32581 + Interview Questions in Mathematics Page 41 InterviewSolution

2001.	Identify the figure that completes the pattern.
Answer» Identify the figure that completes the pattern.

2001.

Identify the figure that completes the pattern.

Answer»

Identify the figure that completes the pattern.

2002.	Draw the graph of the lines x = -2 and y = 3 . Write the vertices of the figure formed by these lines , the x-axis and the y-axis . Also , find the area of the figure.
Answer» Draw the graph of the lines x = $-$ 2 and y = 3 . Write the vertices of the figure formed by these lines , the x-axis and the y-axis . Also , find the area of the figure.

Discussion

2003.	If a piece of cloth costs ₹10/m2, then find the total cost to build a square pyramid tent of base edge 10 m and slant height 10 m.
Answer» If a piece of cloth costs $₹ 10 / m^{2},$ then find the total cost to build a square pyramid tent of base edge 10 m and slant height 10 m.

Discussion

2004.	Find the value of p for which the quadratic equation p+1x2-6(p+1)x+3(p+9)=0, p≠-1 has equal roots. Hence, find the roots of the equation.Disclaimer: There is a misprinting in the given question. In the question 'q' is printed instead of 9.
Answer» Find the value of p for which the quadratic equation $(p + 1) x^{2} - 6 (p + 1) x + 3 (p + 9) = 0, p \neq - 1$ has equal roots. Hence, find the roots of the equation. Disclaimer: There is a misprinting in the given question. In the question 'q' is printed instead of 9.

Discussion

2005.	The square of (2x -1) is equal to 5. What is x?
Answer» The square of (2 $x$ -1) is equal to 5. What is $x$ ?

Discussion

2006.	Question 2(iv)Represent the following situations in the form of quadratic equations.(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Answer» Question 2(iv) Represent the following situations in the form of quadratic equations. (iv) A train travels a distance of $480 k m$ at a uniform speed. If the speed had been $8 k m / h$ less, then it would have taken $3$ hours more to cover the same distance. We need to find the speed of the train.

Discussion

2007.	99. If One vertex of an equilateral is 1+i and centroid is at origin, then find other two vertices of triangle
Answer» 99. If One vertex of an equilateral is 1+i and centroid is at origin, then find other two vertices of triangle

Discussion

2008.	In the figure, it is given that XY = 6 cm, ∠XOY=∠MON=85∘. The length of the chord MN is ____ cm.
Answer» In the figure, it is given that XY = 6 cm, $∠ X O Y = ∠ M O N = 85^{\circ}$ . The length of the chord MN is ____ cm.

2008.

In the figure, it is given that XY = 6 cm, ∠XOY=∠MON=85∘. The length of the chord MN is ____ cm.

Answer»

In the figure, it is given that XY = 6 cm,
$∠ X O Y = ∠ M O N = 85^{\circ}$ .
The length of the chord MN is ____ cm.

Discussion

2009.	Question 1 Write ‘True’ or ‘False’ and justify your answer in each of the following: tan47∘cot43∘=1
Answer» Question 1 Write ‘True’ or ‘False’ and justify your answer in each of the following: $\frac{t a n 47^{\circ}}{c o t 43^{\circ}} = 1$

Discussion

2010.	44. if 5-1 / 5+1 + 5+1 / 5-1 = a+b5 find the value of a & b
Answer» 44. if 5-1 / 5+1 + 5+1 / 5-1 = a+b5 find the value of a & b

Discussion

2011.	In a potato race, a bucket is placed at the starting point, which is 5 meters from the first potato, and the other potatoes are placed 3 meters apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
Answer» In a potato race, a bucket is placed at the starting point, which is 5 meters from the first potato, and the other potatoes are placed 3 meters apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

Discussion

2012.	As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30∘ and 45∘. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
Answer» As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are $30^{\circ}$ and $45^{\circ}$ . If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Discussion

2013.	An unbiased die is thrown, then the probability of getting an even number and a multiple of 3 is
Answer» An unbiased die is thrown, then the probability of getting an even number and a multiple of 3 is

Discussion

2014.	Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.
Answer» Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.

