25365 + Interview Questions in Mathematics Page 41 InterviewSolution

2001.	(i) Examine if Rolle's theorem is applicable to the given function. Can you say something about the converse of Rolle's theorem from these example?f(x)=[x] for x∈[5,9](ii) Examine if Rolle's theorem is applicable to the given function. Can you say something about the converse of Rolle's theorem from this example?f(x)=[x] for x∈[−2,2](iii) Examine if Rolle's theorem is applicable to the given function. Can you say something about the converse of Rolle's theorem from this example?f(x)=x2−1 for x∈[1,2]
Answer» $(i)$ Examine if Rolle's theorem is applicable to the given function. Can you say something about the converse of Rolle's theorem from these example? $f (x) = [x] for x \in [5, 9]$ $(i i)$ Examine if Rolle's theorem is applicable to the given function. Can you say something about the converse of Rolle's theorem from this example? $f (x) = [x] for x \in [- 2, 2]$ $(i i i)$ Examine if Rolle's theorem is applicable to the given function. Can you say something about the converse of Rolle's theorem from this example? $f (x) = x^{2} - 1 for x \in [1, 2]$

Discussion

2002.	A manufacturing company finds out the number of defective calculators in each of the last 10 batches of 100 calculators.The mean number of defective calculators with outlier is and without outlier is .
Answer» A manufacturing company finds out the number of defective calculators in each of the last $10$ batches of $100$ calculators. The mean number of defective calculators with outlier is and without outlier is .

Discussion

2003.	Define the following terms: (i) Quadrilateral (ii) Convex Quadrilateral.
Answer» Define the following terms: (i) Quadrilateral (ii) Convex Quadrilateral.

Discussion

2004.	Find the volume of the given cuboid. Volume of each cube is 1 cm3.
Answer» Find the volume of the given cuboid. Volume of each cube is $1 c m^{3}$ .

Discussion

2005.	The area of one of the most common Indian sweets as per the given dimensions is \( ___~cm^2\).
Answer» The area of one of the most common Indian sweets as per the given dimensions is \( ___~cm^2\).

2005.

The area of one of the most common Indian sweets as per the given dimensions is $ ___~cm^2$.

Answer»

The area of one of the most common Indian sweets as per the given dimensions is $ ___~cm^2$.

Discussion

2006.	In the given figure, x + y =(a) 270(b) 230(c) 210(d) 190°
Answer» In the given figure, x + y = (a) 270 (b) 230 (c) 210 (d) 190°

Discussion

2007.	Factorize x^2 + y^2 - 5xy -2x + 7y - 4 = 0 into two linear equations in two variables
Answer» Factorize x^2 + y^2 - 5xy -2x + 7y - 4 = 0 into two linear equations in two variables

Discussion

2008.	EdWear has printing facilities in y cities. Each city has two factories. Each factory has 5 T- shirt printing machines. If each machine can print x T-shirts daily, how many T- Shirts will be printed by EdWear each day?
Answer» EdWear has printing facilities in $y$ cities. Each city has two factories. Each factory has $5$ T- shirt printing machines. If each machine can print $x$ T-shirts daily, how many T- Shirts will be printed by EdWear each day?

Discussion

2009.	The capacities of two bottles are in the ratio 5: 3. If the smaller bottle is emptied thrice and larger bottle once into a vessel; in another vessel, only the larger one is emptied twice then find the ratio of liquid in both vessels.
Answer» The capacities of two bottles are in the ratio 5: 3. If the smaller bottle is emptied thrice and larger bottle once into a vessel; in another vessel, only the larger one is emptied twice then find the ratio of liquid in both vessels.

Discussion

2010.	Solve equation, given below, using factorisation method: x2−(a+b)x+ab=0
Answer» Solve equation, given below, using factorisation method: $x^{2} - (a + b) x + a b = 0$

2010.

