32581 + Interview Questions in Mathematics Page 121 InterviewSolution

6001.	∆ABC ∼ ∆PQR such that ar(∆ABC) = 4 ar(∆PQR). If BC = 12 cm, then QR =(a) 9 cm(b) 10 cm(c) 6 cm(d) 8 cm
Answer» ∆ABC ∼ ∆PQR such that ar(∆ABC) = 4 ar(∆PQR). If BC = 12 cm, then QR = (a) 9 cm (b) 10 cm (c) 6 cm (d) 8 cm

Discussion

6002.	The range of the function f(x)=13−sin 3x, x∈R is
Answer» The range of the function $f (x) = \frac{1}{3 - sin 3 x}, x \in R$ is

Discussion

6003.	Water is flowing at the rate of 10 cm/minute through a pipe of diameter 10 cm into an emptybucket, which is in the form of frustum of a cone of height 30 cm with radii of its lower andupper ends as 10 cm and 20 cm respectively. Then, the time in which the level of water inthe bucket will rise 15 cm, is1. √17/10 minutes2. √19/5 minutes3. √17/5 minutes4. √19/10 minutes
Answer» Water is flowing at the rate of 10 cm/minute through a pipe of diameter 10 cm into an empty bucket, which is in the form of frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Then, the time in which the level of water in the bucket will rise 15 cm, is 1. √17/10 minutes 2. √19/5 minutes 3. √17/5 minutes 4. √19/10 minutes

Discussion

6004.	Which of the following is a solution to 3x+4y=38?
Answer» Which of the following is a solution to $3 x + 4 y = 38 ?$

Discussion

6005.	Two types of boxes A, B are to be placed in a truck having capacity of 10 tons. When 150 boxes of type A and 100 boxes of type B are loaded in the truck, it weighes 10 tons. But when 260 boxes of type A are loaded in the truck, it can still accommodate 40 boxes of type B, so that it is fully loaded. Find the weight of each type of box.
Answer» Two types of boxes A, B are to be placed in a truck having capacity of 10 tons. When 150 boxes of type A and 100 boxes of type B are loaded in the truck, it weighes 10 tons. But when 260 boxes of type A are loaded in the truck, it can still accommodate 40 boxes of type B, so that it is fully loaded. Find the weight of each type of box.

Discussion

6006.	The value of the polynomial: x2−3x+5 at x=0 is
Answer» The value of the polynomial: $x^{2} - 3 x + 5$ at x=0 is

Discussion

6007.	Find the greatest number that can divide 101 and 115 leaving remainders 5 and 7 respectively.
Answer» Find the greatest number that can divide 101 and 115 leaving remainders 5 and 7 respectively.

Discussion

6008.	In the given figure, two equal circles touch each other at T, if OP = 4.5 cm, then QR = (a) 9 cm(b) 18 cm(c) 15 cm(d) 13.5 cm
Answer» In the given figure, two equal circles touch each other at T, if OP = 4.5 cm, then QR = (a) 9 cm (b) 18 cm (c) 15 cm (d) 13.5 cm

Discussion

6009.	The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is (A) y – x + 1 = 0 (B) y – x – 1 = 0 (C) y – x + 2 = 0 (D) y – x – 2 = 0
Answer» The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is (A) y – x + 1 = 0 (B) y – x – 1 = 0 (C) y – x + 2 = 0 (D) y – x – 2 = 0

Discussion

6010.	Sachin scored twice as many as fun as Rahul .Together that runs fell to short of a double century how many runs did each one score?
Answer» Sachin scored twice as many as fun as Rahul .Together that runs fell to short of a double century how many runs did each one score?

Discussion

6011.	Explain why 7 × 11 × 13 + 13 is a composite number.
Answer» Explain why 7 × 11 × 13 + 13 is a composite number.

Discussion

6012.	34. the sum of n terms of two AP are in the ratio (3n+8):(7n+15), find the ratio of their 12 terms
Answer» 34. the sum of n terms of two AP are in the ratio (3n+8):(7n+15), find the ratio of their 12 terms

Discussion

6013.	Find the values of k for the following quadratic equation, so that they have two equal roots. kx (x - 2) + 6 = 0
Answer» Find the values of k for the following quadratic equation, so that they have two equal roots. kx (x - 2) + 6 = 0

Discussion

6014.	The product of 1, 2, 3, 4, 5, 6...... and 25 has _______ number of zeroes in the end.
Answer» The product of 1, 2, 3, 4, 5, 6...... and 25 has _______ number of zeroes in the end.

