32581 + Interview Questions in Mathematics Page 272 InterviewSolution

13551.	There are two temples one on each Bank of river just opposite to each other. Once temple is 50m high from the top of the temple. The angles of depression of the top and foot of other temple are 30 degree and 60 degree. Find the width of the river and the height of the other temple.
Answer» There are two temples one on each Bank of river just opposite to each other. Once temple is 50m high from the top of the temple. The angles of depression of the top and foot of other temple are 30 degree and 60 degree. Find the width of the river and the height of the other temple.

Discussion

13552.	A plumb line (sahul) is the combination of a _________ and a _________.
Answer» A plumb line (sahul) is the combination of a _________ and a _________.

Discussion

13553.	A card is drawn from a well- shuffled pack of 52 cards. Find the probability of getting (i) a red face card (ii) a black king.
Answer» A card is drawn from a well- shuffled pack of 52 cards. Find the probability of getting (i) a red face card (ii) a black king.

Discussion

13554.	Find sum of all 3 digit number which leaves reminder 3 when divided by 5.
Answer» Find sum of all 3 digit number which leaves reminder 3 when divided by 5.

Discussion

13555.	Mark the correct alternative in the following question:8 men can finish a piece of work in 40 days. If 2 more men join them, then the work will be computed in(a) 30 days (b) 32 days (c) 36 days (d) 25 days
Answer» Mark the correct alternative in the following question: 8 men can finish a piece of work in 40 days. If 2 more men join them, then the work will be computed in (a) 30 days (b) 32 days (c) 36 days (d) 25 days

Discussion

13556.	Question 74 In the year 2001, the number of malaria patients admitted in the hospitals of a state was 4375. Every year this number decreases by 8%. Find the number of patients in 2003.
Answer» Question 74 In the year 2001, the number of malaria patients admitted in the hospitals of a state was 4375. Every year this number decreases by 8%. Find the number of patients in 2003.

13556.

Question 74 In the year 2001, the number of malaria patients admitted in the hospitals of a state was 4375. Every year this number decreases by 8%. Find the number of patients in 2003.

Answer»

Question 74

In the year 2001, the number of malaria patients admitted in the hospitals of a state was 4375. Every year this number decreases by 8%. Find the number of patients in 2003.

Discussion

13557.	If length of a diagonal of a rhombus is 30 cm and its area is 240 sq cm, find its perimeter.
Answer» If length of a diagonal of a rhombus is 30 cm and its area is 240 sq cm, find its perimeter.

Discussion

13558.	Find the distance of the point (1, 2) from the mid-point of the line segment joining the points (6, 8) and (2, 4).
Answer» Find the distance of the point (1, 2) from the mid-point of the line segment joining the points (6, 8) and (2, 4).

Discussion

13559.	Solve the following systems of equations: 3x−y+711+2=10 2y+x+117=10
Answer» Solve the following systems of equations: $3 x - \frac{y + 7}{11} + 2 = 10$ $2 y + \frac{x + 11}{7} = 10$

13559.

Solve the following systems of equations: 3x−y+711+2=10 2y+x+117=10

Answer»

Solve the following systems of equations:

$3 x - \frac{y + 7}{11} + 2 = 10$

$2 y + \frac{x + 11}{7} = 10$

Discussion

13560.	Prove that the points (3, 0), (6, 4) and (-1, 3) are verticies of a right-angled isoceles triangle.
Answer» Prove that the points (3, 0), (6, 4) and (-1, 3) are verticies of a right-angled isoceles triangle.

Discussion

13561.	In the given figure, PT touches the circle with centre O at point R. Diameter SQ is produced to meet the tangent TR at P. Given ∠SPR = xo and ∠QRP = yo prove that: (i) ∠ORS = yo (ii) write an expression connecting x and y.
Answer» In the given figure, PT touches the circle with centre O at point R. Diameter SQ is produced to meet the tangent TR at P. Given $∠ S P R = x^{o}$ and $∠ Q R P = y^{o}$ prove that: (i) $∠ O R S = y^{o}$ (ii) write an expression connecting x and y.

13561.

In the given figure, PT touches the circle with centre O at point R. Diameter SQ is produced to meet the tangent TR at P. Given ∠SPR = xo and ∠QRP = yo prove that: (i) ∠ORS = yo (ii) write an expression connecting x and y.