Solve equation, given below, using factorisation method: x2−(a+b)x+ab=0

Answer»

Solve equation, given below, using factorisation method:

$x^{2} - (a + b) x + a b = 0$

Discussion

2011.	Question 1(ix)Find the cube root of each of the following numbers by prime factorization method:175616
Answer» Question 1(ix) Find the cube root of each of the following numbers by prime factorization method: 175616

Discussion

2012.	Choose the correct alternative in the following question:If 2n=4096, then 2n-5=a 128 b 64 c 256 d 32
Answer» Choose the correct alternative in the following question: $If 2^{n} = 4096, then 2^{n - 5} = (a) 128 (b) 64 (c) 256 (d) 32$

Discussion

2013.	Factorise:7x-2y2-25x-2y+12
Answer» Factorise: $7 {(x - 2 y)}^{2} - 25 (x - 2 y) + 12$

Discussion

2014.	If the value of X+Y=1, then the value of X⨁Y is equal to
Answer» If the value of $X + Y = 1$ , then the value of $X ⨁ Y$ is equal to

Discussion

2015.	How many rectangular faces does a triangular prism have?
Answer» How many rectangular faces does a triangular prism have?

Discussion

2016.	What is the appoximate area of a circle whose diameter measures 14 units? ( take π=227)
Answer» What is the appoximate area of a circle whose diameter measures $14$ units? $(take π = \frac{22}{7})$

Discussion

2017.	Find the number of factors and sum of factors of 25920 excluding 1 and itself.
Answer» Find the number of factors and sum of factors of 25920 excluding 1 and itself.

Discussion

2018.	If each edge of a cube is doubled, how many times will its volume increase?
Answer» If each edge of a cube is doubled, how many times will its volume increase?

Discussion

2019.	If A×B= {(a,x),(a,y),(b,x),(b,y)}. Find set A and B.
Answer» If $A \times B =$ { $(a, x), (a, y), (b, x), (b, y)$ }. Find set $A$ and $B$ .

Discussion

2020.	In below shown figure, PSSQ= PTTR and∠PST= ∠PRQ. Then ΔPQR is a/an __ triangle.
Answer» In below shown figure, $\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST= $∠$ PRQ. Then $Δ$ PQR is a/an __ triangle.

2020.

In below shown figure, PSSQ= PTTR and∠PST= ∠PRQ. Then ΔPQR is a/an __ triangle.

Answer»

In below shown figure, $\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST= $∠$ PRQ. Then $Δ$ PQR is a/an __ triangle.

Discussion

2021.	A table which has a marked price of ₹800 is sold at ₹600. Then, the discount % given on this table is ____ 25
Answer» A table which has a marked price of ₹800 is sold at ₹600. Then, the discount % given on this table is ____ 25

Discussion

2022.	Sharda can walk 813 km in one hour. How much distance will she cover in 225 hours ?
Answer» Sharda can walk $8 \frac{1}{3} km$ in one hour. How much distance will she cover in $2 \frac{2}{5} hours ?$

Discussion

2023.	By what number should we multiply 4−3 so that the product may be equal to 64?
Answer» By what number should we multiply $4^{- 3}$ so that the product may be equal to 64?

Discussion

2024.	Divide 0.256 by 100000 and express the result in standard form.
Answer» Divide 0.256 by 100000 and express the result in standard form.

Discussion

2025.	Identify the arithmetic sequence(s).
Answer» Identify the arithmetic sequence(s).

Discussion

2026.	Rationalise 13+2.
Answer» Rationalise $\frac{1}{\sqrt{3} + \sqrt{2}}$ .

Discussion

2027.	Choose the correct answer from the given alternative:In a triangle ABC, ∠B = ∠C = 45°, then the triangle is ____________.A. right triangleB. acute angled triangleC. obtuse angle triangleD. equilateral triangle
Answer» Choose the correct answer from the given alternative: In a triangle ABC, ∠B = ∠C = 45°, then the triangle is ____________. A. right triangle B. acute angled triangle C. obtuse angle triangle D. equilateral triangle

2027.