Discussion

6015.	Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
Answer» Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.

6015.

Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.

Answer»

Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.

Discussion

6016.	If the lines x+3−3=y−11=z−k5 and x+1−1=y−22=z−55 are coplanar, then the value of k is
Answer» If the lines $\frac{x + 3}{- 3} = \frac{y - 1}{1} = \frac{z - k}{5}$ and $\frac{x + 1}{- 1} = \frac{y - 2}{2} = \frac{z - 5}{5}$ are coplanar, then the value of $k$ is

Discussion

6017.	What least number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion?
Answer» What least number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion?

Discussion

6018.	What is the hcf of smallest prime and composite number?
Answer» What is the hcf of smallest prime and composite number?

Discussion

6019.	Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n.
Answer» Find the sum of the first 25 terms of an A.P. whose nth term is given by a_n= 7 − 3n.

Discussion

6020.	Find the derivative of the following function: f(x) = (x+cos x)(x−tan x)
Answer» Find the derivative of the following function: f(x) = $(x + c o s x) (x - t a n x)$

Discussion

6021.	Find domain and range of the following function : a. 1/\surd(x+\vert x\vert) b. 1/\surd(x-\vert x\vert)
Answer» Find domain and range of the following function : a. 1/\surd(x+\vert x\vert) b. 1/\surd(x-\vert x\vert)

Discussion

6022.

From the following Trial Balance prepare Trading and Profit & Loss Account for the year ended 31st March, 2019 and Balance Sheet as at that date:- Dr. (₹) Cr. (₹) Stock 1st April, 2018 22,300 Purchases and Purchases Return 2,30,000 5,200 Freehold Premises 1,00,000 Incidental Trade Exp. 11,200 Insurance 1,850 Audit Fees 800 Commission Received 2,700 Interest 1,400 Debtors and Creditors 32,400 24,830 Wages 30,200 Salaries 15,200 Capital 1,50,000 Drawings 12,000 Income-Tax 3,600 Investments 8,000 Discount allowed & received 7,500 4,200 Sales Return & Sales 6,400 3,17,400 B/R 5,200 Office Furniture 9,000 Rent 2,600 Cash in hand 5,080 Bank Balance 7,600 5,08,330 5,08,330 Adjustments:-1. Stock at 31st March 2019 is ₹ 70,000.2. Write off 5% Depreciation on Freehold Premises and 20% on office furniture.3. Commission earned but not received ₹ 500.4. Interest earned but not received ₹ 600.5. ₹ 200 for rent have been received in advance.6. Charge interest on Capital 6% and ₹ 500 on Drawings.

Answer» From the following Trial Balance prepare Trading and Profit & Loss Account for the year ended 31st March, 2019 and Balance Sheet as at that date:-

	Dr. (₹)	Cr. (₹)
Stock 1st April, 2018	22,300
Purchases and Purchases Return	2,30,000	5,200
Freehold Premises	1,00,000
Incidental Trade Exp.	11,200
Insurance	1,850
Audit Fees	800
Commission Received		2,700
Interest		1,400
Debtors and Creditors	32,400	24,830
Wages	30,200
Salaries	15,200
Capital		1,50,000
Drawings	12,000
Income-Tax	3,600
Investments	8,000
Discount allowed & received	7,500	4,200
Sales Return & Sales	6,400	3,17,400
B/R	5,200
Office Furniture	9,000
Rent		2,600
Cash in hand	5,080
Bank Balance	7,600
	5,08,330	5,08,330

Adjustments:-

1. Stock at 31st March 2019 is ₹ 70,000.

2. Write off 5% Depreciation on Freehold Premises and 20% on office furniture.

3. Commission earned but not received ₹ 500.

4. Interest earned but not received ₹ 600.

5. ₹ 200 for rent have been received in advance.

6. Charge interest on Capital 6% and ₹ 500 on Drawings.

Discussion

6023.

