32581 + Interview Questions in Mathematics Page 258 InterviewSolution

12851.	Prove the following trigonometric identities.1-cos A1+cos A+1+cos A1-cos A=2 cosec A
Answer» Prove the following trigonometric identities. $\sqrt{\frac{1 - \cos A}{1 + \cos A}} + \sqrt{\frac{1 + \cos A}{1 - \cos A}} = 2 \cos e c A$

Discussion

12852.	Shweta, Piyush and Nachiket together invested 80000 rupees and started a business of selling sheets and towels from Solapur. Shweta’s share of the capital was 30000 rupees and Piyush’s 12000. At the end of the year they had made a profit of 24%. What was Nachiket’s investment and what was his share of the profit?
Answer» Shweta, Piyush and Nachiket together invested 80000 rupees and started a business of selling sheets and towels from Solapur. Shweta’s share of the capital was 30000 rupees and Piyush’s 12000. At the end of the year they had made a profit of 24%. What was Nachiket’s investment and what was his share of the profit?

Discussion

12853.	A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see the given figure). Find(i) The area of that part of the field in which the horse can graze.(ii) The increase in the grazing area of the rope were 10 m long instead of 5 m.[Use π = 3.14]
Answer» A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see the given figure). Find (i) The area of that part of the field in which the horse can graze. (ii) The increase in the grazing area of the rope were 10 m long instead of 5 m. [Use π = 3.14]

12853.

A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see the given figure). Find(i) The area of that part of the field in which the horse can graze.(ii) The increase in the grazing area of the rope were 10 m long instead of 5 m.[Use π = 3.14]

Answer»

A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see the given figure). Find

(i) The area of that part of the field in which the horse can graze.

(ii) The increase in the grazing area of the rope were 10 m long instead of 5 m.

[Use π = 3.14]

Discussion

12854.	Find compound Interst of 6 six monthly (P=20000, R=5%, N=2 years)
Answer» Find compound Interst of 6 six monthly (P=20000, R=5%, N=2 years)

Discussion

12855.	A bucket is in the form of a frustum of a cone and holds 15.25 litres of water. The diameters of the top and bottom are 25 cm and 20 cm respectively. Find its height and area of tin used in its construction.
Answer» A bucket is in the form of a frustum of a cone and holds 15.25 litres of water. The diameters of the top and bottom are 25 cm and 20 cm respectively. Find its height and area of tin used in its construction.

Discussion

12856.	Given that 2 is irrational, prove that 5+32 is an irrational number.
Answer» Given that $\sqrt{2}$ is irrational, prove that $(5 + 3 \sqrt{2})$ is an irrational number.

Discussion

12857.	What are the roots of the quadratic equation (x+2)2-16 = 0?
Answer» What are the roots of the quadratic equation $(x + 2)^{2}$ -16 = 0?

Discussion

12858.	ABC is an isosceles triangle such that AB=AC=17 and base BC = 16 find the length of median AG
Answer» ABC is an isosceles triangle such that AB=AC=17 and base BC = 16 find the length of median AG

Discussion

12859.	From a certain spot, the top of a flagpole has an angle of elevation of 30°. After moving 10 m in a straight line towards the flagpole, the top has an angle of elevation of 50° . Find the height of the flagpole.(Use sin 50° = 0.766, cos 50° = 0.643, tan 50° = 1.192)
Answer» From a certain spot, the top of a flagpole has an angle of elevation of 30°. After moving 10 m in a straight line towards the flagpole, the top has an angle of elevation of 50° . Find the height of the flagpole. (Use sin 50° = 0.766, cos 50° = 0.643, tan 50° = 1.192)

Discussion

12860.	Find the sum of the first 15 terms of each of the following sequences having nth term as(i) an = 3 + 4n(ii) bn = 5 + 2n(iii) xn = 6 − n(iv) yn = 9 − 5n
Answer» Find the sum of the first 15 terms of each of the following sequences having nth term as (i) a_n= 3 + 4n (ii) b_n = 5 + 2n (iii) x_n = 6 − n (iv) y_n = 9 − 5n

