32581 + Interview Questions in Mathematics Page 218 InterviewSolution

10851.	The distance between the points (a cos 25°, 0) and (0, a cos 65°) is(a) a (b) 2a(c) 3a(d) None of these
Answer» The distance between the points (a cos 25°, 0) and (0, a cos 65°) is (a) a (b) 2a (c) 3a (d) None of these

Discussion

10852.	Question 3 In the given figure, ∠PQR=100∘, where P, Q and R are points on a circle with centre O. Find ∠OPR.
Answer» Question 3 In the given figure, $∠ P Q R = 100^{\circ}$ , where P, Q and R are points on a circle with centre O. Find $∠ O P R$ .

Discussion

10853.	If (x + 1) is a factor of 2x3+ax2+2bx+1, then find the values of a and b given that 2a − 3b = 4.
Answer» If (x + 1) is a factor of $2 x^{3} + a x^{2} + 2 b x + 1$ , then find the values of a and b given that 2a − 3b = 4.

Discussion

10854.	Arrange the following quadratic equations based on the ascending order of their linear coefficients.
Answer» Arrange the following quadratic equations based on the ascending order of their linear coefficients.

Discussion

10855.	In the figure below, ABCD is a rectangle with the origin O as its centre and sides parallel to the axis.What are the coordinates of B, C, D?
Answer» In the figure below, ABCD is a rectangle with the origin O as its centre and sides parallel to the axis. What are the coordinates of B, C, D?

10855.

In the figure below, ABCD is a rectangle with the origin O as its centre and sides parallel to the axis.What are the coordinates of B, C, D?

Answer»

In the figure below, ABCD is a rectangle with the origin O as its centre and sides parallel to the axis.

What are the coordinates of B, C, D?

Discussion

10856.	Assume that boy and girl babies are equally likely. If a couple have three children, find the probability that at least one is a boy.
Answer» Assume that boy and girl babies are equally likely. If a couple have three children, find the probability that at least one is a boy.

Discussion

10857.	find (1+x)6-(1-x)6 hence evaluate (1+root 3)6-(1-root 3)6
Answer» find (1+x)6-(1-x)6 hence evaluate (1+root 3)6-(1-root 3)6

Discussion

10858.	The fourth rerm from the end of the Ap:-11,-8,-5, _ 49 is
Answer» The fourth rerm from the end of the Ap:-11,-8,-5, _ 49 is

Discussion

10859.	For what value of a the point (a, 1), (1, -1) and (11, 4) are collinear?
Answer» For what value of a the point (a, 1), (1, -1) and (11, 4) are collinear?

Discussion

10860.	Two men on either side of the cliff 80 m high observes the angles of a elevation of the top of the cliff to be 30° and 60° respectively. Find the distance between the two men.
Answer» Two men on either side of the cliff 80 m high observes the angles of a elevation of the top of the cliff to be 30° and 60° respectively. Find the distance between the two men.

Discussion

10861.	Find the roots of the quadratic equation √2x2 + 7x + 5√2 = 0 .
Answer» Find the roots of the quadratic equation $\sqrt{2}$ $x^{2}$ + 7x + 5 $\sqrt{2}$ = 0 .

Discussion

10862.	To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80∘ to a distance of 16.5 km. Find the area in km2 of the sea over which the ships are warned. (Use π = 3.14)
Answer» To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $80^{\circ}$ to a distance of 16.5 km. Find the area in $k m^{2}$ of the sea over which the ships are warned. (Use $π$ = 3.14)

Discussion

10863.

Prepare the Vouchers to be recorded in the books of M/s. Computer Aids: 2018 ₹ Jan. 1 Bought computer for resale for cash vide Cash Memo No. 512* 7,200 Jan. 8 Salary paid for the month of December, 2017 10,000 Jan. 10 Sold computer for cash vide Cash Memo No. 64* 12,000 Jan. 15 Withdraw cash from bank for office use vide cheque No.13456 1,700 Transactions marked with * are subject to levy of CGST and SGST 6% each.

Answer» Prepare the Vouchers to be recorded in the books of M/s. Computer Aids:

2018		₹
Jan. 1	Bought computer for resale for cash vide Cash Memo No. 512*	7,200
Jan. 8	Salary paid for the month of December, 2017	10,000
Jan. 10	Sold computer for cash vide Cash Memo No. 64*	12,000
Jan. 15	Withdraw cash from bank for office use vide cheque No.13456	1,700

Transactions marked with * are subject to levy of CGST and SGST 6% each.

