32581 + Interview Questions in Mathematics Page 146 InterviewSolution

7251.	The polynomial equation P(x)= 3x2+5x+2 can be represented as
Answer» The polynomial equation P(x)= $3 x^{2} + 5 x + 2$ can be represented as

Discussion

7252.	Simplify: cos45°÷(sec30°+cosec30°)
Answer» Simplify: $cos 45 ° \div (sec 30 ° + cos e c 30 °)$

Discussion

7253.	1. The Corvette described parametrically by x=t²+t+1, y=t²-t+1 represents 1. Pair of straight lines 2. Ellipse 3. Hyperbola 4. Parabola
Answer» 1. The Corvette described parametrically by x=t²+t+1, y=t²-t+1 represents 1. Pair of straight lines 2. Ellipse 3. Hyperbola 4. Parabola

Discussion

7254.	If θ is an acute angle such that sec2 θ = 3, then the value of tan2 θ-cosec2 θtan2 θ+cosec2 θis(a) 47(b) 37(c) 27(d) 17
Answer» If θ is an acute angle such that sec² θ = 3, then the value of $\frac{\tan^{2} θ - {cosec}^{2} θ}{\tan^{2} θ + {cosec}^{2} θ}$ is (a) $\frac{4}{7}$ (b) $\frac{3}{7}$ (c) $\frac{2}{7}$ (d) $\frac{1}{7}$

Discussion

7255.	If 3x+y+2x-y=2 and 9x+y-4x-y=1 then(a) x=12, y=32 (b) x=52, y=12 (c) x=32, y=12 (d) x=12, y=52
Answer» If $\frac{3}{x + y} + \frac{2}{x - y} = 2 and \frac{9}{x + y} - \frac{4}{x - y} = 1$ then (a) $x = \frac{1}{2}, y = \frac{3}{2}$ (b) $x = \frac{5}{2}, y = \frac{1}{2}$ (c) $x = \frac{3}{2}, y = \frac{1}{2}$ (d) $x = \frac{1}{2}, y = \frac{5}{2}$

Discussion

7256.	Find the cardial number of the relation, R = {x:x∈N and 3≤x<7}.4
Answer» Find the cardial number of the relation, R = { $x : x \in N a n d 3 \leq x < 7$ }. 4

Discussion

7257.	A solid metal cylinder is of base-radius 12 centimetres and height 20 centimetres. By melting and recasting, how many cones of base-radius 4 centimetres and height 5 centimetres can be made?
Answer» A solid metal cylinder is of base-radius 12 centimetres and height 20 centimetres. By melting and recasting, how many cones of base-radius 4 centimetres and height 5 centimetres can be made?

Discussion

7258.	Find the value of t, given thatp(x)=x3−tx2+5x−3,g(x)=x2−2,q(x)=x−3,r(x)=7x−9Where,p(x) is the dividend,g(x) is the divisor,q(x) is the quotient, and r(x) is the remainder3
Answer» Find the value of t, given that $p (x) = x^{3} - t x^{2} + 5 x - 3,$ $g (x) = x^{2} - 2,$ $q (x) = x - 3,$ $r (x) = 7 x - 9$ Where, $p (x)$ is the dividend, $g (x)$ is the divisor, $q (x)$ is the quotient, and $r (x)$ is the remainder 3

Discussion

7259.	Find the area of the region bounded by the ellipse
Answer» Find the area of the region bounded by the ellipse

Discussion

7260.	Identify the number corresponding to the ‘?’
Answer» Identify the number corresponding to the ‘?’

7260.

Identify the number corresponding to the ‘?’

Answer»

Identify the number corresponding to the ‘?’

Discussion

7261.	If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =(a) 1n(b) n-1n(c) n+12n(d) n+1n
Answer» If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k = (a) $\frac{1}{n}$ (b) $\frac{n - 1}{n}$ (c) $\frac{n + 1}{2 n}$ (d) $\frac{n + 1}{n}$

Discussion

7262.	If n is an integer, then every integral multiple of 3 can be represented by the expression ___.
Answer» If n is an integer, then every integral multiple of 3 can be represented by the expression ___.

Discussion

7263.	Prove that if 1 < x < 4 and 1 < y < 4, then \|x − y\| < 3.
Answer» Prove that if 1 < x < 4 and 1 < y < 4, then \|x − y\| < 3.

7263.

Prove that if 1 < x < 4 and 1 < y < 4, then |x − y| < 3.

