32581 + Interview Questions in Mathematics Page 210 InterviewSolution

10451.	Two vertices of a triangle have coordinates (−8, 7) and (9, 4) . If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?
Answer» Two vertices of a triangle have coordinates (−8, 7) and (9, 4) . If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?

Discussion

10452.	A match box measures 4 cm × 2.5 cm × 1.5 cm. Which of the following does not represent the volume of a packet containing 12 such boxes?
Answer» A match box measures 4 cm $\times$ 2.5 cm $\times$ 1.5 cm. Which of the following does not represent the volume of a packet containing 12 such boxes?

Discussion

10453.	The polynomial equations P1(x) = x3+x2+x+1 and P2(x) = x2−1 have how many factors in common?
Answer» The polynomial equations $P_{1}$ (x) = $x^{3} + x^{2} + x + 1$ and $P_{2}$ (x) = $x^{2} - 1$ have how many factors in common?

Discussion

10454.	An express train takes 1hour less than a passenger train to travel 132 Km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of Express train is 1 Km/h more than that of the passenger train, find the average speeds of the train.
Answer» An express train takes 1hour less than a passenger train to travel 132 Km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of Express train is 1 Km/h more than that of the passenger train, find the average speeds of the train.

Discussion

10455.	You are given a circle with radius 'r' and centre 'O'. You are asked to draw a pair of tangents which are inclined at an angle of 60° with each other, from a point E.Refer to the figure and select the option which would lead you to the required construction. The distance d is the distance OE.
Answer» You are given a circle with radius 'r' and centre 'O'. You are asked to draw a pair of tangents which are inclined at an angle of 60° with each other, from a point E. Refer to the figure and select the option which would lead you to the required construction. The distance d is the distance OE.

10455.

You are given a circle with radius 'r' and centre 'O'. You are asked to draw a pair of tangents which are inclined at an angle of 60° with each other, from a point E.Refer to the figure and select the option which would lead you to the required construction. The distance d is the distance OE.

Answer»

You are given a circle with radius 'r' and centre 'O'. You are asked to draw a pair of tangents which are inclined at an angle of 60° with each other, from a point E.

Refer to the figure and select the option which would lead you to the required construction. The distance d is the distance OE.

Discussion

10456.	If sin θ = cos (θ − 45°), where θ and θ − 45° are acute angles, find the degree measure of θ.
Answer» If sin θ = cos (θ − 45°), where θ and θ − 45° are acute angles, find the degree measure of θ.

Discussion

10457.	The sum of first m terms of an AP is (4m2 − m). If its nth term is 107, find the value of n. Also, find the 21st term of this AP. [CBSE 2013]
Answer» The sum of first m terms of an AP is (4m² − m). If its nth term is 107, find the value of n. Also, find the 21st term of this AP. [CBSE 2013]

Discussion

10458.	Question 4 (ii) Which is greater: 12of67or23of37
Answer» Question 4 (ii) Which is greater: $\frac{1}{2} o f \frac{6}{7} o r \frac{2}{3} o f \frac{3}{7}$

Discussion

10459.	Prove that 1÷cosec A-cot A -1÷sin A =1÷sin A -1÷cosex A+cot A
Answer» Prove that 1÷cosec A-cot A -1÷sin A =1÷sin A -1÷cosex A+cot A

Discussion

10460.	A mansion has twelve cylindrical pillars each having the circumference 50 cm and height 3.5 m. Find the cost of painting the lateral surface of the pillars at Rs 25 per sq. m.
Answer» A mansion has twelve cylindrical pillars each having the circumference 50 cm and height 3.5 m. Find the cost of painting the lateral surface of the pillars at Rs 25 per sq. m.

Discussion

10461.	Water is flowing at the rate of 6 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 60 m long and 22 m wide. Determine the time in which the level of water in the tank will rise by 7 cm.
Answer» Water is flowing at the rate of $6 k m / h r$ through a pipe of diameter $14 c m$ into a rectangular tank which is 60 m long and $22 m$ wide. Determine the time in which the level of water in the tank will rise by $7 c m .$

Discussion

10462.	Write the value of k for which the system of equations has infinitely many solutions.2x-y=56x+ky=15
Answer» Write the value of k for which the system of equations has infinitely many solutions. $2 x - y = 5 6 x + k y = 15$

Discussion

10463.	The base radius and height of a right circular solid cone are 12 cm and 24 cm respectively. It is melted and recast into spheres of diameter 6 cm each. Find the number of spheres so formed.
Answer» The base radius and height of a right circular solid cone are 12 cm and 24 cm respectively. It is melted and recast into spheres of diameter 6 cm each. Find the number of spheres so formed.