Answer»

In the given figure, PT touches the circle with centre O at point R. Diameter SQ is produced to meet the tangent TR at P.

Given $∠ S P R = x^{o}$ and $∠ Q R P = y^{o}$

prove that:

(i) $∠ O R S = y^{o}$

(ii) write an expression connecting x and y.

Discussion

13562.	what is elecrticity in general form
Answer» what is elecrticity in general form

Discussion

13563.	How cos theta is equals to a/√r^2+a2 ??
Answer» How cos theta is equals to a/√r^2+a2 ??

Discussion

13564.	GURU was born in AD 1809. in the year x2AD he was x-3 years old. find the value of x
Answer» GURU was born in AD 1809. in the year x2AD he was x-3 years old. find the value of x

Discussion

13565.	Construct a circle in a regular hexagon of side 3 cm.
Answer» Construct a circle in a regular hexagon of side 3 cm.

Discussion

13566.	If α and β are the zeros of the quadratic polynomial f(x) = x2 − p(x + 1) − c, show that (α + 1) (β + 1) = 1 − c.
Answer» If α and β are the zeros of the quadratic polynomial f(x) = x² − p(x + 1) − c, show that (α + 1) (β + 1) = 1 − c.

Discussion

13567.	In the given figure, A, B and C are three points on the circle with centre O such that ∠BOC=30∘ and ∠AOB=60∘. If D is a point on the circle that is not on the arc ABC, then find ∠ADC.
Answer» In the given figure, A, B and C are three points on the circle with centre O such that $∠ B O C = 30^{\circ}$ and $∠ A O B = 60^{\circ}$ . If D is a point on the circle that is not on the arc ABC, then find $∠ A D C .$

Discussion

13568.	Question 1 If cosA=45, then the value of tan A is (A) 35 (B) 34 (C) 43 (D) 53
Answer» Question 1 If $c o s A = \frac{4}{5}$ , then the value of tan A is (A) $\frac{3}{5}$ (B) $\frac{3}{4}$ (C) $\frac{4}{3}$ (D) $\frac{5}{3}$

Discussion

13569.	A bag contains coins numbered from 1 to 50. If one coin is picked up at random, find the probability that it bears a square number.
Answer» A bag contains coins numbered from 1 to 50. If one coin is picked up at random, find the probability that it bears a square number.

Discussion

13570.	Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.
Answer» Find the $31^{st}$ term of an AP whose $11^{th}$ term is 38 and $16^{th}$ term is 73.

Discussion

13571.	If O is the center of the circle, then the value of θ in the adjoining figure is
Answer» If O is the center of the circle, then the value of $θ$ in the adjoining figure is

Discussion

13572.

The weights of tea in 70 packets are shown in the following table: Weight (in grams) 200−201 201−202 202−203 203−204 204−205 205−206 Number of packets 13 27 18 10 1 1 Find the mean weight of packets using step-deviation method. [CBSE 2013]

Answer» The weights of tea in 70 packets are shown in the following table:

Weight (in grams)	200−201	201−202	202−203	203−204	204−205	205−206
Number of packets	13	27	18	10	1	1

Find the mean weight of packets using step-deviation method. [CBSE 2013]

Discussion

13573.	Question 19Find the values of k, if the points A(k+1, 2k), B(3k,2k+3) and C(5k-1,5k) are collinear.
Answer» Question 19 Find the values of k, if the points A(k+1, 2k), B(3k,2k+3) and C(5k-1,5k) are collinear.

Discussion

13574.	The Mean weight of 60 Students in a class is 60 kgs. The Mean weight of boys is 70 kgs while that of girls is 55 kgs. Find the number of boys and girls in the class respectively.
Answer» The Mean weight of 60 Students in a class is 60 kgs. The Mean weight of boys is 70 kgs while that of girls is 55 kgs. Find the number of boys and girls in the class respectively.

13574.

The Mean weight of 60 Students in a class is 60 kgs. The Mean weight of boys is 70 kgs while that of girls is 55 kgs. Find the number of boys and girls in the class respectively.

Answer»

The Mean weight of 60 Students in a class is 60 kgs. The Mean weight of boys is 70 kgs while that of girls is 55 kgs.

Find the number of boys and girls in the class respectively.