Choose the correct answer from the given alternative:In a triangle ABC, ∠B = ∠C = 45°, then the triangle is ____________.A. right triangleB. acute angled triangleC. obtuse angle triangleD. equilateral triangle

Answer»

Choose the correct answer from the given alternative:

In a triangle ABC, ∠B = ∠C = 45°, then the triangle is ____________.

A. right triangle

B. acute angled triangle

C. obtuse angle triangle

D. equilateral triangle

Discussion

2028.	Rohan and Shalu are playing with 5 cards as shown in the figure. What is the probability of Rohan picking a card without seeing, that has the number 2 on it?
Answer» Rohan and Shalu are playing with 5 cards as shown in the figure. What is the probability of Rohan picking a card without seeing, that has the number 2 on it?

Discussion

2029.	The mean of first 10 natural number is:
Answer» The mean of first 10 natural number is:

Discussion

2030.	Question 6 In the figure given, the radius of the circle is 15 cm. The angle subtended by the chord AB at the centre O is 60∘. Find the area of the major and minor segments.
Answer» Question 6 In the figure given, the radius of the circle is 15 cm. The angle subtended by the chord AB at the centre O is $60^{\circ}$ . Find the area of the major and minor segments.

Discussion

2031.	Shorter side of a parallelogram is 3.6cm and longer side is half than shorter side. Find perimeter of parallelogram.
Answer» Shorter side of a parallelogram is 3.6cm and longer side is half than shorter side. Find perimeter of parallelogram.

Discussion

2032.	let S be a set of positive integers such that every element n of S satisfies the condition1. 1000
Answer» let S be a set of positive integers such that every element n of S satisfies the condition 1. 1000

Discussion

2033.	The square of a number is 64. What is the cube root of that number?
Answer» The square of a number is 64. What is the cube root of that number?

Discussion

2034.

Prepare Sales Return Book of Shiv Shankar, Delhi from the following transactions and post them into Ledger: 2018 Feb. 10 Rama Stores Delhi returned: 2 Televisions Sony sold ₹ 20,000 each plus CGST and SGST 9% each Feb. 20 Sohan Singh & Co. Dehradun returned: 3 Washing Machines Videocon sold ₹ 10,000 each plus IGST 18%

Answer» Prepare Sales Return Book of Shiv Shankar, Delhi from the following transactions and post them into Ledger:

2018
Feb. 10	Rama Stores Delhi returned:
	2 Televisions Sony sold ₹ 20,000 each plus CGST and SGST 9% each
Feb. 20	Sohan Singh & Co. Dehradun returned:
	3 Washing Machines Videocon sold ₹ 10,000 each plus IGST 18%

Discussion

2035.	Solve: 33−23
Answer» Solve: $3^{3} - 2^{3}$

Discussion

2036.	The factors of ax + bx - ay - by are __________.
Answer» The factors of ax + bx - ay - by are __________.

Discussion

2037.	Study the bar graph and answer the given questions. Two types of hats sold by seller A and Seller B in five days Q. The total number of hats sold by A and B together on Wednesday is how much percentage more than the number of hats sold by A and B together on Tuesday?
Answer» Study the bar graph and answer the given questions. Two types of hats sold by seller A and Seller B in five days Q. The total number of hats sold by A and B together on Wednesday is how much percentage more than the number of hats sold by A and B together on Tuesday?

Discussion

2038.	A no multiplied 6 exceeds itself by 40 the number is
Answer» A no multiplied 6 exceeds itself by 40 the number is

Discussion

2039.	Question 3Write True or False and give reasons for your answer:A ΔABC can be constructed in which AB = 5cm, ∠A=45∘ and BC + AC = 5cm.
Answer» Question 3 Write True or False and give reasons for your answer: A $Δ A B C$ can be constructed in which AB = 5cm, $∠ A = 45^{\circ}$ and BC + AC = 5cm.

Discussion

2040.	A mother and her two daughters constructed a room for ₹62,000. The elder daughter contributes 3/8 of her mother's contribution while the younger daughter contributes 1/2 of her mother share. How much do the three contribute individually?
Answer» A mother and her two daughters constructed a room for ₹62,000. The elder daughter contributes 3/8 of her mother's contribution while the younger daughter contributes 1/2 of her mother share. How much do the three contribute individually?

