25365 + Interview Questions in Mathematics Page 224 InterviewSolution

11151.	In the given figure, the total number of parts is 8.i) The number of shaded parts is .ii) The fraction represented by the figure is .
Answer» In the given figure, the total number of parts is 8. i) The number of shaded parts is . ii) The fraction represented by the figure is .

Discussion

11152.	Question 9The following is the distribution of weights (in kg) of 40 persons.Weight (in kg)40−4545−5050−5555−6060−6565−7070−7575−80Number of persons441356521Construct a cumulative frequency distribution (of the less than type) table for the data above.
Answer» Question 9 The following is the distribution of weights (in kg) of 40 persons. $\begin{matrix} W e i g h t (i n k g) & 40 - 45 & 45 - 50 & 50 - 55 & 55 - 60 & 60 - 65 & 65 - 70 & 70 - 75 & 75 - 80 N u m b e r o f p e r s o n s & 4 & 4 & 13 & 5 & 6 & 5 & 2 & 1 \end{matrix}$ Construct a cumulative frequency distribution (of the less than type) table for the data above.

Discussion

11153.	Arun’s salary is decreased by 50% and then subsequently increased by 50%. What percent of his salary does he lose?
Answer» Arun’s salary is decreased by 50% and then subsequently increased by 50%. What percent of his salary does he lose?

Discussion

11154.	Question 48Sate weather the given statement is true or false.If d varies directly as t2, then we can write dt2=k, where k is some constant.
Answer» Question 48 Sate weather the given statement is true or false. If d varies directly as $t^{2}$ , then we can write $d t^{2} = k,$ where k is some constant.

11154.

Question 48Sate weather the given statement is true or false.If d varies directly as t2, then we can write dt2=k, where k is some constant.

Answer»

Question 48

Sate weather the given statement is true or false.

If d varies directly as $t^{2}$ , then we can write $d t^{2} = k,$ where k is some constant.

Discussion

11155.	The value of the expression a→×b→2+a→·b→2 is ______________.
Answer» The value of the expression ${\|\vec{a} \times \vec{b}\|}^{2} + {(\vec{a} \cdot \vec{b})}^{2}$ is ______________.

Discussion

11156.	If the coefficients of x7 and x8 in 2+x3n are equal, then n is(a) 56(b) 55(c) 45(d) 15
Answer» If the coefficients of x⁷ and x⁸ in ${(2 + \frac{x}{3})}^{n}$ are equal, then n is (a) 56 (b) 55 (c) 45 (d) 15

Discussion

11157.	Find the mean age in years from the frequency distribution given below:Class interval of age in yearsFrequency(fi)25−29430−341435−392240−441645−49650−54555−593Total70 39.35
Answer» Find the mean age in years from the frequency distribution given below: $\begin{matrix} Class interval of age in years & Frequency (f_{i}) 25 - 29 & 4 30 - 34 & 14 35 - 39 & 22 40 - 44 & 16 45 - 49 & 6 50 - 54 & 5 55 - 59 & 3 Total & 70 \end{matrix}$ 39.35

Discussion

11158.	A large tank initially contains 1 L of water. A tap is connected to the tank, which fills the tank at a rate of 3 L per minute. Determine the quantity of water in the tank as function of time and find the quantity water in the tank after 10 minutes of the tap opening, given that there is no over flowing or loss of water from the tank. L
Answer» A large tank initially contains 1 L of water. A tap is connected to the tank, which fills the tank at a rate of 3 L per minute. Determine the quantity of water in the tank as function of time and find the quantity water in the tank after 10 minutes of the tap opening, given that there is no over flowing or loss of water from the tank. L

Discussion

11159.	Question 44.Answer True/False.The additive inverse of an integer x is 2x.
Answer» Question 44. Answer True/False. The additive inverse of an integer x is 2x.

11159.

Question 44.Answer True/False.The additive inverse of an integer x is 2x.

Answer»

Question 44.

Answer True/False.

The additive inverse of an integer x is 2x.

Discussion

11160.	Compare the irrational numbers: 3,3√8,√2,3√125,√31,6
Answer» Compare the irrational numbers: $3, \sqrt[3]{8}, \sqrt{2}, \sqrt[3]{125}, \sqrt{31}, 6$

Discussion

11161.	Consider the linear equation y=2x+5. For consecutive interger values of x, can it be used to form an arithmetic sequence? Answer in Yes/No.
Answer» Consider the linear equation $y = 2 x + 5.$ For consecutive interger values of $x,$ can it be used to form an arithmetic sequence? Answer in Yes/No.