Discussion

13575.	In the given figure, O is the centre of the circle ∠PBA=45∘. The value of ∠PQB is
Answer» In the given figure, O is the centre of the circle $∠ P B A = 45^{\circ}$ . The value of $∠ P Q B$ is

Discussion

13576.	If the points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p. [CBSE 2015]
Answer» If the points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p. [CBSE 2015]

Discussion

13577.	Question 7(i)If each edge of a cube is doubledHow many times will its surface area increase?
Answer» Question 7(i) If each edge of a cube is doubled How many times will its surface area increase?

Discussion

13578.	Question 113From a pipe of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the piper in 1 h.
Answer» Question 113 From a pipe of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the piper in 1 h.

13578.

Question 113From a pipe of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the piper in 1 h.

Answer»

Question 113

From a pipe of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the piper in 1 h.

Discussion

13579.	31.Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side will intersect on the circumference of the triangle.
Answer» 31.Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side will intersect on the circumference of the triangle.

Discussion

13580.	13. A metallic disc is being heated. Its area A(inm2) at any time f (in second) is given by A - 5t2+ 4+rate of increase in area at t 3 s is(1) 30 m2/s) 65 m2/s(2) 24 m2/s(4) 34 m2/s
Answer» 13. A metallic disc is being heated. Its area A(in m2) at any time f (in second) is given by A - 5t2+ 4+ rate of increase in area at t 3 s is (1) 30 m2/s ) 65 m2/s (2) 24 m2/s (4) 34 m2/s

Discussion

13581.	Prove that (2√3−1) is an irrational number.
Answer» Prove that $(2 \sqrt{3} - 1)$ is an irrational number.

Discussion

13582.	Question 42The closed curve which is also a non-intersecting polygon, is:a)b)c)d)
Answer» Question 42 The closed curve which is also a non-intersecting polygon, is: a) b) c) d)

Discussion

13583.	In the figure given above, ∠DCE=20∘, ∠EDC=60∘. Find ∠CED.
Answer» In the figure given above, $∠ D C E = 20^{\circ}, ∠ E D C = 60^{\circ} .$ Find $∠ C E D .$

13583.

In the figure given above, ∠DCE=20∘, ∠EDC=60∘. Find ∠CED.

Answer»

In the figure given above, $∠ D C E = 20^{\circ}, ∠ E D C = 60^{\circ} .$ Find $∠ C E D .$

Discussion

13584.	A girls is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.
Answer» A girls is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

Discussion

13585.	AP and PQ are tangents drawn from a point A to a circle with centre O and radius 9 cm. If OA = 15 cm, then AP + AQ =(a) 12 cm(b) 18 cm(c) 24 cm(d) 36 cm
Answer» AP and PQ are tangents drawn from a point A to a circle with centre O and radius 9 cm. If OA = 15 cm, then AP + AQ = (a) 12 cm (b) 18 cm (c) 24 cm (d) 36 cm

Discussion

13586.	The sum of first m terms of an A.P. is 4m2 − m. If its nth term is 107. find the value of n. Also, find the 21st term of this A.P.
Answer» The sum of first m terms of an A.P. is 4m² − m. If its nth term is 107. find the value of n. Also, find the 21st term of this A.P.

Discussion

13587.	Using Euclid’s division algorithm, find the HCF of405 and 2520
Answer» Using Euclid’s division algorithm, find the HCF of 405 and 2520

13587.

Using Euclid’s division algorithm, find the HCF of405 and 2520

Answer»

Using Euclid’s division algorithm, find the HCF of

405 and 2520

Discussion

13588.	Show that points P(2, –2), Q(7, 3), R(11, –1) and S (6, –6) are vertices of a parallelogram.
Answer» Show that points P(2, –2), Q(7, 3), R(11, –1) and S (6, –6) are vertices of a parallelogram.

Discussion

13589.	If two positive integers m and n are expressible in the form m = pq3 and n = p3q2, where p, q are prime numbers, then HCF (m, n) =(a) pq(b) pq2(c) p3q2(d) p2q2
Answer» If two positive integers m and n are expressible in the form m = pq³ and n = p³q², where p, q are prime numbers, then HCF (m, n) = (a) pq (b) pq2 (c) p³q² (d) p²q²

Discussion

13590.	Prove that (cosec θ − sin θ) (sec θ − cos θ) = 1tan θ+cot θ.
Answer» Prove that (cosec θ − sin θ) (sec θ − cos θ) = $\frac{1}{\tan θ + c o t θ}$ .