Discussion

10864.	The sum of the numerator and denominator of a fraction is 4 more than twice the numerator.If the numerator and denominator are increased by 3, they are in the ratio 2:3.Determine the fraction.
Answer» The sum of the numerator and denominator of a fraction is 4 more than twice the numerator.If the numerator and denominator are increased by 3, they are in the ratio 2:3.Determine the fraction.

Discussion

10865.	If the point C(k, 4) divides the join of A(2, 6) and B(5, 1) in the ratio 2 : 3 then find the value of k. [CBSE 2013C]
Answer» If the point C(k, 4) divides the join of A(2, 6) and B(5, 1) in the ratio 2 : 3 then find the value of k. [CBSE 2013C]

Discussion

10866.	A bag contains 6 black, 7 red and 2 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is black or white.
Answer» A bag contains 6 black, 7 red and 2 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is black or white.

Discussion

10867.	cos 1° cos 2° cos 3° ... cos 180° = ?(a) 0(b) 1(c) –1(d) 12
Answer» cos 1° cos 2° cos 3° ... cos 180° = ? (a) 0 (b) 1 (c) –1 (d) $\frac{1}{2}$

Discussion

10868.	Question 6 A shuttle cock used for playing badminton has the shape of the combination of (A) a cylinder and a sphere (B) a cylinder and a hemisphere (C) a sphere and a cone (D) frustum of a cone and a hemisphere
Answer» Question 6 A shuttle cock used for playing badminton has the shape of the combination of (A) a cylinder and a sphere (B) a cylinder and a hemisphere (C) a sphere and a cone (D) frustum of a cone and a hemisphere

Discussion

10869.	The sum of the radii of two circles is 140 cm and the difference of their circumferences is 88 cm. Find the diameters of the circles.
Answer» The sum of the radii of two circles is 140 cm and the difference of their circumferences is 88 cm. Find the diameters of the circles.

Discussion

10870.	8. find the numbers of 6 digit numbers formed by 1,2,3,4,5,6. that are divisible by 6
Answer» 8. find the numbers of 6 digit numbers formed by 1,2,3,4,5,6. that are divisible by 6

Discussion

10871.	the first term of infinite GP is k and its sum is 12 then the range of k is
Answer» the first term of infinite GP is k and its sum is 12 then the range of k is

Discussion

10872.	Question 20(i)Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is 7?
Answer» Question 20(i) Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is 7?

Discussion

10873.	A man rowing a boat away from a lighthouse which is 100m high takes 2 mins to change the angle of elevation of the lighthouse from 60∘ to 45∘. The speed of the boat is:
Answer» A man rowing a boat away from a lighthouse which is 100m high takes 2 mins to change the angle of elevation of the lighthouse from $60^{\circ} t o 45^{\circ}$ . The speed of the boat is:

Discussion

10874.	Burst out the irrational numbers.
Answer» Burst out the irrational numbers.

Discussion

10875.	Pass necessary Journal entries relating to the issue of debentures for the following:(a) Issued ₹ 4,00,000; 9% Debentures of ₹ 100 each at a premium of 8% redeemable at 10% premium.(b) Issued ₹ 6,00,000; 9% Debentures of ₹ 100 each at par, repayable at a premium of 10%.(c) Issued ₹ 10,00,000; 9% Debentures of ₹ 100 each at a premium of 5%, redeemable at par.
Answer» Pass necessary Journal entries relating to the issue of debentures for the following: (a) Issued ₹ 4,00,000; 9% Debentures of ₹ 100 each at a premium of 8% redeemable at 10% premium. (b) Issued ₹ 6,00,000; 9% Debentures of ₹ 100 each at par, repayable at a premium of 10%. (c) Issued ₹ 10,00,000; 9% Debentures of ₹ 100 each at a premium of 5%, redeemable at par.

Discussion

10876.	Let Tr be the rth term of an A.P. for r = 1, 2, 3, - - - - -. If T3=18 nd T6=39, find T18.
Answer» Let $T_{r}$ be the $r^{t h}$ term of an A.P. for r = 1, 2, 3, - - - - -. If $T_{3} = 18$ nd $T_{6} = 39$ , find $T_{18}$ .