Discussion

2015.	Write the set of value of k for which the quadratic equations has 2x2 + kx − 8 = 0 has real roots.
Answer» Write the set of value of k for which the quadratic equations has 2x² + kx − 8 = 0 has real roots.

Discussion

2016.	The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
Answer» The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.

Discussion

2017.	The slope of the side BC of a rectangle ABCD is 23. Find : (i) the slope of the side AB, (ii) the slope of the side AD.
Answer» The slope of the side BC of a rectangle ABCD is $\frac{2}{3}$ . Find : (i) the slope of the side AB, (ii) the slope of the side AD.

2017.

The slope of the side BC of a rectangle ABCD is 23. Find : (i) the slope of the side AB, (ii) the slope of the side AD.

Answer»

The slope of the side BC of a rectangle ABCD is $\frac{2}{3}$ . Find :

(i) the slope of the side AB,

(ii) the slope of the side AD.

Discussion

2018.	In the adjoining figure, ∠B=90°, ∠BAC=θ°, BC=CD=4 cm and AD=10 cm. Find i sinθ and ii cosθ.
Answer» In the adjoining figure, $∠ B = 90 °, ∠ BAC = θ °, BC = CD = 4 cm and AD = 10 cm . Find (i) \sin θ and (ii) \cos θ .$

Discussion

2019.	Prove the following trigonometric identities.If xacos θ+ybsin θ=1 and xasin θ-ybcos θ=1, prove that x2a2+y2b2=2
Answer» Prove the following trigonometric identities. If $\frac{x}{a} \cos θ + \frac{y}{b} \sin θ = 1 and \frac{x}{a} \sin θ - \frac{y}{b} \cos θ = 1, prove that \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 2$

Discussion

2020.	If x[23]+y[−11]=[105], find the values of x and y
Answer» If $x [\begin{matrix} 23 \end{matrix}] + y [\begin{matrix} - 1 1 \end{matrix}] = [\begin{matrix} 105 \end{matrix}]$ , find the values of $x$ and $y$

Discussion

2021.	48x^2-13x-1=0 by using squaring method
Answer» 48x^2-13x-1=0 by using squaring method

Discussion

2022.	Which of the following is a factor of (49x2−1)+(1+7x)2?
Answer» Which of the following is a factor of $(49 x^{2} - 1) + (1 + 7 x)^{2}$ ?

Discussion

2023.	Which of the following options is equal to cot θ+cosec θ−1cot θ−cosec θ+1
Answer» Which of the following options is equal to $\frac{c o t θ + c o s e c θ - 1}{c o t θ - c o s e c θ + 1}$

Discussion

2024.	If x − a is a factor of x3 −3x2a + 2a2x + b, then the value of b is(a) 0(b) 2(c) 1(d) 3
Answer» If x − a is a factor of x³ −3x²a + 2a²x + b, then the value of b is (a) 0 (b) 2 (c) 1 (d) 3

Discussion

2025.	Determine. if 3 is a root of the equation given below:x2-4x+3+x2-9=4x2-14x+16
Answer» Determine. if 3 is a root of the equation given below: $\sqrt{x^{2} - 4 x + 3} + \sqrt{x^{2} - 9} = \sqrt{4 x^{2} - 14 x + 16}$

Discussion

2026.	If secθ+tanθ=43, then the value of secθtanθ is
Answer» If $sec θ + tan θ = \frac{4}{3},$ then the value of $sec θ tan θ$ is

Discussion

2027.	This is the graph of two linear equations that have
Answer» This is the graph of two linear equations that have

2027.

This is the graph of two linear equations that have

Answer»

This is the graph of two linear equations that have

Discussion

2028.	If the lines representing the pair of equations 2x+3y−5=0 and 8x+py+q=0 are coincident, then
Answer» If the lines representing the pair of equations $2 x + 3 y - 5 = 0$ and $8 x + p y + q = 0$ are coincident, then

Discussion

2029.	Find the dimensions of a square whose area is same as that of an equilateral triangle of dimensions 3 cm. (Use construction)
Answer» Find the dimensions of a square whose area is same as that of an equilateral triangle of dimensions 3 cm. (Use construction)