Discussion

11162.	Question 203Construct a trapezium ABCD, where AB∥CD, AD = BC = 3.2 cm, AB = 6.4 cm and CD = 9.6 cm. Measure ∠B and ∠A.[Hint Difference of two parallel sides gives an equilateral triangle]
Answer» Question 203 Construct a trapezium ABCD, where $A B ∥ C D$ , AD = BC = 3.2 cm, AB = 6.4 cm and CD = 9.6 cm. Measure $∠ B$ and $∠ A$ . [Hint Difference of two parallel sides gives an equilateral triangle]

Discussion

11163.	Question 86(iv)A die is rolled once. What is the probability that the number on top will be less than 1 ?
Answer» Question 86(iv) A die is rolled once. What is the probability that the number on top will be less than 1 ?

11163.

Question 86(iv)A die is rolled once. What is the probability that the number on top will be less than 1 ?

Answer»

Question 86(iv)

A die is rolled once. What is the probability that the number on top will be less than 1 ?

Discussion

11164.	The mean of the following distribution is: xi10131619fi2576
Answer» The mean of the following distribution is: $\begin{matrix} x_{i} & 10 & 13 & 16 & 19 f_{i} & 2 & 5 & 7 & 6 \end{matrix}$

Discussion

11165.	Question 72 State whether the following statement is true or false: The square root of a perfect square of n digits will have (n+12) digits, if n is odd.
Answer» Question 72 State whether the following statement is true or false: The square root of a perfect square of n digits will have $(\frac{n + 1}{2})$ digits, if n is odd.

11165.

Question 72 State whether the following statement is true or false: The square root of a perfect square of n digits will have (n+12) digits, if n is odd.

Answer»

Question 72

State whether the following statement is true or false:

The square root of a perfect square of n digits will have $(\frac{n + 1}{2})$ digits, if n is odd.

Discussion

11166.	A shopkeeper buys 80 articles for ₹ 2400 and sells them at a profit of 16%. Find the selling price of one article.
Answer» A shopkeeper buys 80 articles for ₹ 2400 and sells them at a profit of 16%. Find the selling price of one article.

Discussion

11167.	The dimensions of a cuboid is 10 cm×8 cm×5 cm. Calculate the volume of the new cuboid if the scale factor is 0.5. 50
Answer» The dimensions of a cuboid is $10 c m \times 8 c m \times 5 c m$ . Calculate the volume of the new cuboid if the scale factor is $0.5$ . 50

Discussion

11168.	Construct a line segment of length 5.6 cm using ruler and compasses.
Answer» Construct a line segment of length 5.6 cm using ruler and compasses.

Discussion

11169.	If n(A∩ B^c)=5 , n(B∩ A^c)=6 , n(A∩ B)=4 then the value of n(AUB) is
Answer» If n(A∩ B^c)=5 , n(B∩ A^c)=6 , n(A∩ B)=4 then the value of n(AUB) is

Discussion

11170.	Prove that the function fgiven by f(x) = x - [x] is increasing on (0, 1).
Answer» Prove that the function f given by f(x) = x - [x] is increasing on (0, 1).

Discussion

11171.	Find all positive integers m, n such that (3m)n = 3m × 3n.
Answer» Find all positive integers m, n such that (3^m)ⁿ= 3^m × 3ⁿ.

Discussion

11172.	The angle between the tangents from (α,β) to the circle x2+y2=a2, is
Answer» The angle between the tangents from $(α, β)$ to the circle $x^{2} + y^{2} = a^{2}$ , is

Discussion

11173.	{ If }f^'(x)=g(x) and }g^'(x)=-f(x) for all }x and }}{f(2)=4=f^'(2) then }f^2(24)+g^2(24) is equal to
Answer» { If }f^'(x)=g(x) and }g^'(x)=-f(x) for all }x and }}{f(2)=4=f^'(2) then }f^2(24)+g^2(24) is equal to

Discussion

11174.	In the parallelogram, D is the mid point of side PQ. Which of the following options is NOT true?
Answer» In the parallelogram, D is the mid point of side PQ. Which of the following options is NOT true?

11174.

In the parallelogram, D is the mid point of side PQ. Which of the following options is NOT true?

Answer»

In the parallelogram, D is the mid point of side PQ. Which of the following options is NOT true?