Answer»

Prove that if 1 < x < 4 and 1 < y < 4, then |x − y| < 3.

Discussion

7264.	If the zeros of the polynomial f(x) = 2x3 − 15x2 + 37x − 30 are in A.P., find them.
Answer» If the zeros of the polynomial f(x) = 2x³ − 15x² + 37x − 30 are in A.P., find them.

Discussion

7265.	Write a cubic polynomial whose zeroes are 2-2root5, 2+2root5 and 1
Answer» Write a cubic polynomial whose zeroes are 2-2root5, 2+2root5 and 1

Discussion

7266.	Solve the following pair of linear equations by the elimination method and the substitution method:
Answer» Solve the following pair of linear equations by the elimination method and the substitution method:

7266.

Solve the following pair of linear equations by the elimination method and the substitution method:

Answer»

Solve the following pair of linear equations by the elimination method and the substitution method:

Discussion

7267.	If sin θ+cos θ=a and sec θ+cosec θ=b, then what is the value of b(a2−1)?
Answer» If $s i n θ + c o s θ = a$ and $s e c θ + c o s e c θ = b$ , then what is the value of $b (a^{2} - 1)$ ?

Discussion

7268.	Let A(4,7,8), B(2,3,4) and C(2,5,7) be the position vectors of the vertices of a triangle △ABC. Then the length (in units) of the internal angular bisector of angle A is
Answer» Let $A (4, 7, 8), B (2, 3, 4)$ and $C (2, 5, 7)$ be the position vectors of the vertices of a triangle $△ A B C$ . Then the length $(in units)$ of the internal angular bisector of angle $A$ is

Discussion

7269.	If α and β are the zeros of x2+5x+8 then the value of (α+β) is (a) 5 (b) -5 (c) 8 (d) -8
Answer» If $α a n d β$ are the zeros of $x^{2} + 5 x + 8$ then the value of $(α + β)$ is (a) 5 (b) -5 (c) 8 (d) -8

7269.

If α and β are the zeros of x2+5x+8 then the value of (α+β) is (a) 5 (b) -5 (c) 8 (d) -8

Answer»

If $α a n d β$ are the zeros of $x^{2} + 5 x + 8$ then the value of $(α + β)$ is

(a) 5 (b) -5 (c) 8 (d) -8

Discussion

7270.	Question 9Find the area of the triangle whose vertices are (-8,4), (-6,6) and (-3,9).
Answer» Question 9 Find the area of the triangle whose vertices are (-8,4), (-6,6) and (-3,9).

Discussion

7271.	Find three consecutive odd integers ,the sum of whose squares is 83
Answer» Find three consecutive odd integers ,the sum of whose squares is 83

Discussion

7272.	Points A(4, 3), B(x, 4), C(5, -6) and D(3, y) in order are the vertices of a parallelogram. The distance between AB and CD is??
Answer» Points A(4, 3), B(x, 4), C(5, -6) and D(3, y) in order are the vertices of a parallelogram. The distance between AB and CD is??

Discussion

7273.	Statement 1 : The graph of a linear equation is a straight line. Statement 2 : The solution of a pair of linear equations is a point common to two lines.
Answer» Statement 1 : The graph of a linear equation is a straight line. Statement 2 : The solution of a pair of linear equations is a point common to two lines.

7273.

Statement 1 : The graph of a linear equation is a straight line. Statement 2 : The solution of a pair of linear equations is a point common to two lines.

Answer»

Statement 1 : The graph of a linear equation is a straight line.

Statement 2 : The solution of a pair of linear equations is a point common to two lines.

Discussion

7274.	A solid object made up of wood is in the shape of a cylinder with 4 cuboidal depressions. The radius and height of the cylinder is 7 cm and 10 cm, respectively. The dimensions of the cuboid are 2 cm × 3 cm × 4 cm. Find the volume of wood in the solid object.
Answer» A solid object made up of wood is in the shape of a cylinder with 4 cuboidal depressions. The radius and height of the cylinder is 7 cm and 10 cm, respectively. The dimensions of the cuboid are 2 cm $\times$ 3 cm $\times$ 4 cm. Find the volume of wood in the solid object.

Discussion

7275.	In triangle ABC ,CD is a line on AB & BE is a line on AC, BE & CD intersect at point O BO:OE = 5:7 & OD: OC = 1:2 find AE: EC
Answer» In triangle ABC ,CD is a line on AB & BE is a line on AC, BE & CD intersect at point O BO:OE = 5:7 & OD: OC = 1:2 find AE: EC

Discussion

7276.	The sum of a number and its positive square root is 6/25. Find the number.
Answer» The sum of a number and its positive square root is 6/25. Find the number.

