABC has been produced to a point D such that ∠ACD = 120°. If ∠B = 12 ∠A is equal to(a) 80°(b) 75°(c) 60°(d) 90°

Question 96Every whole number is a rational number

If x100+2x99+k is divisible by (x+1), what is the value of k?

Factorise:x2 + 2xy + y2 – a2 + 2ab – b2

If the point (2, -2) lies on the graph of the linear equation 5x + ky = 4, find the value of k.

Which property of a rectangle do we use to construct a rectangle given one diagonal and angle between diagonals?

Find the Zeros of the polynomial 1.7x-2 2.14+9x

Factorise (5x6−7x3−6)

Question 2 (i)Consider the following parallelograms. Find the values of the unknowns x,y,z(i)

How many values of 'x' are possible such that x is a whole number less than 50 and √x is an integer.8

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes: Outcome 3 heads 2 heads 1 head No Head Frequency 23 72 77 28 Find the experimental probability of getting(i) 2 Heads(ii) at least 2 Heads

The medians of a triangle ABC is intersect at G. Then

Which of the following is not an irrational number?

Explain the meaning of each of the following terms:(i) Variate(ii) Class interval(iii) Class size(iv) Class mark(v) Class limit(vi) True class limits(vii) Frequency of a class(viii) Cumulative frequency of a class

The function f:A→B defined by f(x)=−x2+6x−8 is a bijection if

If a→ and b→ are two unit vectors such that a→+b→ is also a unit vector, then a⇀-b⇀ ______________________.

A point lies on. x axis at a distance of 9 units from y axis what are its coordinates

Question 04.A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

Find the value of 0.111.... + 0.333.....

XY and X'Y' are two parallel †an gents to a circle with center O and another †an gent AB with point of contact C intersecting XY at A and X'Y' at B.Prove that\angle AOB=90^°

Angles of a quadrilateral are given as 85∘, 95∘, x∘, (x+10)∘. Find the value of x.

Factorise:6x2 – 11x – 35

E and F are points on diagonal AC of parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

Express 8−4 as a power with the base 2.

Question 13Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

If x=3+2√2, then the value of (√x−1√x) = _____. 2

Question 4The number of polynomials having zeroes as –2 and 5 is(A) 1(B) 2(C) 3(D) more than 3

10 If the supplement of an angle is two third of itself, then its supplement is

Using ruler and compasses only, construct a Δ ABC from the following data:AB + BC + CA = 12 cm, ∠B = 45° and ∠C = 60°.

Measure the angles given below using the Protractor and write downthe measure.

Irrational number between 1.011243... and 1.012243... is

In the given figure, circles with centres X and Y touch internally at point Z . Seg BZ is a chord of bigger circle and it itersects smaller circle at point A. Prove that, seg AX || seg BY.

Let ABC be an equilateral triangle. The bisector of ∠BAC meets the circumcircle of ABC in D. Suppose DB + DC = 4. The diameter of the circumcircle of triangle ABC is

If roots of the equation x4−8x3+bx2+cx+16=0 are positive, then

If 3a+2b+4c=0, then show that the equation ax+by+c=0 represents a family of concurrent straight lines and find the point of concurrency.

Find three different irrational no between the rational numbers 5/7 & 9/11

14 If the line y-3x+3=0 cuts the parabola y=x+2 at A and B.If P(3,0) then PA.PB is

The base of a prism is a right angled triangle with dimensions as follows:Base = 15 cmAltitude = 8 cmIf the height of the prism is 20 cm, find the total surface area of the prism.

limx→1 xm-1xn-1 is(a) 1 (b) mn (c) -mn (d) m2n2