Discussion

12861.	In the given right angle triangle ABC, if = 30∘ and then the sides AB and BC would be………………………………………cm __
Answer» In the given right angle triangle ABC, if = $30^{\circ}$ and then the sides AB and BC would be………………………………………cm __

Discussion

12862.	How many balls, each of radius I cm, can be made from a solid sphere of lead of radius 8 cm?
Answer» How many balls, each of radius I cm, can be made from a solid sphere of lead of radius 8 cm?

Discussion

12863.	The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method.Literacy rate (in %)No. of cities45−55355−651065−751175−85885−953
Answer» The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method. $\begin{matrix} Literacy rate (in %) & No. of cities 45 - 55 & 3 55 - 65 & 10 65 - 75 & 11 75 - 85 & 8 85 - 95 & 3 \end{matrix}$

Discussion

12864.	Find the volume and surface area of a cuboid of ℓ = 10 cm, b = 8 cm and h = 6 cm.
Answer» Find the volume and surface area of a cuboid of $ℓ$ = 10 cm, b = 8 cm and h = 6 cm.

Discussion

12865.

Calculate Mean and standard deviation for the following distribution X 5 15 25 35 45 f 5 8 15 16 6

Answer»

Calculate Mean and standard deviation for the following distribution

X	5	15	25	35	45
f	5	8	15	16	6

Discussion

12866.	From the given ogive, which of the following can be determined?
Answer» From the given ogive, which of the following can be determined?

12866.

From the given ogive, which of the following can be determined?

Answer»

From the given ogive, which of the following can be determined?

Discussion

12867.	A bucket can hold 19 L of milk. If there is 256 L of milk with Govind then how many buckets can he fill and what is the leftover milk with him?
Answer» A bucket can hold 19 L of milk. If there is 256 L of milk with Govind then how many buckets can he fill and what is the leftover milk with him?

Discussion

12868.	→a×(→b×→c),→b×(→c×→a),→c×(→a×→b) are
Answer» $\to a \times (\to b \times \to c), \to b \times (\to c \times \to a), \to c \times (\to a \times \to b)$ are

Discussion

12869.	There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn -(1) shows an even number.(2) shows a number which is a multiple of 5.
Answer» There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn - (1) shows an even number. (2) shows a number which is a multiple of 5.

Discussion

12870.	The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is(a) 2: 1(b) 1 : 2(c) −2 : 1(d) 1 : −2
Answer» The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is (a) 2: 1 (b) 1 : 2 (c) −2 : 1 (d) 1 : −2

Discussion

12871.	Question 7 A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.
Answer» Question 7 A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.

Discussion

12872.	PROVE THAT Sin2A = 2SinACosA
Answer» PROVE THAT Sin2A = 2SinACosA

Discussion

12873.	Apply division algorithm to find the quotient q(x) and remainder r(x) in dividing f(x) by g(x) in each of the following :(i) f(x) = x3 − 6x2 + 11x − 6, g(x) = x2 + x + 1(ii) f(x) = 10x4 + 17x3 − 62x2 + 30x − 3, g(x) = 2x2 + 7x + 1(iii) f(x) = 4x3 + 8x + 8x2 + 7, g(x) = 2x2 − x + 1(iv) f(x) = 15x3 − 20x2 + 13x − 12, g(x) = 2 − 2x + x2
Answer» Apply division algorithm to find the quotient q(x) and remainder r(x) in dividing f(x) by g(x) in each of the following : (i) f(x) = x³ − 6x² + 11x − 6, g(x) = x² + x + 1 (ii) f(x) = 10x⁴ + 17x³ − 62x² + 30x − 3, g(x) = 2x² + 7x + 1 (iii) f(x) = 4x³+ 8x + 8x² + 7, g(x) = 2x² − x + 1 (iv) f(x) = 15x³ − 20x² + 13x − 12, g(x) = 2 − 2x + x²