Discussion

7277.	If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is(a) > 0.5 (b) 0.5 (c) ≤ 0.5 (d) 0
Answer» If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is (a) > 0.5 (b) 0.5 (c) ≤ 0.5 (d) 0

Discussion

7278.	If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =(a) 1(b) 2(c) 4(d) 3
Answer» If x = 1 is a common root of ax² + ax + 2 = 0 and x² + x + b = 0, then, ab = (a) 1 (b) 2 (c) 4 (d) 3

Discussion

7279.	Find the coordinates of the centroid of a triangle whose vertices are (0, 6), (8, 12) and (8, 0). [2 MARKS]
Answer» Find the coordinates of the centroid of a triangle whose vertices are (0, 6), (8, 12) and (8, 0). [2 MARKS]

Discussion

7280.	The value of k for which the system of equations has no solution isx+2y=53x+ky+15=0(a) 6(b) −6(c) 3/2(d) None of these
Answer» The value of k for which the system of equations has no solution is $x + 2 y = 5 3 x + k y + 15 = 0$ (a) 6 (b) −6 (c) 3/2 (d) None of these

Discussion

7281.	6. If sides of triangle ABC are a,b,c . so find the area of triangle in all trigonometric functions?
Answer» 6. If sides of triangle ABC are a,b,c . so find the area of triangle in all trigonometric functions?

Discussion

7282.	Which of these is the graph of a quadratic equation?
Answer» Which of these is the graph of a quadratic equation?

Discussion

7283.	Find the value of k for which each of the following system of equations have infinitely many solutions :2x+3y=kk-1x+k+2y=3k
Answer» Find the value of k for which each of the following system of equations have infinitely many solutions : $2 x + 3 y = k (k - 1) x + (k + 2) y = 3 k$

Discussion

7284.	Factorise the bi quadratic equation4x(2x+3)(2x-1)(x+1) - 54
Answer» Factorise the bi quadratic equation 4x(2x+3)(2x-1)(x+1) - 54

Discussion

7285.	S1: AM = AP2, BN= BP2 S2: OO' = AM + BN Which of the above statements are true ?
Answer» S1: AM = $\frac{A P}{2}$ , BN= $\frac{B P}{2}$ S2: OO' = AM + BN Which of the above statements are true ?

7285.

S1: AM = AP2, BN= BP2 S2: OO' = AM + BN Which of the above statements are true ?

Answer»

S1: AM = $\frac{A P}{2}$ , BN= $\frac{B P}{2}$

S2: OO' = AM + BN

Which of the above statements are true ?

Discussion

7286.	If the LCM of two polynomials is (x−3)2(x−5)3 and their product is (x−3)2(x−5)4, then the HCF of the polynomials is:
Answer» If the LCM of two polynomials is $(x - 3)^{2} (x - 5)^{3}$ and their product is $(x - 3)^{2} (x - 5)^{4}$ , then the HCF of the polynomials is:

Discussion

7287.	The following images are the graph of a ______ polynomial.
Answer» The following images are the graph of a ______ polynomial.

Discussion

7288.	Solve each of the following quadratic equations:x2+5x-a2+a-6=0 [CBSE 2015]
Answer» Solve each of the following quadratic equations: $x^{2} + 5 x - (a^{2} + a - 6) = 0$ [CBSE 2015]

Discussion

7289.	The figure consists of 2 cylinders, the inner cylinder is a solid cylinder whose radius is r and the outer cylinder is a hollow cylinder whose radius is R and height is h, the volume of fluid it can hold is:
Answer» The figure consists of 2 cylinders, the inner cylinder is a solid cylinder whose radius is r and the outer cylinder is a hollow cylinder whose radius is R and height is h, the volume of fluid it can hold is:

7289.

The figure consists of 2 cylinders, the inner cylinder is a solid cylinder whose radius is r and the outer cylinder is a hollow cylinder whose radius is R and height is h, the volume of fluid it can hold is:

Answer»

The figure consists of 2 cylinders, the inner cylinder is a solid cylinder whose radius is r and the outer cylinder is a hollow cylinder whose radius is R and height is h, the volume of fluid it can hold is:

Discussion

7290.	two chords of a circle of radius r are such that AB=2AC. and p and q are dis†an ces of AB andAC from origin then prove that 4q}^2=p}^2+3r}^2.
Answer» two chords of a circle of radius r are such that AB=2AC. and p and q are dis†an ces of AB andAC from origin then prove that 4q}^2=p}^2+3r}^2.