Discussion

11175.	The weights (in kg) of 30 students of a class are39, 43, 32, 37, 29, 26, 31, 45, 46, 31, 37, 38, 30, 39, 36, 41, 35, 34, 41, 46, 39, 38, 36, 38, 40, 42, 33, 43, 44, 33.Prepare a frequency distribution table using one class interval as 30–35, in which 30 is included and 35 excluded. Using the above data. draw a histogram.
Answer» The weights (in kg) of 30 students of a class are 39, 43, 32, 37, 29, 26, 31, 45, 46, 31, 37, 38, 30, 39, 36, 41, 35, 34, 41, 46, 39, 38, 36, 38, 40, 42, 33, 43, 44, 33. Prepare a frequency distribution table using one class interval as 30–35, in which 30 is included and 35 excluded. Using the above data. draw a histogram.

Discussion

11176.	(a) Given that the diagram has 5 lines of symmetry. Draw all the lines of symmetry and then divide the figure into 10 parts. Given here is a part of the diagram. Complete the diagram. (b) How many lines of symmetry do a polygon with its adjacent sides equal and perpendicular have? [4 MARKS]
Answer» (a) Given that the diagram has 5 lines of symmetry. Draw all the lines of symmetry and then divide the figure into 10 parts. Given here is a part of the diagram. Complete the diagram. (b) How many lines of symmetry do a polygon with its adjacent sides equal and perpendicular have? [4 MARKS]

11176.

(a) Given that the diagram has 5 lines of symmetry. Draw all the lines of symmetry and then divide the figure into 10 parts. Given here is a part of the diagram. Complete the diagram. (b) How many lines of symmetry do a polygon with its adjacent sides equal and perpendicular have? [4 MARKS]

Answer»

(a) Given that the diagram has 5 lines of symmetry. Draw all the lines of symmetry and then divide the figure into 10 parts. Given here is a part of the diagram. Complete the diagram.

(b) How many lines of symmetry do a polygon with its adjacent sides equal and perpendicular have?
[4 MARKS]

Discussion

11177.	Question 6 (ii) Verify Euler’s formula for these solids.
Answer» Question 6 (ii) Verify Euler’s formula for these solids.

Discussion

11178.	A team is to be formed consisting of 2 players for a tennis tournament. 3 players P, A, and R are available for selection. In how many ways can the team be selected?
Answer» A team is to be formed consisting of $2$ players for a tennis tournament. $3$ players P, A, and R are available for selection. In how many ways can the team be selected?

Discussion

11179.	Find the equation of a line drawn perpendicular to the line x4+y6=1 through the point, where it meets the y-axis.
Answer» Find the equation of a line drawn perpendicular to the line $\frac{x}{4} + \frac{y}{6} = 1$ through the point, where it meets the y-axis.

Discussion

11180.	Find the top view of the figure below.
Answer» Find the top view of the figure below.

Discussion

11181.	A motorbike was bought for ₹80,000 and then sold for ₹60,000. Find the profit or loss percentage.
Answer» A motorbike was bought for ₹80,000 and then sold for ₹60,000. Find the profit or loss percentage.

Discussion

11182.	A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8:15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100 sq. units, the resulting box has maximum volume. Then the length of the side of the rectangular sheet is
Answer» A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8 : 15$ is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is $100$ sq. units, the resulting box has maximum volume. Then the length of the side of the rectangular sheet is

Discussion

11183.	Factorise : xy-pq+qy-px
Answer» Factorise : xy-pq+qy-px

Discussion

11184.	What is the size of a partical ?
Answer» What is the size of a partical ?

Discussion

11185.	If a quadrilateral with 4 sides and a diagonal is given, which of the following conditions is used in the construction?
Answer» If a quadrilateral with 4 sides and a diagonal is given, which of the following conditions is used in the construction?

Discussion

11186.	Find the conjugate of √43−√34 and simplify it.
Answer» Find the conjugate of $\sqrt{\frac{4}{3}} - \sqrt{\frac{3}{4}}$ and simplify it.

Discussion

11187.	3 persons can build a wall in 4 days, then 4 persons can build it in (a) 513days (b) 3 days (c) 413days (d) none of these
Answer» 3 persons can build a wall in 4 days, then 4 persons can build it in (a) $5 \frac{1}{3} d a y s$ (b) 3 days (c) $4 \frac{1}{3} d a y s$ (d) none of these

11187.