Discussion

2041.	Expenditure on education of a country during a five years period (2002 – 2006), in crore of rupees, is given below:Elementary Education240Secondary Education120University Education190Teachers, training20Social Education10Other Educational Programmes115Cultural Programmes25Technical Education125Represent the information above by a bar graph.
Answer» Expenditure on education of a country during a five years period (2002 – 2006), in crore of rupees, is given below: $\begin{matrix} Elementary Education & 240 Secondary Education & 120 University Education & 190 Teachers, training & 20 Social Education & 10 Other Educational Programmes & 115 Cultural Programmes & 25 Technical Education & 125 \end{matrix}$ Represent the information above by a bar graph.

Discussion

2042.	Given that a chord with length l subtends an angle θ at the centre of the circle with diameter d and radius r, find the perimeter of the segment.
Answer» Given that a chord with length $l$ subtends an angle $θ$ at the centre of the circle with diameter $d$ and radius $r$ , find the perimeter of the segment.

Discussion

2043.	f(x) =sin^2x, g(x) is polynomial function and f(g(x))is periodic. If g(1)= 5 and g(5) 1, then g(0) is
Answer» f(x) =sin^2x, g(x) is polynomial function and f(g(x))is periodic. If g(1)= 5 and g(5) 1, then g(0) is

Discussion

2044.	How many bricks, each of size 25 cm × 13.5 cm × 6 cm, will be required to build a wall 8 m long, 5.4 in high and 33 cm thick?
Answer» How many bricks, each of size 25 cm $\times$ 13.5 cm $\times$ 6 cm, will be required to build a wall 8 m long, 5.4 in high and 33 cm thick?

Discussion

2045.	For a number ending with 7, the unit digit of its cube is equal to:
Answer» For a number ending with 7, the unit digit of its cube is equal to:

Discussion

2046.	Question 88Solve the following:Divide 54 into two parts, such that one part is 27 of the other.
Answer» Question 88 Solve the following: Divide 54 into two parts, such that one part is $\frac{2}{7}$ of the other.

2046.

Question 88Solve the following:Divide 54 into two parts, such that one part is 27 of the other.

Answer»

Question 88

Solve the following:

Divide 54 into two parts, such that one part is $\frac{2}{7}$ of the other.

Discussion

2047.	Fifteen people took part in a chess competition. Every player plays with other players once. Find the number of games played in the tournament
Answer» Fifteen people took part in a chess competition. Every player plays with other players once. Find the number of games played in the tournament

Discussion

2048.	Question 11Write the correct answer from the given four options.The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 isa) 81b) 64c) 49d) 36
Answer» Question 11 Write the correct answer from the given four options. The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is a) 81 b) 64 c) 49 d) 36

2048.

Question 11Write the correct answer from the given four options.The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 isa) 81b) 64c) 49d) 36

Answer»

Question 11

Write the correct answer from the given four options.

The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is

a) 81

b) 64

c) 49

d) 36

Discussion

2049.	If (211)x=(152)8the value of base x will be _______ 7
Answer» If $(211)_{x} = (152)_{8}$ the value of base x will be _______ 7

Discussion

2050.

In the figure below, PQ = PR. Prove that the point P is one the bisector of ∠ABC.

Answer»

In the figure below, PQ = PR. Prove that the point P is one the bisector of ∠ABC.

Discussion

Explore topic-wise InterviewSolutions in .

A manufacturing company finds out the number of defective calculators in each of the last 10 batches of 100 calculators.The mean number of defective calculators with outlier is and without outlier is .

Define the following terms: (i) Quadrilateral (ii) Convex Quadrilateral.

Find the volume of the given cuboid. Volume of each cube is 1 cm3.

The area of one of the most common Indian sweets as per the given dimensions is \( ___~cm^2\).