Discussion

12874.	ABCD is a paralle\log ram and X is the midpoint of BC and Y is the midpoint of DC and arCXY = 1/2 ar BCD. To prove - arAXY = 3/8 ar ABCD
Answer» ABCD is a paralle\log ram and X is the midpoint of BC and Y is the midpoint of DC and arCXY = 1/2 ar BCD. To prove - arAXY = 3/8 ar ABCD

Discussion

12875.	The volume of a cube is 729 cm3. Find its surface area.
Answer» The volume of a cube is 729 cm³. Find its surface area.

Discussion

12876.	The value/s of x when (x - 4) (3x + 2) = 0 ________
Answer» The value/s of x when (x - 4) (3x + 2) = 0 ________

Discussion

12877.	The number of Science and Mathematics projects submitted by Model high school, Nandpur in last 20 years at the state level science exhibition is:2,3,4,1,2,3,1,5,4,2,3,1,3,5,4,3,2,2,3,2. Prepare a frequency table and find the mean of the data.
Answer» The number of Science and Mathematics projects submitted by Model high school, Nandpur in last $20$ years at the state level science exhibition is: $2, 3, 4, 1, 2, 3, 1, 5, 4, 2, 3, 1, 3, 5, 4, 3, 2, 2, 3, 2$ . Prepare a frequency table and find the mean of the data.

12877.

The number of Science and Mathematics projects submitted by Model high school, Nandpur in last 20 years at the state level science exhibition is:2,3,4,1,2,3,1,5,4,2,3,1,3,5,4,3,2,2,3,2. Prepare a frequency table and find the mean of the data.

Answer»

The number of Science and Mathematics projects submitted by Model high school, Nandpur in last $20$ years at the state level science exhibition is:

$2, 3, 4, 1, 2, 3, 1, 5, 4, 2, 3, 1, 3, 5, 4, 3, 2, 2, 3, 2$ .

Prepare a frequency table and find the mean of the data.

Discussion

12878.	A group of 48 workers can complete a piece of work in 11 days. But 48 workers worked on first day, 44 workers worked on second day, 40 workers worked on third day and so on. Unfortunately, on the 10th day, they had to restart the entire work . Then, find the time taken by the remaining workers to complete the entire work.
Answer» A group of 48 workers can complete a piece of work in 11 days. But 48 workers worked on first day, 44 workers worked on second day, 40 workers worked on third day and so on. Unfortunately, on the 10th day, they had to restart the entire work . Then, find the time taken by the remaining workers to complete the entire work.

Discussion

12879.	Question 4 (xi) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xi) a,a2,a3,a4……
Answer» Question 4 (xi) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xi) $a, a^{2}, a^{3}, a^{4} \dots \dots$

Discussion

12880.	The prime triplet is ................
Answer» The prime triplet is ................

Discussion

12881.	M is a point on the side BC of a parallelogram ABCD. DM when produced meets AB produced at N. Prove thatiDMMN=DCBNiiDNDM=ANDC
Answer» M is a point on the side BC of a parallelogram ABCD. DM when produced meets AB produced at N. Prove that $(i) \frac{DM}{MN} = \frac{DC}{BN} (ii) \frac{DN}{DM} = \frac{AN}{DC}$

Discussion

12882.	In the given figure, ABC is a triangle with ∠EDB=∠ACB. Prove that ΔABC∼ΔEBD.IfBE=6 cm,EC=4 CM,bd=5 cmandareaofΔBED=9cm2, calculate: [4 MARKS] (i) Leight of AB (ii) Area of ΔABC.
Answer» In the given figure, ABC is a triangle with $∠ E D B = ∠ A C B$ . Prove that $Δ A B C \sim Δ E B D . I f B E = 6 c m, E C = 4 C M, b d = 5 c m a n d a r e a o f Δ B E D = 9 c m^{2}$ , calculate: [4 MARKS] (i) Leight of AB (ii) Area of $Δ A B C$ .