3 persons can build a wall in 4 days, then 4 persons can build it in (a) 513days (b) 3 days (c) 413days (d) none of these

Answer»

3 persons can build a wall in 4 days, then 4 persons can build it in

(a) $5 \frac{1}{3} d a y s$ (b) 3 days

(c) $4 \frac{1}{3} d a y s$ (d) none of these

Discussion

11188.	Which of the following is a linear equation in one variable?
Answer» Which of the following is a linear equation in one variable?

Discussion

11189.	13 and 31 is a strange pair of numbers such that their square 169 and did 961 are also Mirror image of each other can you find one other such pair
Answer» 13 and 31 is a strange pair of numbers such that their square 169 and did 961 are also Mirror image of each other can you find one other such pair

Discussion

11190.	The value of (0.9)2−(0.6)2 is
Answer» $The value of (0.9)^{2} - (0.6)^{2} is$

Discussion

11191.	Which least number should be subtracted from 1000 so that the difference is exactly divisible by 35
Answer» Which least number should be subtracted from 1000 so that the difference is exactly divisible by 35

Discussion

11192.	Diagonals are of equal length in
Answer» Diagonals are of equal length in

Discussion

11193.	Two groups consisting of 108 and 156 students participate in sports meet. In how many rooms cfan all these students be accommodated at the minimum, it all the rooms should have equal number of students and no two students in a room should be from different groups ?
Answer» Two groups consisting of 108 and 156 students participate in sports meet. In how many rooms cfan all these students be accommodated at the minimum, it all the rooms should have equal number of students and no two students in a room should be from different groups ?

Discussion

11194.	In a circle of radius 'r' and center 'O', P and Q are points on the circle such that OP ⊥ OQ. Suppose a = 1√2. Find PQ in terms of a and r.
Answer» In a circle of radius 'r' and center 'O', P and Q are points on the circle such that OP $⊥$ OQ. Suppose a = $\frac{1}{\sqrt{2}}$ . Find PQ in terms of a and r.

11194.

In a circle of radius 'r' and center 'O', P and Q are points on the circle such that OP ⊥ OQ. Suppose a = 1√2. Find PQ in terms of a and r.

Answer»

In a circle of radius 'r' and center 'O', P and Q are points on the circle such that OP $⊥$ OQ.

Suppose a = $\frac{1}{\sqrt{2}}$ . Find PQ in terms of a and r.

Discussion

11195.	The bacteria count after 4 hours is
Answer» The bacteria count after 4 hours is

Discussion

11196.	Determinenif(i) (ii)
Answer» Determine n if (i) (ii)

11196.

Determinenif(i) (ii)

Answer»

Determine
n
if

(i) (ii)

Discussion

11197.	If x-1x=-1, find the value of x2+1x2
Answer» If $x - \frac{1}{x} = - 1$ , find the value of $x^{2} + \frac{1}{x^{2}}$

Discussion

11198.	A and B are any two non-empty sets and A is proper subset of B. If n(A) = 5, then the minimum possible value of n(A ∆ B) is ____________.
Answer» A and B are any two non-empty sets and A is proper subset of B. If n(A) = 5, then the minimum possible value of n(A ∆ B) is ____________.

Discussion

11199.	The shorter side of a parallelogram is 4.8 cm and the longer side is half as much again as the shorter side. Find the perimeter of the parallelogram.
Answer» The shorter side of a parallelogram is 4.8 cm and the longer side is half as much again as the shorter side. Find the perimeter of the parallelogram.

Discussion

11200.	In ∆ABC, AB = 10, AC = 7, BC = 9 then find the length of the median drawn from point C to side AB
Answer» In ∆ABC, AB = 10, AC = 7, BC = 9 then find the length of the median drawn from point C to side AB

Discussion

Explore topic-wise InterviewSolutions in .

In the given figure, the total number of parts is 8.i) The number of shaded parts is .ii) The fraction represented by the figure is .

Question 9The following is the distribution of weights (in kg) of 40 persons.Weight (in kg)40−4545−5050−5555−6060−6565−7070−7575−80Number of persons441356521Construct a cumulative frequency distribution (of the less than type) table for the data above.

Arun’s salary is decreased by 50% and then subsequently increased by 50%. What percent of his salary does he lose?

Question 48​​​​​​​Sate weather the given statement is true or false.If d varies directly as t2, then we can write dt2=k, where k is some constant.