Discussion

7291.	If x+a is a factor of the polynomial 2x2+2ax+5x+10, find the value of a.
Answer» If $(x + a)$ is a factor of the polynomial $2 x^{2} + 2 a x + 5 x + 10$ , find the value of a.

Discussion

7292.	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° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Discussion

7293.	State the type of the conditional clause in the sentence. If I were in the office I would receive the update.
Answer» State the type of the conditional clause in the sentence. If I were in the office I would receive the update.

Discussion

7294.	A right angle triangle of base 4 cm and height 3 cm is rotated about its height. The curved surface area and volume of the solid obtained are _____ (in cm2) and _____ (in cm3) respectively.
Answer» A right angle triangle of base 4 cm and height 3 cm is rotated about its height. The curved surface area and volume of the solid obtained are _____ ( $i n c m^{2}$ ) and _____ ( $i n c m^{3}$ ) respectively.

Discussion

7295.	If sin A=34, calculate sec A.
Answer» If sin $A = \frac{3}{4}$ , calculate sec A.

Discussion

7296.	If A and B are square matrices of order 3 and \|A\| = 5, \|B\| = 5, then \|3AB\| = ____________.
Answer» If A and B are square matrices of order 3 and \|A\| = 5, \|B\| = 5, then \|3AB\| = ____________.

Discussion

7297.	Sam have 6 denomination of 1 dollars, 5 denomination of 10 dollars and 4 denomination of 5 dollars. 2 denominations are chosen randomly with replacement. Find the probability of drawing 10 dollar followed by 10 dollar?
Answer» Sam have 6 denomination of 1 dollars, 5 denomination of 10 dollars and 4 denomination of 5 dollars. 2 denominations are chosen randomly with replacement. Find the probability of drawing 10 dollar followed by 10 dollar?

Discussion

7298.	Half the perimeter of a garden, whose length is 4 more than its width is 36 m. Find the dimensions of the garden.
Answer» Half the perimeter of a garden, whose length is 4 more than its width is 36 m. Find the dimensions of the garden.

Discussion

7299.	Question 9 (i)In the following figure, ABC and AMP are two right triangles, right angled at B and M respectively, prove that(i)ΔABC∼ΔAMP
Answer» Question 9 (i) In the following figure, ABC and AMP are two right triangles, right angled at B and M respectively, prove that $(i) Δ A B C \sim Δ A M P$

Discussion

7300.	The angle of elevation of the top of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation of the top is 45°. Calculate the height of the tower.
Answer» The angle of elevation of the top of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation of the top is 45°. Calculate the height of the tower.

Discussion

Explore topic-wise InterviewSolutions in .

The polynomial equation P(x)= 3x2+5x+2 can be represented as

Simplify: cos45°÷(sec30°+cosec30°)

1. The Corvette described parametrically by x=t²+t+1, y=t²-t+1 represents 1. Pair of straight lines 2. Ellipse 3. Hyperbola 4. Parabola

If θ is an acute angle such that sec2 θ = 3, then the value of tan2 θ-cosec2 θtan2 θ+cosec2 θis(a) 47(b) 37(c) 27(d) 17

If 3x+y+2x-y=2 and 9x+y-4x-y=1 then(a) x=12, y=32 (b) x=52, y=12 (c) x=32, y=12 (d) x=12, y=52

Find the cardial number of the relation, R = {x:x∈N and 3≤x&lt;7}.4

A solid metal cylinder is of base-radius 12 centimetres and height 20 centimetres. By melting and recasting, how many cones of base-radius 4 centimetres and height 5 centimetres can be made?

Find the value of t, given thatp(x)=x3−tx2+5x−3,g(x)=x2−2,q(x)=x−3,r(x)=7x−9Where,p(x) is the dividend,g(x) is the divisor,q(x) is the quotient, and r(x) is the remainder3

Find the area of the region bounded by the ellipse

Identify the number corresponding to the ‘?’

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =(a) 1n(b) n-1n(c) n+12n(d) n+1n

If n is an integer, then every integral multiple of 3 can be represented by the expression ___.

Prove that if 1 &lt; x &lt; 4 and 1 &lt; y &lt; 4, then |x − y| &lt; 3.