Discussion

2030.	28. The value of m in -3(m-2)>12 is
Answer» 28. The value of m in -3(m-2)>12 is

Discussion

2031.	In Fig. 10.86, PQL and PRM are tangents to the circle with centre O at the points Q and R respectively and S is a point on the circle such that ∠SQL = 500 and ∠SRM = 600. Then , find ∠QSR.figure
Answer» In Fig. 10.86, PQL and PRM are tangents to the circle with centre O at the points Q and R respectively and S is a point on the circle such that $∠$ SQL = 50⁰and $∠$ SRM = 60⁰. Then , find $∠$ QSR. figure

Discussion

2032.	Square matrix [aij]n×n will be an upper triangular matrix, if
Answer» Square matrix $[a_{i j}]_{n \times n}$ will be an upper triangular matrix, if

Discussion

2033.	If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes 6/5. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. find the fraction.
Answer» If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes 6/5. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. find the fraction.

Discussion

2034.	The probability that the month of April has exactly 5 Mondays is _________.
Answer» The probability that the month of April has exactly 5 Mondays is _________.

Discussion

2035.	A bag contains 12 balls of which 'x' are white. (i) If one ball is drawn at random, what is the probability that it will be a white ball? (ii) If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that in case (i), Find x. [4 MARKS]
Answer» A bag contains 12 balls of which 'x' are white. (i) If one ball is drawn at random, what is the probability that it will be a white ball? (ii) If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that in case (i), Find x. [4 MARKS]

Discussion

2036.	A bag contains tickets numbered 11,12,13,...,30. A ticket is taken out from the bag at random. Find the probability that the numberon the drawn ticket (i) is a multiple of 7 (ii) is greater than 15 and a multiple of 5.
Answer» A bag contains tickets numbered 11,12,13,...,30. A ticket is taken out from the bag at random. Find the probability that the numberon the drawn ticket (i) is a multiple of 7 (ii) is greater than 15 and a multiple of 5.

Discussion

2037.	Find and algebraic expression to compute the sum of the first n terms of the arithmetic sequence with first term f and common difference d.
Answer» Find and algebraic expression to compute the sum of the first n terms of the arithmetic sequence with first term f and common difference d.

Discussion

2038.	Find the values of a and b for which the following system of equations has infinitely many solutions:i 2a-1x-3y=5 3x+b-2y=3(ii) 2x-2a+5y=5 2b+1x-9y=15(iii) a-1x+3y=2 6x+1-2by=6(iv) 3x+4y=12 a+bx+2a-by=5a-1v 2x+3y=7 a-bx+a+by=3a+b-2vi 2x+3y-7=0 a-1x+a+1y=3a-1vii 2x+3y=7 a-1x+a+2y=3aviii x+2y=1a-bx+a+by=a+b-2 ix 2x+3y=72ax+ay=28-by
Answer» Find the values of a and b for which the following system of equations has infinitely many solutions: $(i) (2 a - 1) x - 3 y = 5 3 x + (b - 2) y = 3 (i i) 2 x - (2 a + 5) y = 5 (2 b + 1) x - 9 y = 15 (i i i) (a - 1) x + 3 y = 2 6 x + (1 - 2 b) y = 6 (i v) 3 x + 4 y = 12 (a + b) x + 2 (a - b) y = 5 a - 1 (v) 2 x + 3 y = 7 (a - b) x + (a + b) y = 3 a + b - 2 (v i) 2 x + 3 y - 7 = 0 (a - 1) x + (a + 1) y = (3 a - 1) (v i i) 2 x + 3 y = 7 (a - 1) x + (a + 2) y = 3 a$ $(v i i i) x + 2 y = 1 (a - b) x + (a + b) y = a + b - 2$ $(i x) 2 x + 3 y = 7 2 a x + a y = 28 - b y$

Discussion

2039.	If TP and TQ are two tangents drawn to a circle with center O such that ∠POQ =110∘, then, ∠PTQ is equal to:
Answer» If TP and TQ are two tangents drawn to a circle with center O such that $∠$ POQ $= 110^{\circ}$ , then, $∠$ PTQ is equal to:

Discussion

2040.	The product of two numbers is 1530 and their HCF is 15. The LCM of these numbers is(a) 102(b) 120(c) 84(d) 112
Answer» The product of two numbers is 1530 and their HCF is 15. The LCM of these numbers is (a) 102 (b) 120 (c) 84 (d) 112

Discussion

2041.	If ∆ABC and ∆AMP are two right triangles, right angled at B and M respectively such that ∠MAP = ∠BAC. Prove that(i) ∆ABC ∼ ∆AMP(ii) CAPA=BCMP
Answer» If ∆ABC and ∆AMP are two right triangles, right angled at B and M respectively such that ∠MAP = ∠BAC. Prove that (i) ∆ABC ∼ ∆AMP (ii) $\frac{CA}{PA} = \frac{BC}{MP}$

Discussion

2042.	The number of value(s) of x satisfying sin(13cos−1x)=1 is
Answer» The number of value(s) of $x$ satisfying $sin (\frac{1}{3} {cos}^{- 1} x) = 1$ is

Discussion

2043.	One angle of a ΔABC is 150∘ and its opposite side is 3 cm as shown in the figure. The diameter of its circumcircle is equal to
Answer» One angle of a $Δ A B C$ is $150^{\circ}$ and its opposite side is 3 cm as shown in the figure. The diameter of its circumcircle is equal to

2043.

One angle of a ΔABC is 150∘ and its opposite side is 3 cm as shown in the figure. The diameter of its circumcircle is equal to

Answer»

One angle of a $Δ A B C$ is $150^{\circ}$ and its opposite side is 3 cm as shown in the figure. The diameter of its circumcircle is equal to

Discussion

2044.	If one zero of polynomial 3x2-8x+2k+1 in seven times other find the zero and the value of the k
Answer» If one zero of polynomial 3x2-8x+2k+1 in seven times other find the zero and the value of the k

Discussion

2045.	One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is(a) (–1, –1)(b) (2, 2)(c) (–2, –2)(d) (2, –2)
Answer» One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is (a) (–1, –1) (b) (2, 2) (c) (–2, –2) (d) (2, –2)

Discussion

2046.	A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Find the cost of cloth required to make the tent at the rate of Rs 80 per square metre. [Take π=227.]
Answer» A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Find the cost of cloth required to make the tent at the rate of Rs 80 per square metre. $[T a k e π = \frac{22}{7.}]$

Discussion

2047.	Solve the following system of equation graphically: 2x+3y+5=03x-2y-12=0
Answer» Solve the following system of equation graphically: $2 x + 3 y + 5 = 0 3 x - 2 y - 12 = 0$

Discussion

2048.	Question 3 (iii)In an AP:(iii) Given a12=37,d=3, find a and S12.
Answer» Question 3 (iii) In an AP: (iii) Given $a_{12} = 37, d = 3$ , find a and $S_{12}$ .

Discussion

2049.	Can (y+1) be the remainder on division of a polynomial p(y) by y-5? Give reason
Answer» Can (y+1) be the remainder on division of a polynomial p(y) by y-5? Give reason

Discussion

2050.	A solid sphere of radius 'r' is melted and recast into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm, its height 24 cm and thickness 2 cm, find the value of 'r'.
Answer» A solid sphere of radius 'r' is melted and recast into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm, its height 24 cm and thickness 2 cm, find the value of 'r'.

Discussion

Explore topic-wise InterviewSolutions in .

Identify the figure that completes the pattern.

Draw the graph of the lines x = -2 and y = 3 . Write the vertices of the figure formed by these lines , the x-axis and the y-axis . Also , find the area of the figure.

If a piece of cloth costs ₹10/m2, then find the total cost to build a square pyramid tent of base edge 10 m and slant height 10 m.

Find the value of p for which the quadratic equation p+1x2-6(p+1)x+3(p+9)=0, p≠-1 has equal roots. Hence, find the roots of the equation.Disclaimer: There is a misprinting in the given question. In the question 'q' is printed instead of 9.

The square of (2x -1) is equal to 5. What is x?