Discussion

10877.	When a dice is thrown, the total number of possible outcomes is(a) 6 (b) 1 (c) 3 (d) 4
Answer» When a dice is thrown, the total number of possible outcomes is (a) 6 (b) 1 (c) 3 (d) 4

Discussion

10878.	The length of the tangent from a point A at a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle is(a) 7 cm(b) 7 cm(c) 5 cm(d) 25 cm
Answer» The length of the tangent from a point A at a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle is (a) $\sqrt{7} c m$ (b) 7 cm (c) 5 cm (d) 25 cm

Discussion

10879.	If from a positive number, twice its reciprocal is subtracted, we get 1. Then the number is ___.
Answer» If from a positive number, twice its reciprocal is subtracted, we get 1. Then the number is ___.

Discussion

10880.	Show that: (i) 1−sin 60∘cos 60∘=tan 60∘−1tan 60∘+1 (ii) cos 30∘+sin 60∘1+sin 30∘+cos 60∘=cos 30∘
Answer» Show that: (i) $\frac{1 - sin 60^{\circ}}{cos 60^{\circ}} = \frac{tan 60^{\circ} - 1}{tan 60^{\circ} + 1}$ (ii) $\frac{cos 30^{\circ} + sin 60^{\circ}}{1 + sin 30^{\circ} + cos 60^{\circ}} = cos 30^{\circ}$

10880.

Show that: (i) 1−sin 60∘cos 60∘=tan 60∘−1tan 60∘+1 (ii) cos 30∘+sin 60∘1+sin 30∘+cos 60∘=cos 30∘

Answer»

Show that:

(i) $\frac{1 - sin 60^{\circ}}{cos 60^{\circ}} = \frac{tan 60^{\circ} - 1}{tan 60^{\circ} + 1}$

(ii) $\frac{cos 30^{\circ} + sin 60^{\circ}}{1 + sin 30^{\circ} + cos 60^{\circ}} = cos 30^{\circ}$

Discussion

10881.	Perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone.
Answer» Perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone.

Discussion

10882.	PQRS is a cyclic quadrilateral. Given ∠QPS =730, ∠PQS=550 and ∠PSR=820. Find ∠RQS
Answer» PQRS is a cyclic quadrilateral. Given ∠QPS =73⁰, ∠PQS=55⁰ and ∠PSR=82⁰. Find ∠RQS

Discussion

10883.	Question 8 A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
Answer» Question 8 A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

Discussion

10884.	identify how many monochloroderivative will form in C- C- C- C- C I C
Answer» identify how many monochloroderivative will form in C- C- C- C- C I C

Discussion

10885.	A well of diameter 14m is dug 8m deep. The earth taken out of it is evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment( in cm).
Answer» A well of diameter 14m is dug 8m deep. The earth taken out of it is evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment( in cm).

Discussion

10886.	In a circle of radius 14 cm, an arc subtends an angle of 120° at the centre. If 3= 1.73 then the area of the segment of the circle is(a) 120.56 cm2(b) 124.63 cm2(c) 118.24 cm2(d) 130.57 cm2
Answer» In a circle of radius 14 cm, an arc subtends an angle of 120° at the centre. If $\sqrt{3}$ = 1.73 then the area of the segment of the circle is (a) 120.56 cm² (b) 124.63 cm² (c) 118.24 cm² (d) 130.57 cm²

Discussion

10887.	The locus of the point which moves in such a way that its distance from the line y=−6 is always equal to 1 unit is
Answer» The locus of the point which moves in such a way that its distance from the line $y = - 6$ is always equal to 1 unit is

Discussion

10888.	Question 3To divide a line segment AB in the ratio 5:6, draw AX such that ∠ BAX is an acute angle, the draw a ray by parallel to AX and the points A1,A2,A3... and B1,B2,B3... are located to equal distances on ray AX and BY, respectively. Then, the points joined are(A) A5 and B6(B) A6 and B5(C) A4 and B5(D) A5 and B4
Answer» Question 3 To divide a line segment AB in the ratio 5:6, draw AX such that $∠$ BAX is an acute angle, the draw a ray by parallel to AX and the points $A_{1}, A_{2}, A_{3} . . .$ and $B_{1}, B_{2}, B_{3} . . .$ are located to equal distances on ray AX and BY, respectively. Then, the points joined are (A) $A_{5}$ and $B_{6}$ (B) $A_{6}$ and $B_{5}$ (C) $A_{4}$ and $B_{5}$ (D) $A_{5}$ and $B_{4}$

Discussion

10889.	16. Let p(x)be a polynomial,when divide by (x-19) gives 91 as a remainder and when divided by (x-91) gives 19 as remainder.Find the remainder when p(x) is divided by (x-19) (x-91).
Answer» 16. Let p(x)be a polynomial,when divide by (x-19) gives 91 as a remainder and when divided by (x-91) gives 19 as remainder.Find the remainder when p(x) is divided by (x-19) (x-91).