Discussion

10464.	If U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}A = {x : x is a perfect square less than 10}B = {x : x is a multiple of 3 less than 10}Verify (i) (A ∪ B)′ = A′ ∩ B′ (ii) (A ∩ B)′ = A′ ∪ B′
Answer» If U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} A = {x : x is a perfect square less than 10} B = {x : x is a multiple of 3 less than 10} Verify (i) (A ∪ B)′ = A′ ∩ B′ (ii) (A ∩ B)′ = A′ ∪ B′

10464.

If U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}A = {x : x is a perfect square less than 10}B = {x : x is a multiple of 3 less than 10}Verify (i) (A ∪ B)′ = A′ ∩ B′ (ii) (A ∩ B)′ = A′ ∪ B′

Answer»

If U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {x : x is a perfect square less than 10}

B = {x : x is a multiple of 3 less than 10}

Verify (i) (A ∪ B)′ = A′ ∩ B′ (ii) (A ∩ B)′ = A′ ∪ B′

Discussion

10465.	The perimeter of a right triangle is 40 cm and its hypotenuse measures 17 cm. Find the area of the triangle.
Answer» The perimeter of a right triangle is 40 cm and its hypotenuse measures 17 cm. Find the area of the triangle.

Discussion

10466.	In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If ∠PRQ=l and ∠OPQ=m, then find l+m.
Answer» In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If $∠ P R Q = l$ and $∠ O P Q = m,$ then find $l + m$ .

Discussion

10467.	The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, then the length of the wire is(a) 12 m(b) 10 m(c) 8 m(d) 6 m
Answer» The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, then the length of the wire is (a) 12 m (b) 10 m (c) 8 m (d) 6 m

Discussion

10468.	22.A bullet is fired from the bottom of the inclined plane at angle 37 degree with the inclined plane. The angle of incline is 30 degree with the horizontal. Find (a) position of maximum height of bullet(b) time of flight (c) range along incline.
Answer» 22.A bullet is fired from the bottom of the inclined plane at angle 37 degree with the inclined plane. The angle of incline is 30 degree with the horizontal. Find (a) position of maximum height of bullet(b) time of flight (c) range along incline.

Discussion

10469.	Three numbers that are co - prime to each other are such that the product of the first two is 551 and that of the last two is 1073. Find, the sum of all the three numbers.
Answer» Three numbers that are co - prime to each other are such that the product of the first two is 551 and that of the last two is 1073. Find, the sum of all the three numbers.

Discussion

10470.	Three cubes of a metal whose edges are in the ratio 3 : 4 : 5 are melted and converted into a single cube whose diagonal is 123 cm. Find theedges of the three cubes. [CBSE 2013C]
Answer» Three cubes of a metal whose edges are in the ratio 3 : 4 : 5 are melted and converted into a single cube whose diagonal is $12 \sqrt{3}$ cm. Find the edges of the three cubes. [CBSE 2013C]

Discussion

10471.	Question 1 (ii)For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.iii) −2√3,−9
Answer» Question 1 (ii) For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization. iii) $- 2 \sqrt{3}, - 9$

Discussion

10472.	a, b, c are in continued proportion. If a = 3 and c = 27 then find b.
Answer» a, b, c are in continued proportion. If a = 3 and c = 27 then find b.

Discussion

10473.	The value of sec2 60° – tan2 60° is __________.
Answer» The value of sec² 60° – tan² 60° is __________.

Discussion

10474.	Prove the following trigonometric identities.1-cos θ1+cos θ=cosec θ-cot θ
Answer» Prove the following trigonometric identities. $\sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = cosec θ - \cot θ$

Discussion

10475.	Question 32Fill in the blanks to make each statement true:The sum of two consecutive multiples of 10 is 210. The smaller multiple is ................
Answer» Question 32 Fill in the blanks to make each statement true: The sum of two consecutive multiples of 10 is 210. The smaller multiple is ................

10475.

Question 32Fill in the blanks to make each statement true:The sum of two consecutive multiples of 10 is 210. The smaller multiple is ................

Answer»

Question 32

Fill in the blanks to make each statement true:

The sum of two consecutive multiples of 10 is 210. The smaller multiple is ................