Discussion

13591.	Value of sin(90+theta)=sin(90-theta)=cos(90+theta)=cos(90-theta)=
Answer» Value of sin(90+theta)= sin(90-theta)= cos(90+theta)= cos(90-theta)=

Discussion

13592.	Solve the following system using Cramer’s Rule.3x+5y=−7x+4y=−14
Answer» Solve the following system using Cramer’s Rule. $3 x + 5 y = - 7$ $x + 4 y = - 14$

Discussion

13593.	Find the value of the side AC of the △ABC in terms of AB, whose length is √3 units.
Answer» Find the value of the side AC of the $△$ ABC in terms of AB, whose length is $\sqrt{3}$ units.

Discussion

13594.	Insert 3 Geometric means between 1 and 9.
Answer» Insert 3 Geometric means between 1 and 9.

Discussion

13595.	In an AP. Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp+q is equal to(a) 0(b) −(p + q)(c) p + q(d) pq
Answer» In an AP. S_p = q, S_q = p and S_r denotes the sum of first r terms. Then, S_p_+q is equal to (a) 0 (b) −(p + q) (c) p + q (d) pq

Discussion

13596.	The area of a rhombus is 119 cm2 and its perimeter is 56 cm. The height of the rhombus is(a) 7.5 cm (b) 6.5 cm (c) 8.5 cm (d) 9.5 cm
Answer» The area of a rhombus is 119 cm² and its perimeter is 56 cm. The height of the rhombus is (a) 7.5 cm (b) 6.5 cm (c) 8.5 cm (d) 9.5 cm

Discussion

13597.	Find the sum of : (i) all odd natural numbers less than 50. (ii) first 12 natural numbers each of which is a multiple of 7.
Answer» Find the sum of : (i) all odd natural numbers less than 50. (ii) first 12 natural numbers each of which is a multiple of 7.

13597.

Find the sum of : (i) all odd natural numbers less than 50. (ii) first 12 natural numbers each of which is a multiple of 7.

Answer»

Find the sum of :

(i) all odd natural numbers less than 50.

(ii) first 12 natural numbers each of which is a multiple of 7.

Discussion

13598.	The height and radius of a cone are 4 cm and 3 cm respectively. The curved surface area of is is .
Answer» The height and radius of a cone are $4 c m$ and $3 c m$ respectively. The curved surface area of is is .

Discussion

13599.	Question 4 (sin α+cos α)(tan α+cot α)=sec α+cosec α
Answer» Question 4 $(s i n α + c o s α) (t a n α + c o t α) = s e c α + c o s e c α$

Discussion

13600.	A function is described as:For the function, its range will be
Answer» A function is described as: For the function, its range will be

Discussion

Explore topic-wise InterviewSolutions in .

There are two temples one on each Bank of river just opposite to each other. Once temple is 50m high from the top of the temple. The angles of depression of the top and foot of other temple are 30 degree and 60 degree. Find the width of the river and the height of the other temple.

A plumb line (sahul) is the combination of a _________ and a _________.

A card is drawn from a well- shuffled pack of 52 cards. Find the probability of getting (i) a red face card (ii) a black king.

Find sum of all 3 digit number which leaves reminder 3 when divided by 5.

Mark the correct alternative in the following question:8 men can finish a piece of work in 40 days. If 2 more men join them, then the work will be computed in(a) 30 days (b) 32 days (c) 36 days (d) 25 days

Question 74 In the year 2001, the number of malaria patients admitted in the hospitals of a state was 4375. Every year this number decreases by 8%. Find the number of patients in 2003.

If length of a diagonal of a rhombus is 30 cm and its area is 240 sq cm, find its perimeter.

Find the distance of the point (1, 2) from the mid-point of the line segment joining the points (6, 8) and (2, 4).

Solve the following systems of equations: 3x−y+711+2=10 2y+x+117=10

Prove that the points (3, 0), (6, 4) and (-1, 3) are verticies of a right-angled isoceles triangle.

In the given figure, PT touches the circle with centre O at point R. Diameter SQ is produced to meet the tangent TR at P. Given ∠SPR = xo and ∠QRP = yo prove that: (i) ∠ORS = yo (ii) write an expression connecting x and y.

what is elecrticity in general form

How cos theta is equals to a/√r^2+a2 ??