Discussion

10890.	In a trapezium ABCD, AB\|\| DC and DC = 2AB, FE drawn parallel to AB cuts AD in F and BC in E such that 4BE = 3EC. Diagonal DB intersects EF at G. Prove that 7FE = 10 AB. [4 MARKS]
Answer» In a trapezium ABCD, AB\|\| DC and DC = 2AB, FE drawn parallel to AB cuts AD in F and BC in E such that 4BE = 3EC. Diagonal DB intersects EF at G. Prove that 7FE = 10 AB. [4 MARKS]

Discussion

10891.	The mode is the
Answer» The mode is the

Discussion

10892.	Find the mirror image of the figure about the given line.
Answer» Find the mirror image of the figure about the given line.

Discussion

10893.	Which of the following options are equal to √1+cos A1−cos A ?
Answer» Which of the following options are equal to $\sqrt{\frac{1 + c o s A}{1 - c o s A}} ?$

Discussion

10894.	Question 2A surahi is the combination of(A) a sphere and a cylinder(B) a hemisphere and a cylinder(C) two hemispheres(D) a cylinder and a cone
Answer» Question 2 A surahi is the combination of (A) a sphere and a cylinder (B) a hemisphere and a cylinder (C) two hemispheres (D) a cylinder and a cone

Discussion

10895.	Proof for binomial theorem
Answer» Proof for binomial theorem

Discussion

10896.	The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm, respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder. [CBSE 2012]
Answer» The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm, respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder. [CBSE 2012]

Discussion

10897.	if 2 vertices of a right isosceles triangle are A(-1,-7) and B(-7,-1) then find C(x,y) when C= 90 degree
Answer» if 2 vertices of a right isosceles triangle are A(-1,-7) and B(-7,-1) then find C(x,y) when C= 90 degree

Discussion

10898.	In a ∆ABC, ∠A = x°, ∠B = 3x° and ∠C = y°. If 3y − 5x = 30, prove that the triangle is right angled.
Answer» In a ∆ABC, ∠A = x°, ∠B = 3x° and ∠C = y°. If 3y − 5x = 30, prove that the triangle is right angled.

Discussion

10899.	Find the annual income derived from 800 shares , at ₹ 40 shares paying 25% dividend.
Answer» Find the annual income derived from 800 shares , at ₹ 40 shares paying $25 %$ dividend.

Discussion

10900.

Question 11The volume of a cube is 64 cm3. Its surface area is(a) 16 cm2 (b) 64 cm2(c) 96 cm2 (d) 128 cm2

Answer»

Question 11

The volume of a cube is $64 c m^{3} .$ Its surface area is

(a) $16 c m^{2}$ (b) $64 c m^{2}$

(c) $96 c m^{2}$ (d) $128 c m^{2}$

Discussion

Explore topic-wise InterviewSolutions in .

The distance between the points (a cos 25°, 0) and (0, a cos 65°) is(a) a (b) 2a(c) 3a(d) None of these

Question 3 In the given figure, ∠PQR=100∘, where P, Q and R are points on a circle with centre O. Find ∠OPR.

If (x + 1) is a factor of 2x3+ax2+2bx+1, then find the values of a and b given that 2a − 3b = 4.

Arrange the following quadratic equations based on the ascending order of their linear coefficients.

In the figure below, ABCD is a rectangle with the origin O as its centre and sides parallel to the axis.What are the coordinates of B, C, D?

Assume that boy and girl babies are equally likely. If a couple have three children, find the probability that at least one is a boy.

find (1+x)6-(1-x)6 hence evaluate (1+root 3)6-(1-root 3)6

The fourth rerm from the end of the Ap:-11,-8,-5, _ 49 is

For what value of a the point (a, 1), (1, -1) and (11, 4) are collinear?