The value of the expression a→×b→2+a→·b→2 is ______________.

If the coefficients of x7 and x8 in 2+x3n are equal, then n is(a) 56(b) 55(c) 45(d) 15

Find the mean age in years from the frequency distribution given below:Class interval of age in yearsFrequency(fi)25−29430−341435−392240−441645−49650−54555−593Total70 39.35

Question 44.Answer True/False.The additive inverse of an integer x is 2x.

Compare the irrational numbers: 3,3√8,√2,3√125,√31,6

Consider the linear equation y=2x+5. For consecutive interger values of x, can it be used to form an arithmetic sequence? Answer in Yes/No.

Question 203Construct a trapezium ABCD, where AB∥CD, AD = BC = 3.2 cm, AB = 6.4 cm and CD = 9.6 cm. Measure ∠B and ∠A.[Hint Difference of two parallel sides gives an equilateral triangle]

Question 86(iv)A die is rolled once. What is the probability that the number on top will be less than 1 ?

The mean of the following distribution is: xi10131619fi2576

Question 72 State whether the following statement is true or false: The square root of a perfect square of n digits will have (n+12) digits, if n is odd.

A shopkeeper buys 80 articles for ₹ 2400 and sells them at a profit of 16%. Find the selling price of one article.

The dimensions of a cuboid is 10 cm×8 cm×5 cm. Calculate the volume of the new cuboid if the scale factor is 0.5. 50

Construct a line segment of length 5.6 cm using ruler and compasses.

If n(A∩ B^c)=5 , n(B∩ A^c)=6 , n(A∩ B)=4 then the value of n(AUB) is

Prove that the function fgiven by f(x) = x - [x] is increasing on (0, 1).

Find all positive integers m, n such that (3m)n = 3m × 3n.

The angle between the tangents from (α,β) to the circle x2+y2=a2, is

{ If }f^'(x)=g(x) and }g^'(x)=-f(x) for all }x and }}{f(2)=4=f^'(2) then }f^2(24)+g^2(24) is equal to

In the parallelogram, D is the mid point of side PQ. Which of the following options is NOT true?

(a) Given that the diagram has 5 lines of symmetry. Draw all the lines of symmetry and then divide the figure into 10 parts. Given here is a part of the diagram. Complete the diagram. (b) How many lines of symmetry do a polygon with its adjacent sides equal and perpendicular have? [4 MARKS]

Question 6 (ii) Verify Euler’s formula for these solids.

A team is to be formed consisting of 2 players for a tennis tournament. 3 players P, A, and R are available for selection. In how many ways can the team be selected?

Find the equation of a line drawn perpendicular to the line x4+y6=1 through the point, where it meets the y-axis.

Find the top view of the figure below.

A motorbike was bought for ₹80,000 and then sold for ₹60,000. Find the profit or loss percentage.

Factorise : xy-pq+qy-px

What is the size of a partical ?

If a quadrilateral with 4 sides and a diagonal is given, which of the following conditions is used in the construction?

Find the conjugate of √43−√34 and simplify it.

3 persons can build a wall in 4 days, then 4 persons can build it in (a) 513days (b) 3 days (c) 413days (d) none of these

Which of the following is a linear equation in one variable?

13 and 31 is a strange pair of numbers such that their square 169 and did 961 are also Mirror image of each other can you find one other such pair

The value of (0.9)2−(0.6)2 is

Which least number should be subtracted from 1000 so that the difference is exactly divisible by 35

Diagonals are of equal length in

Two groups consisting of 108 and 156 students participate in sports meet. In how many rooms cfan all these students be accommodated at the minimum, it all the rooms should have equal number of students and no two students in a room should be from different groups ?

In a circle of radius 'r' and center 'O', P and Q are points on the circle such that OP ⊥ OQ. Suppose a = 1√2. Find PQ in terms of a and r.

The bacteria count after 4 hours is

Determinenif(i) (ii)

If x-1x=-1, find the value of x2+1x2

A and B are any two non-empty sets and A is proper subset of B. If n(A) = 5, then the minimum possible value of n(A ∆ B) is ____________.

The shorter side of a parallelogram is 4.8 cm and the longer side is half as much again as the shorter side. Find the perimeter of the parallelogram.

In ∆ABC, AB = 10, AC = 7, BC = 9 then find the length of the median drawn from point C to side AB

Question 48Sate weather the given statement is true or false.If d varies directly as t2, then we can write dt2=k, where k is some constant.