Question 2(iv)Represent the following situations in the form of quadratic equations.(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

99. If One vertex of an equilateral is 1+i and centroid is at origin, then find other two vertices of triangle

In the figure, it is given that XY = 6 cm, ∠XOY=∠MON=85∘. The length of the chord MN is ____ cm.

Question 1 Write ‘True’ or ‘False’ and justify your answer in each of the following: tan47∘cot43∘=1

44. if 5-1 / 5+1 + 5+1 / 5-1 = a+b5 find the value of a & b

As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30∘ and 45∘. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

An unbiased die is thrown, then the probability of getting an even number and a multiple of 3 is

Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.

Write the set of value of k for which the quadratic equations has 2x2 + kx − 8 = 0 has real roots.

The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.

The slope of the side BC of a rectangle ABCD is 23. Find : (i) the slope of the side AB, (ii) the slope of the side AD.

In the adjoining figure, ∠B=90°, ∠BAC=θ°, BC=CD=4 cm and AD=10 cm. Find i sinθ and ii cosθ.

Prove the following trigonometric identities.If xacos θ+ybsin θ=1 and xasin θ-ybcos θ=1, prove that x2a2+y2b2=2

If x[23]+y[−11]=[105], find the values of x and y

48x^2-13x-1=0 by using squaring method

Which of the following is a factor of (49x2−1)+(1+7x)2?

Which of the following options is equal to cot θ+cosec θ−1cot θ−cosec θ+1

If x − a is a factor of x3 −3x2a + 2a2x + b, then the value of b is(a) 0(b) 2(c) 1(d) 3

Determine. if 3 is a root of the equation given below:x2-4x+3+x2-9=4x2-14x+16

If secθ+tanθ=43, then the value of secθtanθ is

This is the graph of two linear equations that have

If the lines representing the pair of equations 2x+3y−5=0 and 8x+py+q=0 are coincident, then

Find the dimensions of a square whose area is same as that of an equilateral triangle of dimensions 3 cm. (Use construction)

28. The value of m in -3(m-2)>12 is

In Fig. 10.86, PQL and PRM are tangents to the circle with centre O at the points Q and R respectively and S is a point on the circle such that ∠SQL = 500 and ∠SRM = 600. Then , find ∠QSR.figure

Square matrix [aij]n×n will be an upper triangular matrix, if

If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes 6/5. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. find the fraction.

The probability that the month of April has exactly 5 Mondays is _________.

A bag contains 12 balls of which 'x' are white. (i) If one ball is drawn at random, what is the probability that it will be a white ball? (ii) If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that in case (i), Find x. [4 MARKS]

A bag contains tickets numbered 11,12,13,...,30. A ticket is taken out from the bag at random. Find the probability that the numberon the drawn ticket (i) is a multiple of 7 (ii) is greater than 15 and a multiple of 5.

Find and algebraic expression to compute the sum of the first n terms of the arithmetic sequence with first term f and common difference d.

If TP and TQ are two tangents drawn to a circle with center O such that ∠POQ =110∘, then, ∠PTQ is equal to:

The product of two numbers is 1530 and their HCF is 15. The LCM of these numbers is(a) 102(b) 120(c) 84(d) 112

If ∆ABC and ∆AMP are two right triangles, right angled at B and M respectively such that ∠MAP = ∠BAC. Prove that(i) ∆ABC ∼ ∆AMP(ii) CAPA=BCMP

The number of value(s) of x satisfying sin(13cos−1x)=1 is

One angle of a ΔABC is 150∘ and its opposite side is 3 cm as shown in the figure. The diameter of its circumcircle is equal to

If one zero of polynomial 3x2-8x+2k+1 in seven times other find the zero and the value of the k

One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is(a) (–1, –1)(b) (2, 2)(c) (–2, –2)(d) (2, –2)

A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Find the cost of cloth required to make the tent at the rate of Rs 80 per square metre. [Take π=227.]

Solve the following system of equation graphically: 2x+3y+5=03x-2y-12=0

Question 3 (iii)In an AP:(iii) Given a12=37,d=3, find a and S12.

Can (y+1) be the remainder on division of a polynomial p(y) by y-5? Give reason

A solid sphere of radius 'r' is melted and recast into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm, its height 24 cm and thickness 2 cm, find the value of 'r'.