GURU was born in AD 1809. in the year x2AD he was x-3 years old. find the value of x

Construct a circle in a regular hexagon of side 3 cm.

If α and β are the zeros of the quadratic polynomial f(x) = x2 − p(x + 1) − c, show that (α + 1) (β + 1) = 1 − c.

In the given figure, A, B and C are three points on the circle with centre O such that ∠BOC=30∘ and ∠AOB=60∘. If D is a point on the circle that is not on the arc ABC, then find ∠ADC.

Question 1 If cosA=45, then the value of tan A is (A) 35 (B) 34 (C) 43 (D) 53

A bag contains coins numbered from 1 to 50. If one coin is picked up at random, find the probability that it bears a square number.

Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.

If O is the center of the circle, then the value of θ in the adjoining figure is

​The weights of tea in 70 packets are shown in the following table: Weight (in grams) 200−201 201−202 202−203 203−204 204−205 205−206 Number of packets 13 27 18 10 1 1 Find the mean weight of packets using step-deviation method. [CBSE 2013]

Question 19Find the values of k, if the points A(k+1, 2k), B(3k,2k+3) and C(5k-1,5k) are collinear.

The Mean weight of 60 Students in a class is 60 kgs. The Mean weight of boys is 70 kgs while that of girls is 55 kgs. Find the number of boys and girls in the class respectively.

In the given figure, O is the centre of the circle ∠PBA=45∘. The value of ∠PQB is

If the points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p. [CBSE 2015]

Question 7(i)If each edge of a cube is doubledHow many times will its surface area increase?

Question 113From a pipe of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the piper in 1 h.

31.Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side will intersect on the circumference of the triangle.

13. A metallic disc is being heated. Its area A(inm2) at any time f (in second) is given by A - 5t2+ 4+rate of increase in area at t 3 s is(1) 30 m2/s) 65 m2/s(2) 24 m2/s(4) 34 m2/s

Prove that (2√3−1) is an irrational number.

Question 42The closed curve which is also a non-intersecting polygon, is:a)b)c)d)

In the figure given above, ∠DCE=20∘, ∠EDC=60∘. Find ∠CED.

A girls is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

AP and PQ are tangents drawn from a point A to a circle with centre O and radius 9 cm. If OA = 15 cm, then AP + AQ =(a) 12 cm(b) 18 cm(c) 24 cm(d) 36 cm

The sum of first m terms of an A.P. is 4m2 − m. If its nth term is 107. find the value of n. Also, find the 21st term of this A.P.

Using Euclid’s division algorithm, find the HCF of405 and 2520

Show that points P(2, –2), Q(7, 3), R(11, –1) and S (6, –6) are vertices of a parallelogram.

If two positive integers m and n are expressible in the form m = pq3 and n = p3q2, where p, q are prime numbers, then HCF (m, n) =(a) pq(b) pq2(c) p3q2(d) p2q2

Prove that (cosec θ − sin θ) (sec θ − cos θ) = 1tan θ+cot θ.

Value of sin(90+theta)=sin(90-theta)=cos(90+theta)=cos(90-theta)=

Solve the following system using Cramer’s Rule.3x+5y=−7x+4y=−14

Find the value of the side AC of the △ABC in terms of AB, whose length is √3 units.

Insert 3 Geometric means between 1 and 9.

In an AP. Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp+q is equal to(a) 0(b) −(p + q)(c) p + q(d) pq

The area of a rhombus is 119 cm2 and its perimeter is 56 cm. The height of the rhombus is(a) 7.5 cm (b) 6.5 cm (c) 8.5 cm (d) 9.5 cm

Find the sum of : (i) all odd natural numbers less than 50. (ii) first 12 natural numbers each of which is a multiple of 7.

The height and radius of a cone are 4 cm and 3 cm respectively. The curved surface area of is is .

Question 4 (sin α+cos α)(tan α+cot α)=sec α+cosec α

A function is described as:For the function, its range will be

A plumb line (sahul) is the combination of a _ and a _.

The weights of tea in 70 packets are shown in the following table: Weight (in grams) 200−201 201−202 202−203 203−204 204−205 205−206 Number of packets 13 27 18 10 1 1 Find the mean weight of packets using step-deviation method. [CBSE 2013]