Discussion

12883.	If GCD of x^3 + cx^2 + 2c and x^2 + CX - 2 is a linear polynomial then, what are the possible values of c?
Answer» If GCD of x^3 + cx^2 + 2c and x^2 + CX - 2 is a linear polynomial then, what are the possible values of c?

Discussion

12884.	Question 9 In ΔABC∼ΔDFE,∠A=30∘,∠C=50∘, AB=5cm,AC=8cm and DF=7.5cm ,then which of the following is true? (A) DE=12cm,∠F=50∘ (B) DE=12cm,∠F=100∘ (C) EF=12cm,∠D=100∘ (D) EF=12cm,∠D=30∘
Answer» Question 9 $I n Δ A B C \sim Δ D F E, ∠ A = 30^{\circ}, ∠ C = 50^{\circ},$ $A B = 5 c m, A C = 8 c m a n d D F = 7.5 c m$ ,then which of the following is true? (A) $D E = 12 c m, ∠ F = 50^{\circ}$ (B) $D E = 12 c m, ∠ F = 100^{\circ}$ (C) $E F = 12 c m, ∠ D = 100^{\circ}$ (D) $E F = 12 c m, ∠ D = 30^{\circ}$

Discussion

12885.	What is the solution for the following pair of linear equations?12x−1y=−11x+12y=8(Given: x≠0 and y≠0)
Answer» What is the solution for the following pair of linear equations? $\frac{1}{2 x} - \frac{1}{y} = - 1$ $\frac{1}{x} + \frac{1}{2 y} = 8$ (Given: $x \neq 0 a n d y \neq 0)$

Discussion

12886.	There are two classrooms A and B.If 10 students are sent from A to B, the number of students in each room becomes the same. If 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in each room.
Answer» There are two classrooms A and B.If 10 students are sent from A to B, the number of students in each room becomes the same. If 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in each room.

Discussion

12887.	On a particular crossing, out of 100 people, 9 people jumped traffic lights. Find the probability of people not jumping traffic lights.
Answer» On a particular crossing, out of 100 people, 9 people jumped traffic lights. Find the probability of people not jumping traffic lights.

Discussion

12888.	What is the relation between AM & MB in the given figure?
Answer» What is the relation between AM & MB in the given figure?

12888.

What is the relation between AM & MB in the given figure?

Answer»

What is the relation between AM & MB in the given figure?

Discussion

12889.	if alpha and beta are the zeros of the polynomial x^2 - ax + a then find the value of I)alpha^4 - beta^4 II)-1/alpha^3 + 1/beta^3
Answer» if alpha and beta are the zeros of the polynomial x^2 - ax + a then find the value of I)alpha^4 - beta^4 II)-1/alpha^3 + 1/beta^3

Discussion

12890.	A golf ball has a diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Assuming that the dimples are hemispherical, the total surface area which is exposed to the surroundings is
Answer» A golf ball has a diameter equal to $4.2 c m .$ Its surface has $200$ dimples each of radius $2 m m .$ Assuming that the dimples are hemispherical, the total surface area which is exposed to the surroundings is

Discussion

12891.	The sum of all real solutions of the equation\vert x\vert-3\vert x\vert-10=0 is
Answer» The sum of all real solutions of the equation\vert x\vert-3\vert x\vert-10=0 is

Discussion

12892.	The vertices of a ΔOBC are O(0, 0), B(–3, –1) and C(–1, –3). The equation of a line parallel to BC and intersecting sides OB and OC whose distance from the origin is 12, is
Answer» The vertices of a $Δ O B C$ are O(0, 0), B(–3, –1) and C(–1, –3). The equation of a line parallel to BC and intersecting sides OB and OC whose distance from the origin is $\frac{1}{2}$ , is

Discussion

12893.	Prove that (4−5√2) is an irrational number.
Answer» Prove that $(4 - 5 \sqrt{2})$ is an irrational number.

Discussion

12894.	Draw two triangles and divide them into 4 equal parts. Shade half of the triangles in two different ways.
Answer» Draw two triangles and divide them into 4 equal parts. Shade half of the triangles in two different ways.