Discussion

10476.	Two rectangular gardens have the same width of 10 feet. However, the length of one is 20 feet while the other is 30 feet. Write a numerical expression to show what the area is for the two gardens combined
Answer» Two rectangular gardens have the same width of 10 feet. However, the length of one is 20 feet while the other is 30 feet. Write a numerical expression to show what the area is for the two gardens combined

Discussion

10477.	The circumference of a thin hollow cylindrical pipe is 44 cm and length is 20 m. Find the surface area of the pipe.
Answer» The circumference of a thin hollow cylindrical pipe is 44 cm and length is 20 m. Find the surface area of the pipe.

Discussion

10478.	A vertical tower stands on a horizontal plane and surmounted by a vertical flag staff of height 6m . At a point on plane , the angle of elevation of the bottom and top of the flag staff are 30° and 45° respectively .Find the height of the tower.
Answer» A vertical tower stands on a horizontal plane and surmounted by a vertical flag staff of height 6m . At a point on plane , the angle of elevation of the bottom and top of the flag staff are 30° and 45° respectively . Find the height of the tower.

Discussion

10479.	If the equation 9x2+6kx+4=0 has equal roots, then find the value of k =
Answer» If the equation $9 x^{2} + 6 k x + 4 = 0$ has equal roots, then find the value of k =

Discussion

10480.	A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs 100 and that on a bracelet is Rs 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit?It is being given that at least one of each must be produced.
Answer» A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs 100 and that on a bracelet is Rs 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.

Discussion

10481.	Find the third vertex of a triangle if its two vertices are A (-1, 4) and B (5, 2) and mid- point of one side is (0, 3)
Answer» Find the third vertex of a triangle if its two vertices are A (-1, 4) and B (5, 2) and mid- point of one side is (0, 3)

Discussion

10482.	Question 12In the following question, out of the four options, only one is correct. Write the correct answer:If x be any non-zero integer and m,n be negative integers, then xm×xn is equal to: (a) xm(b) x(m+n)(c) xn(d) x(m−n)
Answer» Question 12 In the following question, out of the four options, only one is correct. Write the correct answer: If x be any non-zero integer and m,n be negative integers, then $x^{m} \times x^{n}$ is equal to: (a) $x^{m}$ (b) $x^{(m + n)}$ (c) $x^{n}$ (d) $x^{(m - n)}$

10482.

Question 12In the following question, out of the four options, only one is correct. Write the correct answer:If x be any non-zero integer and m,n be negative integers, then xm×xn is equal to: (a) xm(b) x(m+n)(c) xn(d) x(m−n)

Answer»

Question 12

In the following question, out of the four options, only one is correct. Write the correct answer:

If x be any non-zero integer and m,n be negative integers, then $x^{m} \times x^{n}$ is equal to:

(a) $x^{m}$

(b) $x^{(m + n)}$

(c) $x^{n}$

(d) $x^{(m - n)}$

Discussion

10483.	The value of ∣∣∣∣11+p1+p+q23+2p4+3p+2q36+3p10+6p+3q∣∣∣∣ is:
Answer» The value of $∣ ∣∣ ∣ \begin{matrix} 1 & 1 + p & 1 + p + q 2 & 3 + 2 p & 4 + 3 p + 2 q 3 & 6 + 3 p & 10 + 6 p + 3 q \end{matrix} ∣ ∣∣ ∣$ is:

Discussion

10484.	A tank is full of 450 L of water. How much water will be filled in 30 tanks? If 18 buckets can be filled with one tank of water, how many buckets in all can be filled with the water in 30 tanks?
Answer» A tank is full of 450 L of water. How much water will be filled in 30 tanks? If 18 buckets can be filled with one tank of water, how many buckets in all can be filled with the water in 30 tanks?

Discussion

10485.	Solve the following inequation, write the solutin set and represent it on the number line : −x3≤x2−113<16,xϵR [3 MARKS]
Answer» Solve the following inequation, write the solutin set and represent it on the number line : $- \frac{x}{3} \leq \frac{x}{2} - 1 \frac{1}{3} < \frac{1}{6}, x ϵ R$ [3 MARKS]

Discussion

10486.	Question 90 (vi)Factorise the following, using the identity, a2−2ab+b2=(a−b)2.p2.y2−2py+1
Answer» Question 90 (vi) Factorise the following, using the identity, $a^{2} - 2 a b + b^{2} = (a - b)^{2}$ . $p^{2} . y^{2} - 2 p y + 1$

Discussion

10487.	What will the ratio AB:AC be if C divides the line segment AB in the ratio 5:12?
Answer» What will the ratio $A B : A C$ be if $C$ divides the line segment $A B$ in the ratio $5 : 12$ ?

Discussion

10488.	Given that first term of the AP is 7 & the common difference is 12.Find n if nth term of an AP is 295.
Answer» Given that first term of the AP is 7 & the common difference is 12.Find n if $n^{t h}$ term of an AP is 295.