Sketch a rough plan and calculate the area of the field ABCDEFG from the following Metre to D To E 90 To F 60 To G 15 225 175 125 100 80 60 20 to C 70 to B From A

Answer»

Sketch a rough plan and calculate the area of the field ABCDEFG from the following

Metre to D

To E 90

To F 60

To G 15

225

175

125

100

80

60

20 to C

70 to B

From A

Discussion

6024.	Find the median class for the given distribution:Weekly wages (in Rs.)0−100100−200200−300300−400400−500No. of workers4039343045
Answer» Find the median class for the given distribution: $\begin{matrix} W e e k l y w a g e s (i n R s .) & 0 - 100 & 100 - 200 & 200 - 300 & 300 - 400 & 400 - 500 N o . o f w o r k e r s & 40 & 39 & 34 & 30 & 45 \end{matrix}$

Discussion

6025.	Find the roots of the following quadratic equations by the factorisation method: 21x^2 – 2x + 121 = 0
Answer» Find the roots of the following quadratic equations by the factorisation method: 21x^2 – 2x + 121 = 0

Discussion

6026.	The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition. ScoresNo. of shooters0−101010−201220−301530−40840−502050−602460−70770−801180−903090−10018 Use a graph sheet to draw the Histogram for the distribution. The mode as seen in the graph is ___
Answer» The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition. $\begin{matrix} Scores & No. of shooters 0 - 10 & 10 10 - 20 & 12 20 - 30 & 15 30 - 40 & 8 40 - 50 & 20 50 - 60 & 24 60 - 70 & 7 70 - 80 & 11 80 - 90 & 30 90 - 100 & 18 \end{matrix}$ Use a graph sheet to draw the Histogram for the distribution. The mode as seen in the graph is ___

6026.

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition. ScoresNo. of shooters0−101010−201220−301530−40840−502050−602460−70770−801180−903090−10018 Use a graph sheet to draw the Histogram for the distribution. The mode as seen in the graph is ___

Answer»

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{matrix} Scores & No. of shooters 0 - 10 & 10 10 - 20 & 12 20 - 30 & 15 30 - 40 & 8 40 - 50 & 20 50 - 60 & 24 60 - 70 & 7 70 - 80 & 11 80 - 90 & 30 90 - 100 & 18 \end{matrix}$

Use a graph sheet to draw the Histogram for the distribution.

The mode as seen in the graph is ___

Discussion

6027.	the lines xy=o and x+y =17 form a triangle in a xy plane . the total number of points having coordinates which are prime numbers and lie inside the triangle is
Answer» the lines xy=o and x+y =17 form a triangle in a xy plane . the total number of points having coordinates which are prime numbers and lie inside the triangle is

Discussion

6028.	A triangle has side lengths 6,7,8. The line through its incentre and parallel to the shortest side is drawn to meet the other two sides at P and Q. The length of the segment PQ is
Answer» A triangle has side lengths $6, 7, 8.$ The line through its incentre and parallel to the shortest side is drawn to meet the other two sides at $P$ and $Q .$ The length of the segment $P Q$ is

Discussion

6029.	If α, β are the zeros of a polynomial such that α + β = −6 and αβ = −4, then write the polynomial.
Answer» If α, β are the zeros of a polynomial such that α + β = −6 and αβ = −4, then write the polynomial.

Discussion

6030.	If PQQR=YZZX and QRPR=ZXYX , then
Answer» If $\frac{P Q}{Q R} = \frac{Y Z}{Z X}$ and $\frac{Q R}{P R} = \frac{Z X}{Y X}$ , then

6030.

If PQQR=YZZX and QRPR=ZXYX , then

Answer»

If $\frac{P Q}{Q R} = \frac{Y Z}{Z X}$ and $\frac{Q R}{P R} = \frac{Z X}{Y X}$ , then

Discussion

6031.	25.Find out the frequency of AabbCcDdee if parents are AabbCCddEe and AabbccDdee (1) 0.78 (2)12.5% (3) 25% (4)50%
Answer» 25.Find out the frequency of AabbCcDdee if parents are AabbCCddEe and AabbccDdee (1) 0.78 (2)12.5% (3) 25% (4)50%

Discussion

6032.	Find the volume of the given shape.
Answer» Find the volume of the given shape.

6032.

Find the volume of the given shape.

Answer»

Find the volume of the given shape.

Discussion

6033.	3x-7 > 5x -1
Answer» 3x-7 > 5x -1

Discussion

6034.	The common ratio of a G.P is 3 and the but term is 486. If the sum of there terms be 728. Find the term
Answer» The common ratio of a G.P is 3 and the but term is 486. If the sum of there terms be 728. Find the term

Discussion

6035.	Question 1 Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.
Answer» Question 1 Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.

Discussion

6036.	In the given figure, if ∠ABC = 20∘ , then ∠AOC is equal to ____________.
Answer» In the given figure, if ∠ABC = 20∘ , then ∠AOC is equal to ____________.