Discussion

12895.	Afloor is paved with rectangular bricks, each of length a and breadth b . A circular disc of diameter c is thrown on the floor. The chance that it falls entirely on one brick is
Answer» Afloor is paved with rectangular bricks, each of length a and breadth b . A circular disc of diameter c is thrown on the floor. The chance that it falls entirely on one brick is

Discussion

12896.	The equation of a line is 3x +4y -7 = 0. Find the slope of the line.
Answer» The equation of a line is 3x +4y -7 = 0. Find the slope of the line.

Discussion

12897.	Question 3 (ii)Write the first three terms of the AP’s, when a and d are as given below:a = -5, d = - 3
Answer» Question 3 (ii) Write the first three terms of the AP’s, when a and d are as given below: a = -5, d = - 3

Discussion

12898.	If α and β are the zeros of the quadratic polynomial p(s) = 3s2 − 6s + 4, find the value of αβ+βa+21α+1β+3αβ.
Answer» If α and β are the zeros of the quadratic polynomial p(s) = 3s² − 6s + 4, find the value of $\frac{α}{β} + \frac{β}{a} + 2 (\frac{1}{α} + \frac{1}{β}) + 3 αβ$ .

Discussion

12899.	A man invests Rs. 20,020 in buying shares of nominal value Rs.26 at 10% premium. The dividend on the shares is 15% per annum. Calculate
Answer» A man invests Rs. 20,020 in buying shares of nominal value Rs.26 at 10% premium. The dividend on the shares is 15% per annum. Calculate

Discussion

12900.	If the circumference of a circle increases from 4π to 8π, then its area is(a) halved(b) doubled(c) tripled(d) quadrupled
Answer» If the circumference of a circle increases from 4π to 8π, then its area is (a) halved (b) doubled (c) tripled (d) quadrupled

Discussion

Explore topic-wise InterviewSolutions in .

Prove the following trigonometric identities.1-cos A1+cos A+1+cos A1-cos A=2 cosec A

Find compound Interst of 6 six monthly (P=20000, R=5%, N=2 years)

A bucket is in the form of a frustum of a cone and holds 15.25 litres of water. The diameters of the top and bottom are 25 cm and 20 cm respectively. Find its height and area of tin used in its construction.

Given that 2 is irrational, prove that 5+32 is an irrational number.

What are the roots of the quadratic equation (x+2)2-16 = 0?

ABC is an isosceles triangle such that AB=AC=17 and base BC = 16 find the length of median AG

From a certain spot, the top of a flagpole has an angle of elevation of 30°. After moving 10 m in a straight line towards the flagpole, the top has an angle of elevation of 50° . Find the height of the flagpole.(Use sin 50° = 0.766, cos 50° = 0.643, tan 50° = 1.192)

Find the sum of the first 15 terms of each of the following sequences having nth term as(i) an = 3 + 4n(ii) bn = 5 + 2n(iii) xn = 6 − n(iv) yn = 9 − 5n

In the given right angle triangle ABC, if = 30∘ and then the sides AB and BC would be………………………………………cm __

How many balls, each of radius I cm, can be made from a solid sphere of lead of radius 8 cm?

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method.Literacy rate (in %)No. of cities45−55355−651065−751175−85885−953

Find the volume and surface area of a cuboid of ℓ = 10 cm, b = 8 cm and h = 6 cm.

Calculate Mean and standard deviation for the following distribution X 5 15 25 35 45 f 5 8 15 16 6

From the given ogive, which of the following can be determined?