Discussion

10489.	If from any point on the common chord of two interesting circle, tangents be drawn to the circles, prove that they are equal.
Answer» If from any point on the common chord of two interesting circle, tangents be drawn to the circles, prove that they are equal.

Discussion

10490.	Question 815(y−4)−2(y−9)+5(y+6)=0
Answer» Question 8 $15 (y - 4) - 2 (y - 9) + 5 (y + 6) = 0$

Discussion

10491.	Jaya has a certain number of word problems with her. She can solve some fixed number of problems every hour. After solving for 6 hours, she is left with 384 problems. If she had kept solving for 12 hours, she would have been left with 144 problems to solve. Find the number of word problems Jaya is left with after 8 hours of solving.
Answer» Jaya has a certain number of word problems with her. She can solve some fixed number of problems every hour. After solving for 6 hours, she is left with 384 problems. If she had kept solving for 12 hours, she would have been left with 144 problems to solve. Find the number of word problems Jaya is left with after 8 hours of solving.

Discussion

10492.	In the above figure ∆ABC~∆ADE. Given that AD=x cm, DB =x-3 cm, AE=4cm, EC=3 cm. What is the value of x?
Answer» In the above figure ∆ABC~∆ADE. Given that AD=x cm, DB =x-3 cm, AE=4cm, EC=3 cm. What is the value of x?

10492.

In the above figure ∆ABC~∆ADE. Given that AD=x cm, DB =x-3 cm, AE=4cm, EC=3 cm. What is the value of x?

Answer»

In the above figure ∆ABC~∆ADE. Given that AD=x cm, DB =x-3 cm, AE=4cm, EC=3 cm. What is the value of x?

Discussion

10493.	The tangent is ____ to the radius at the point of contact.
Answer» The tangent is ____ to the radius at the point of contact.

Discussion

10494.	Prove that 5 + 7^1/2 is irrational
Answer» Prove that 5 + 7^1/2 is irrational

Discussion

10495.	WHAT IS THE FOURTH ROOT OF 124-32\sqrt{15} ?
Answer» WHAT IS THE FOURTH ROOT OF 124-32\sqrt{15} ?

Discussion

10496.	For what value of k are the roots of the quadratic equation kx(x−2√5)+10=0 real and equal?
Answer» For what value of k are the roots of the quadratic equation $k x (x - 2 \sqrt{5}) + 10 = 0$ real and equal?

Discussion

10497.	If 'a' and 'b' are the zeroes of the polynomial f(X)=x²
Answer» If 'a' and 'b' are the zeroes of the polynomial f(X)=x²

Discussion

10498.	In the given figure, find ∠BDC
Answer» In the given figure, find ∠BDC

Discussion

10499.	The arithmetic mean of n observations is ¯x. If the sum of (n – m) observations is A, then the mean of remaining m observations is
Answer» The arithmetic mean of n observations is $¯ x$ . If the sum of (n – m) observations is A, then the mean of remaining m observations is

Discussion

10500.	Pick the correct statement.100 books have to be divided equally in 20 shelves. How many books will each shelf have?
Answer» Pick the correct statement. 100 books have to be divided equally in 20 shelves. How many books will each shelf have?

Discussion

Explore topic-wise InterviewSolutions in .

Two vertices of a triangle have coordinates (−8, 7) and (9, 4) . If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?

A match box measures 4 cm × 2.5 cm × 1.5 cm. Which of the following does not represent the volume of a packet containing 12 such boxes?

The polynomial equations P1(x) = x3+x2+x+1 and P2(x) = x2−1 have how many factors in common?

You are given a circle with radius 'r' and centre 'O'. You are asked to draw a pair of tangents which are inclined at an angle of 60° with each other, from a point E.Refer to the figure and select the option which would lead you to the required construction. The distance d is the distance OE.

If sin θ = cos (θ − 45°), where θ and θ − 45° are acute angles, find the degree measure of θ.

The sum of first m terms of an AP is (4m2 − m). If its nth term is 107, find the value of n. Also, find the 21st term of this AP. [CBSE 2013]

Question 4 (ii) Which is greater: 12of67or23of37

Prove that 1÷cosec A-cot A -1÷sin A =1÷sin A -1÷cosex A+cot A

A mansion has twelve cylindrical pillars each having the circumference 50 cm and height 3.5 m. Find the cost of painting the lateral surface of the pillars at Rs 25 per sq. m.

Water is flowing at the rate of 6 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 60 m long and 22 m wide. Determine the time in which the level of water in the tank will rise by 7 cm.