If the zeros of the polynomial f(x) = 2x3 − 15x2 + 37x − 30 are in A.P., find them.

Write a cubic polynomial whose zeroes are 2-2root5, 2+2root5 and 1

Solve the following pair of linear equations by the elimination method and the substitution method:

If sin θ+cos θ=a and sec θ+cosec θ=b, then what is the value of b(a2−1)?

Let A(4,7,8), B(2,3,4) and C(2,5,7) be the position vectors of the vertices of a triangle △ABC. Then the length (in units) of the internal angular bisector of angle A is

If α and β are the zeros of x2+5x+8 then the value of (α+β) is (a) 5 (b) -5 (c) 8 (d) -8

Question 9Find the area of the triangle whose vertices are (-8,4), (-6,6) and (-3,9).

Find three consecutive odd integers ,the sum of whose squares is 83

Points A(4, 3), B(x, 4), C(5, -6) and D(3, y) in order are the vertices of a parallelogram. The distance between AB and CD is??

Statement 1 : The graph of a linear equation is a straight line. Statement 2 : The solution of a pair of linear equations is a point common to two lines.

A solid object made up of wood is in the shape of a cylinder with 4 cuboidal depressions. The radius and height of the cylinder is 7 cm and 10 cm, respectively. The dimensions of the cuboid are 2 cm × 3 cm × 4 cm. Find the volume of wood in the solid object.

In triangle ABC ,CD is a line on AB & BE is a line on AC, BE & CD intersect at point O BO:OE = 5:7 & OD: OC = 1:2 find AE: EC

The sum of a number and its positive square root is 6/25. Find the number.

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is(a) > 0.5 (b) 0.5 (c) ≤ 0.5 (d) 0

If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =(a) 1(b) 2(c) 4(d) 3

Find the coordinates of the centroid of a triangle whose vertices are (0, 6), (8, 12) and (8, 0). [2 MARKS]

The value of k for which the system of equations has no solution isx+2y=53x+ky+15=0(a) 6(b) −6(c) 3/2(d) None of these

6. If sides of triangle ABC are a,b,c . so find the area of triangle in all trigonometric functions?

Which of these is the graph of a quadratic equation?

Find the value of k for which each of the following system of equations have infinitely many solutions :2x+3y=kk-1x+k+2y=3k

Factorise the bi quadratic equation4x(2x+3)(2x-1)(x+1) - 54

S1: AM = AP2, BN= BP2 S2: OO' = AM + BN Which of the above statements are true ?

If the LCM of two polynomials is (x−3)2(x−5)3 and their product is (x−3)2(x−5)4, then the HCF of the polynomials is:

The following images are the graph of a ______ polynomial.

Solve each of the following quadratic equations:x2+5x-a2+a-6=0 [CBSE 2015]

The figure consists of 2 cylinders, the inner cylinder is a solid cylinder whose radius is r and the outer cylinder is a hollow cylinder whose radius is R and height is h, the volume of fluid it can hold is:

two chords of a circle of radius r are such that AB=2AC. and p and q are dis†an ces of AB andAC from origin then prove that 4q}^2=p}^2+3r}^2.

If x+a is a factor of the polynomial 2x2+2ax+5x+10, find the value of a.

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.

State the type of the conditional clause in the sentence. If I were in the office I would receive the update.

A right angle triangle of base 4 cm and height 3 cm is rotated about its height. The curved surface area and volume of the solid obtained are _____ (in cm2) and _____ (in cm3) respectively.

If sin A=34, calculate sec A.

If A and B are square matrices of order 3 and |A| = 5, |B| = 5, then |3AB| = ____________.

Sam have 6 denomination of 1 dollars, 5 denomination of 10 dollars and 4 denomination of 5 dollars. 2 denominations are chosen randomly with replacement. Find the probability of drawing 10 dollar followed by 10 dollar?

Half the perimeter of a garden, whose length is 4 more than its width is 36 m. Find the dimensions of the garden.

Question 9 (i)In the following figure, ABC and AMP are two right triangles, right angled at B and M respectively, prove that(i)ΔABC∼ΔAMP

The angle of elevation of the top of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation of the top is 45°. Calculate the height of the tower.

Find the cardial number of the relation, R = {x:x∈N and 3≤x<7}.4

Prove that if 1 < x < 4 and 1 < y < 4, then |x − y| < 3.

A right angle triangle of base 4 cm and height 3 cm is rotated about its height. The curved surface area and volume of the solid obtained are _ (in cm2) and _ (in cm3) respectively.