Discussion

6037.	proove that-1+2sin thita+sin^2thita/cos^2thita=sec thita+tan thita/secthita-tanthita
Answer» proove that-1+2sin thita+sin^2thita/cos^2thita=sec thita+tan thita/secthita-tanthita

Discussion

6038.	The 17th term of an AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term. [CBSE 2012]
Answer» The 17th term of an AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term. [CBSE 2012]

Discussion

6039.	Question 8Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.
Answer» Question 8 Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

Discussion

6040.	In △PQR, PQ = 12 cm and PR = 13 cm. ∠Q=90∘. Find tan P - cot R
Answer» In $△$ PQR, PQ = 12 cm and PR = 13 cm. $∠ Q = 90^{\circ}$ . Find tan P - cot R

Discussion

6041.	The boat goes 24km upstream and 28 km downstream in 6hours. It goes 30 km upstream and 21 km downstream in 612.Find the speed of boat in still water and also speed of the stream.
Answer» The boat goes 24km upstream and 28 km downstream in 6hours. It goes 30 km upstream and 21 km downstream in 6 $\frac{1}{2}$ .Find the speed of boat in still water and also speed of the stream.

Discussion

6042.	If A = {1, 5, 6}, B = {4, 8, 9} and f : A→B is a function defined by f(x) = x + 3, represent the function as a set of ordered pairs, table form and arrow diagram.
Answer» If A = {1, 5, 6}, B = {4, 8, 9} and f : A $\to$ B is a function defined by f(x) = x + 3, represent the function as a set of ordered pairs, table form and arrow diagram.

Discussion

6043.	Solve the following pair of linear equations by the substitution and cross-multiplication methods:
Answer» Solve the following pair of linear equations by the substitution and cross-multiplication methods:

6043.

Solve the following pair of linear equations by the substitution and cross-multiplication methods:

Answer»

Solve the following pair of linear equations by the substitution and cross-multiplication methods:

Discussion

6044.	Express (sin 85∘ + cosec 85∘) in terms of trigonometric ratios of angles between 0∘ and 45∘.
Answer» Express (sin $85^{\circ}$ + cosec $85^{\circ}$ ) in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$ .

Discussion

6045.	In the given figure, R is an external point and RP and RQ are tangents drawn to the circle from R. ∠POQ is 90∘. Prove that OPRQ is a prarallelogram, and find the ∠ POR.
Answer» In the given figure, R is an external point and RP and RQ are tangents drawn to the circle from R. $∠ P O Q i s 90^{\circ}$ . Prove that OPRQ is a prarallelogram, and find the $∠$ POR.

Discussion

6046.	Identify the matrix ⎡⎢⎢⎢⎢⎢⎢⎣12345⎤⎥⎥⎥⎥⎥⎥⎦
Answer» Identify the matrix $⎡ ⎢⎢⎢⎢⎢⎢ ⎣ \begin{matrix} 12345 \end{matrix} ⎤ ⎥⎥⎥⎥⎥⎥ ⎦$

Discussion

6047.	A bag contains 100 identical marble stones numbered from 1 to 100. What is the probability of drawing a marble having number divisible by 4 and 5?
Answer» A bag contains 100 identical marble stones numbered from 1 to 100. What is the probability of drawing a marble having number divisible by 4 and 5?

Discussion

6048.	Given that the eqn 12x-4x-5x+2 has two zeros equal find all the zeros.
Answer» Given that the eqn 12x-4x-5x+2 has two zeros equal find all the zeros.

Discussion

6049.

For what value of a and b will the following pair of equations have infinite solution. x+2y = 1 (a-b)x + (a+b)y =2a-b+1

Answer»

For what value of a and b will the following pair of equations have infinite solution.

x+2y = 1

(a-b)x + (a+b)y =2a-b+1

Discussion

6050.	Polynomials are everywhere. It is found in the slope of a hill, the curve of a bridge or the continuity of a mountain range. Based on the given information, answer the following question. If the hills are prepresented by the cubic polynomial t(x)=2x3+8x2+9x+16, then the product of the zeroes is:
Answer» Polynomials are everywhere. It is found in the slope of a hill, the curve of a bridge or the continuity of a mountain range. Based on the given information, answer the following question. If the hills are prepresented by the cubic polynomial $t (x) = 2 x^{3} + 8 x^{2} + 9 x + 16,$ then the product of the zeroes is:

Discussion

Explore topic-wise InterviewSolutions in .

∆ABC ∼ ∆PQR such that ar(∆ABC) = 4 ar(∆PQR). If BC = 12 cm, then QR =(a) 9 cm(b) 10 cm(c) 6 cm(d) 8 cm

The range of the function f(x)=13−sin 3x, x∈R is

Which of the following is a solution to 3x+4y=38?