Write the value of k for which the system of equations has infinitely many solutions.2x-y=56x+ky=15

The base radius and height of a right circular solid cone are 12 cm and 24 cm respectively. It is melted and recast into spheres of diameter 6 cm each. Find the number of spheres so formed.

If U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}A = {x : x is a perfect square less than 10}B = {x : x is a multiple of 3 less than 10}Verify (i) (A ∪ B)′ = A′ ∩ B′ (ii) (A ∩ B)′ = A′ ∪ B′

The perimeter of a right triangle is 40 cm and its hypotenuse measures 17 cm. Find the area of the triangle.

In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If ∠PRQ=l and ∠OPQ=m, then find l+m.

The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, then the length of the wire is(a) 12 m(b) 10 m(c) 8 m(d) 6 m

22.A bullet is fired from the bottom of the inclined plane at angle 37 degree with the inclined plane. The angle of incline is 30 degree with the horizontal. Find (a) position of maximum height of bullet(b) time of flight (c) range along incline.

Three numbers that are co - prime to each other are such that the product of the first two is 551 and that of the last two is 1073. Find, the sum of all the three numbers.

Three cubes of a metal whose edges are in the ratio 3 : 4 : 5 are melted and converted into a single cube whose diagonal is 123 cm. Find theedges of the three cubes. [CBSE 2013C]

Question 1 (ii)For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.iii) −2√3,−9

a, b, c are in continued proportion. If a = 3 and c = 27 then find b.

The value of sec2 60° – tan2 60° is __________.

Prove the following trigonometric identities.1-cos θ1+cos θ=cosec θ-cot θ

Question 32Fill in the blanks to make each statement true:The sum of two consecutive multiples of 10 is 210. The smaller multiple is ................

Two rectangular gardens have the same width of 10 feet. However, the length of one is 20 feet while the other is 30 feet. Write a numerical expression to show what the area is for the two gardens combined

The circumference of a thin hollow cylindrical pipe is 44 cm and length is 20 m. Find the surface area of the pipe.

A vertical tower stands on a horizontal plane and surmounted by a vertical flag staff of height 6m . At a point on plane , the angle of elevation of the bottom and top of the flag staff are 30° and 45° respectively .Find the height of the tower.

If the equation 9x2+6kx+4=0 has equal roots, then find the value of k =

Find the third vertex of a triangle if its two vertices are A (-1, 4) and B (5, 2) and mid- point of one side is (0, 3)

Question 12In the following question, out of the four options, only one is correct. Write the correct answer:If x be any non-zero integer and m,n be negative integers, then xm×xn is equal to: (a) xm(b) x(m+n)(c) xn(d) x(m−n)

The value of ∣∣∣∣11+p1+p+q23+2p4+3p+2q36+3p10+6p+3q∣∣∣∣ is:

A tank is full of 450 L of water. How much water will be filled in 30 tanks? If 18 buckets can be filled with one tank of water, how many buckets in all can be filled with the water in 30 tanks?

Solve the following inequation, write the solutin set and represent it on the number line : −x3≤x2−113&lt;16,xϵR [3 MARKS]

Question 90 (vi)Factorise the following, using the identity, a2−2ab+b2=(a−b)2.p2.y2−2py+1

What will the ratio AB:AC be if C divides the line segment AB in the ratio 5:12?

Given that first term of the AP is 7 &amp; the common difference is 12.Find n if nth term of an AP is 295.

If from any point on the common chord of two interesting circle, tangents be drawn to the circles, prove that they are equal.

Question 815(y−4)−2(y−9)+5(y+6)=0

In the above figure ∆ABC~∆ADE. Given that AD=x cm, DB =x-3 cm, AE=4cm, EC=3 cm. What is the value of x?

The tangent is ____ to the radius at the point of contact.

Prove that 5 + 7^1/2 is irrational

WHAT IS THE FOURTH ROOT OF 124-32\sqrt{15} ?

For what value of k are the roots of the quadratic equation kx(x−2√5)+10=0 real and equal?

If 'a' and 'b' are the zeroes of the polynomial f(X)=x²

In the given figure, find ∠BDC

The arithmetic mean of n observations is ¯x. If the sum of (n – m) observations is A, then the mean of remaining m observations is

Pick the correct statement.100 books have to be divided equally in 20 shelves. How many books will each shelf have?

Solve the following inequation, write the solutin set and represent it on the number line : −x3≤x2−113<16,xϵR [3 MARKS]

Given that first term of the AP is 7 & the common difference is 12.Find n if nth term of an AP is 295.