Two men on either side of the cliff 80 m high observes the angles of a elevation of the top of the cliff to be 30° and 60° respectively. Find the distance between the two men.

Find the roots of the quadratic equation √2x2 + 7x + 5√2 = 0 .

To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80∘ to a distance of 16.5 km. Find the area in km2 of the sea over which the ships are warned. (Use π = 3.14)

The sum of the numerator and denominator of a fraction is 4 more than twice the numerator.If the numerator and denominator are increased by 3, they are in the ratio 2:3.Determine the fraction.

If the point C(k, 4) divides the join of A(2, 6) and B(5, 1) in the ratio 2 : 3 then find the value of k. [CBSE 2013C]

A bag contains 6 black, 7 red and 2 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is black or white.

cos 1° cos 2° cos 3° ... cos 180° = ?(a) 0(b) 1(c) –1(d) 12

Question 6 A shuttle cock used for playing badminton has the shape of the combination of (A) a cylinder and a sphere (B) a cylinder and a hemisphere (C) a sphere and a cone (D) frustum of a cone and a hemisphere

The sum of the radii of two circles is 140 cm and the difference of their circumferences is 88 cm. Find the diameters of the circles.

8. find the numbers of 6 digit numbers formed by 1,2,3,4,5,6. that are divisible by 6

the first term of infinite GP is k and its sum is 12 then the range of k is

Question 20(i)Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is 7?

A man rowing a boat away from a lighthouse which is 100m high takes 2 mins to change the angle of elevation of the lighthouse from 60∘ to 45∘. The speed of the boat is:

Burst out the irrational numbers.

Let Tr be the rth term of an A.P. for r = 1, 2, 3, - - - - -. If T3=18 nd T6=39, find T18.

When a dice is thrown, the total number of possible outcomes is(a) 6 (b) 1 (c) 3 (d) 4

The length of the tangent from a point A at a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle is(a) 7 cm(b) 7 cm(c) 5 cm(d) 25 cm

If from a positive number, twice its reciprocal is subtracted, we get 1. Then the number is ___.

Show that: (i) 1−sin 60∘cos 60∘=tan 60∘−1tan 60∘+1 (ii) cos 30∘+sin 60∘1+sin 30∘+cos 60∘=cos 30∘

Perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone.

PQRS is a cyclic quadrilateral. Given ∠QPS =730, ∠PQS=550 and ∠PSR=820. Find ∠RQS

Question 8 A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

identify how many monochloroderivative will form in C- C- C- C- C I C

A well of diameter 14m is dug 8m deep. The earth taken out of it is evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment( in cm).

In a circle of radius 14 cm, an arc subtends an angle of 120° at the centre. If 3= 1.73 then the area of the segment of the circle is(a) 120.56 cm2(b) 124.63 cm2(c) 118.24 cm2(d) 130.57 cm2

The locus of the point which moves in such a way that its distance from the line y=−6 is always equal to 1 unit is

16. Let p(x)be a polynomial,when divide by (x-19) gives 91 as a remainder and when divided by (x-91) gives 19 as remainder.Find the remainder when p(x) is divided by (x-19) (x-91).

In a trapezium ABCD, AB|| DC and DC = 2AB, FE drawn parallel to AB cuts AD in F and BC in E such that 4BE = 3EC. Diagonal DB intersects EF at G. Prove that 7FE = 10 AB. [4 MARKS]

The mode is the

Find the mirror image of the figure about the given line.

Which of the following options are equal to √1+cos A1−cos A ?

Question 2A surahi is the combination of(A) a sphere and a cylinder(B) a hemisphere and a cylinder(C) two hemispheres(D) a cylinder and a cone

Proof for binomial theorem

The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm, respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder. [CBSE 2012]

if 2 vertices of a right isosceles triangle are A(-1,-7) and B(-7,-1) then find C(x,y) when C= 90 degree

In a ∆ABC, ∠A = x°, ∠B = 3x° and ∠C = y°. If 3y − 5x = 30, prove that the triangle is right angled.

Find the annual income derived from 800 shares , at ₹ 40 shares paying 25% dividend.

Question 11The volume of a cube is 64 cm3. Its surface area is(a) 16 cm2 (b) 64 cm2(c) 96 cm2 (d) 128 cm2