The value of the polynomial: x2−3x+5 at x=0 is

Find the greatest number that can divide 101 and 115 leaving remainders 5 and 7 respectively.

In the given figure, two equal circles touch each other at T, if OP = 4.5 cm, then QR = (a) 9 cm(b) 18 cm(c) 15 cm(d) 13.5 cm

The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is (A) y – x + 1 = 0 (B) y – x – 1 = 0 (C) y – x + 2 = 0 (D) y – x – 2 = 0

Sachin scored twice as many as fun as Rahul .Together that runs fell to short of a double century how many runs did each one score?

Explain why 7 × 11 × 13 + 13 is a composite number.

34. the sum of n terms of two AP are in the ratio (3n+8):(7n+15), find the ratio of their 12 terms

Find the values of k for the following quadratic equation, so that they have two equal roots. kx (x - 2) + 6 = 0

The product of 1, 2, 3, 4, 5, 6...... and 25 has _______ number of zeroes in the end.

Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.

If the lines x+3−3=y−11=z−k5 and x+1−1=y−22=z−55 are coplanar, then the value of k is

What least number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion?

What is the hcf of smallest prime and composite number?

Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n.

Find the derivative of the following function: f(x) = (x+cos x)(x−tan x)

Find domain and range of the following function : a. 1/\surd(x+\vert x\vert) b. 1/\surd(x-\vert x\vert)

Sketch a rough plan and calculate the area of the field ABCDEFG from the following Metre to D To E 90 To F 60 To G 15 225 175 125 100 80 60 20 to C 70 to B From A

Find the median class for the given distribution:Weekly wages (in Rs.)0−100100−200200−300300−400400−500No. of workers4039343045

Find the roots of the following quadratic equations by the factorisation method: 21x^2 – 2x + 121 = 0

the lines xy=o and x+y =17 form a triangle in a xy plane . the total number of points having coordinates which are prime numbers and lie inside the triangle is

A triangle has side lengths 6,7,8. The line through its incentre and parallel to the shortest side is drawn to meet the other two sides at P and Q. The length of the segment PQ is

If α, β are the zeros of a polynomial such that α + β = −6 and αβ = −4, then write the polynomial.

If PQQR=YZZX and QRPR=ZXYX , then

25.Find out the frequency of AabbCcDdee if parents are AabbCCddEe and AabbccDdee (1) 0.78 (2)12.5% (3) 25% (4)50%

Find the volume of the given shape.

3x-7 &gt; 5x -1

The common ratio of a G.P is 3 and the but term is 486. If the sum of there terms be 728. Find the term

Question 1 Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.

In the given figure, if ∠ABC = 20∘ , then ∠AOC is equal to ____________.

proove that-1+2sin thita+sin^2thita/cos^2thita=sec thita+tan thita/secthita-tanthita

The 17th term of an AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term. [CBSE 2012]

Question 8Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

In △PQR, PQ = 12 cm and PR = 13 cm. ∠Q=90∘. Find tan P - cot R

The boat goes 24km upstream and 28 km downstream in 6hours. It goes 30 km upstream and 21 km downstream in 612.Find the speed of boat in still water and also speed of the stream.

If A = {1, 5, 6}, B = {4, 8, 9} and f : A→B is a function defined by f(x) = x + 3, represent the function as a set of ordered pairs, table form and arrow diagram.

Solve the following pair of linear equations by the substitution and cross-multiplication methods:

Express (sin 85∘ + cosec 85∘) in terms of trigonometric ratios of angles between 0∘ and 45∘.

In the given figure, R is an external point and RP and RQ are tangents drawn to the circle from R. ∠POQ is 90∘. Prove that OPRQ is a prarallelogram, and find the ∠ POR.

Identify the matrix ⎡⎢⎢⎢⎢⎢⎢⎣12345⎤⎥⎥⎥⎥⎥⎥⎦

A bag contains 100 identical marble stones numbered from 1 to 100. What is the probability of drawing a marble having number divisible by 4 and 5?

Given that the eqn 12x-4x-5x+2 has two zeros equal find all the zeros.

For what value of a and b will the following pair of equations have infinite solution. x+2y = 1 (a-b)x + (a+b)y =2a-b+1

Polynomials are everywhere. It is found in the slope of a hill, the curve of a bridge or the continuity of a mountain range. Based on the given information, answer the following question. If the hills are prepresented by the cubic polynomial t(x)=2x3+8x2+9x+16, then the product of the zeroes is:

3x-7 > 5x -1