In the given figure, x + y =(a) 270(b) 230(c) 210(d) 190°

Factorize x^2 + y^2 - 5xy -2x + 7y - 4 = 0 into two linear equations in two variables

EdWear has printing facilities in y cities. Each city has two factories. Each factory has 5 T- shirt printing machines. If each machine can print x T-shirts daily, how many T- Shirts will be printed by EdWear each day?

The capacities of two bottles are in the ratio 5: 3. If the smaller bottle is emptied thrice and larger bottle once into a vessel; in another vessel, only the larger one is emptied twice then find the ratio of liquid in both vessels.

Solve equation, given below, using factorisation method: x2−(a+b)x+ab=0

Question 1(ix)Find the cube root of each of the following numbers by prime factorization method:175616

Choose the correct alternative in the following question:If 2n=4096, then 2n-5=a 128 b 64 c 256 d 32

Factorise:7x-2y2-25x-2y+12

If the value of X+Y=1, then the value of X⨁Y is equal to

How many rectangular faces does a triangular prism have?

What is the appoximate area of a circle whose diameter measures 14 units? ( take π=227)

Find the number of factors and sum of factors of 25920 excluding 1 and itself.

If each edge of a cube is doubled, how many times will its volume increase?

If A×B= {(a,x),(a,y),(b,x),(b,y)}. Find set A and B.

In below shown figure, PSSQ= PTTR and∠PST= ∠PRQ. Then ΔPQR is a/an __ triangle.

A table which has a marked price of ₹800 is sold at ₹600. Then, the discount % given on this table is ____ 25

Sharda can walk 813 km in one hour. How much distance will she cover in 225 hours ?

By what number should we multiply 4−3 so that the product may be equal to 64?

Divide 0.256 by 100000 and express the result in standard form.

Identify the arithmetic sequence(s).

Rationalise 13+2.

Choose the correct answer from the given alternative:In a triangle ABC, ∠B = ∠C = 45°, then the triangle is ____________.A. right triangleB. acute angled triangleC. obtuse angle triangleD. equilateral triangle

Rohan and Shalu are playing with 5 cards as shown in the figure. What is the probability of Rohan picking a card without seeing, that has the number 2 on it?

The mean of first 10 natural number is:

Question 6 In the figure given, the radius of the circle is 15 cm. The angle subtended by the chord AB at the centre O is 60∘. Find the area of the major and minor segments.

Shorter side of a parallelogram is 3.6cm and longer side is half than shorter side. Find perimeter of parallelogram.

let S be a set of positive integers such that every element n of S satisfies the condition1. 1000

The square of a number is 64. What is the cube root of that number?

Solve: 33−23

The factors of ax + bx - ay - by are __________.

Study the bar graph and answer the given questions. Two types of hats sold by seller A and Seller B in five days Q. The total number of hats sold by A and B together on Wednesday is how much percentage more than the number of hats sold by A and B together on Tuesday?

A no multiplied 6 exceeds itself by 40 the number is

Question 3Write True or False and give reasons for your answer:A ΔABC can be constructed in which AB = 5cm, ∠A=45∘ and BC + AC = 5cm.

A mother and her two daughters constructed a room for ₹62,000. The elder daughter contributes 3/8 of her mother's contribution while the younger daughter contributes 1/2 of her mother share. How much do the three contribute individually?

Given that a chord with length l subtends an angle θ at the centre of the circle with diameter d and radius r, find the perimeter of the segment.

f(x) =sin^2x, g(x) is polynomial function and f(g(x))is periodic. If g(1)= 5 and g(5) 1, then g(0) is

How many bricks, each of size 25 cm × 13.5 cm × 6 cm, will be required to build a wall 8 m long, 5.4 in high and 33 cm thick?

For a number ending with 7, the unit digit of its cube is equal to:

Question 88Solve the following:Divide 54 into two parts, such that one part is 27 of the other.

Fifteen people took part in a chess competition. Every player plays with other players once. Find the number of games played in the tournament

Question 11Write the correct answer from the given four options.The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 isa) 81b) 64c) 49d) 36

If (211)x=(152)8the value of base x will be _______ 7

In the figure below, PQ = PR. Prove that the point P is one the bisector of ∠ABC.