A bucket can hold 19 L of milk. If there is 256 L of milk with Govind then how many buckets can he fill and what is the leftover milk with him?

→a×(→b×→c),→b×(→c×→a),→c×(→a×→b) are

There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn -(1) shows an even number.(2) shows a number which is a multiple of 5.

The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is(a) 2: 1(b) 1 : 2(c) −2 : 1(d) 1 : −2

Question 7 A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.

PROVE THAT Sin2A = 2SinACosA

ABCD is a paralle\log ram and X is the midpoint of BC and Y is the midpoint of DC and arCXY = 1/2 ar BCD. To prove - arAXY = 3/8 ar ABCD

The volume of a cube is 729 cm3. Find its surface area.

The value/s of x when (x - 4) (3x + 2) = 0 ________

The number of Science and Mathematics projects submitted by Model high school, Nandpur in last 20 years at the state level science exhibition is:2,3,4,1,2,3,1,5,4,2,3,1,3,5,4,3,2,2,3,2. Prepare a frequency table and find the mean of the data.

Question 4 (xi) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xi) a,a2,a3,a4……

The prime triplet is ................

M is a point on the side BC of a parallelogram ABCD. DM when produced meets AB produced at N. Prove thatiDMMN=DCBNiiDNDM=ANDC

In the given figure, ABC is a triangle with ∠EDB=∠ACB. Prove that ΔABC∼ΔEBD.IfBE=6 cm,EC=4 CM,bd=5 cmandareaofΔBED=9cm2, calculate: [4 MARKS] (i) Leight of AB (ii) Area of ΔABC.

If GCD of x^3 + cx^2 + 2c and x^2 + CX - 2 is a linear polynomial then, what are the possible values of c?

Question 9 In ΔABC∼ΔDFE,∠A=30∘,∠C=50∘, AB=5cm,AC=8cm and DF=7.5cm ,then which of the following is true? (A) DE=12cm,∠F=50∘ (B) DE=12cm,∠F=100∘ (C) EF=12cm,∠D=100∘ (D) EF=12cm,∠D=30∘

What is the solution for the following pair of linear equations?12x−1y=−11x+12y=8(Given: x≠0 and y≠0)

There are two classrooms A and B.If 10 students are sent from A to B, the number of students in each room becomes the same. If 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in each room.

On a particular crossing, out of 100 people, 9 people jumped traffic lights. Find the probability of people not jumping traffic lights.

What is the relation between AM &amp; MB in the given figure?

if alpha and beta are the zeros of the polynomial x^2 - ax + a then find the value of I)alpha^4 - beta^4 II)-1/alpha^3 + 1/beta^3

A golf ball has a diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Assuming that the dimples are hemispherical, the total surface area which is exposed to the surroundings is

The sum of all real solutions of the equation\vert x\vert-3\vert x\vert-10=0 is

The vertices of a ΔOBC are O(0, 0), B(–3, –1) and C(–1, –3). The equation of a line parallel to BC and intersecting sides OB and OC whose distance from the origin is 12, is

Prove that (4−5√2) is an irrational number.

Draw two triangles and divide them into 4 equal parts. Shade half of the triangles in two different ways.

Afloor is paved with rectangular bricks, each of length a and breadth b . A circular disc of diameter c is thrown on the floor. The chance that it falls entirely on one brick is

The equation of a line is 3x +4y -7 = 0. Find the slope of the line.

Question 3 (ii)Write the first three terms of the AP’s, when a and d are as given below:a = -5, d = - 3

If α and β are the zeros of the quadratic polynomial p(s) = 3s2 − 6s + 4, find the value of αβ+βa+21α+1β+3αβ.

A man invests Rs. 20,020 in buying shares of nominal value Rs.26 at 10% premium. The dividend on the shares is 15% per annum. Calculate

If the circumference of a circle increases from 4π to 8π, then its area is(a) halved(b) doubled(c) tripled(d) quadrupled

What is the relation between AM & MB in the given figure?