43030 + Interview Questions in Mathematics Page 100 InterviewSolution

4951.	If g(x)=x∫1et2 dt then the value of h(x)=x3∫3et2dt equals
Answer» If $g (x) = x \int 1 e^{t^{2}}$ $d t$ then the value of $h (x) = x^{3} \int 3 e^{t^{2}} d t$ equals

Discussion

4952.	A coin is so biased that the probability of falling head when tossed is 14. If the coin is tossed 5 times the probability of obtaining 2 heads and 3 tails, with heads occurring in succession is
Answer» A coin is so biased that the probability of falling head when tossed is $\frac{1}{4}$ . If the coin is tossed $5$ times the probability of obtaining $2$ heads and $3$ tails, with heads occurring in succession is

Discussion

4953.	Evaluate: √145×142144×2755
Answer» Evaluate: $\sqrt{1 \frac{4}{5} \times 14 \frac{21}{44} \times 2 \frac{7}{55}}$

Discussion

4954.	7. = 4n — 3; an,
Answer» 7. = 4n — 3; an,

Discussion

4955.	Let E and F be two independent events. The probability that both E and F happen is 1/12 and the probability that neither E nor F happens is 1/2 .Then,
Answer» Let E and F be two independent events. The probability that both E and F happen is 1/12 and the probability that neither E nor F happens is 1/2 .Then,

Discussion

4956.	Evaluate ∫∞0sinttdt
Answer» Evaluate $\int_{0}^{\infty} \frac{sin t}{t} d t$

Discussion

4957.	Find the no. Of real roots of equation (x-1)(x-2)(x-3)+1=0 in it's domain.
Answer» Find the no. Of real roots of equation (x-1)(x-2)(x-3)+1=0 in it's domain.

Discussion

4958.	The inverse of the bijective function f(x)=23√x+1−3, is
Answer» The inverse of the bijective function $f (x) = 2 \sqrt[3]{x + 1} - 3,$ is

Discussion

4959.	Minimise Z= −3x + 4ysubjectto.
Answer» Minimise Z = −3x + 4y subject to.

4959.

Minimise Z= −3x + 4ysubjectto.

Answer»

Minimise Z
= −3x + 4y

subject
to.

Discussion

4960.	The range of the function f(x)=7−xPx−3 is
Answer» The range of the function $f (x) =^{7 - x} P_{x - 3}$ is

Discussion

4961.	Which of the following is the principal value branch of tan−1x
Answer» Which of the following is the principal value branch of ${tan}^{- 1} x$

Discussion

4962.	If x, [x], {x} are in GP(geometric progression) then find the value of x.
Answer» If x, [x], {x} are in GP(geometric progression) then find the value of x.

Discussion

4963.	Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cm
Answer» Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cm

Discussion

4964.	Let a real valued function is defined as f(x,y)=x2+y2−xy. If x2+4y2=4 and the range of f(x,y) is [a,b], then the value of ab is
Answer» Let a real valued function is defined as $f (x, y) = x^{2} + y^{2} - x y$ . If $x^{2} + 4 y^{2} = 4$ and the range of $f (x, y)$ is $[a, b]$ , then the value of $a b$ is

Discussion

4965.	If 9∑i=1(xi−5)=9 and 9∑i=1(xi−5)2=45, then the standard deviation of the 9 items x1,x2,⋯,x9 is
Answer» If $9 \sum i = 1 (x_{i} - 5) = 9$ and $9 \sum i = 1 (x_{i} - 5)^{2} = 45,$ then the standard deviation of the $9$ items $x_{1}, x_{2}, \dots, x_{9}$ is

Discussion

4966.	21. Ball is thrown from a urn containing 1 Red ball and 1 black ball. if the ball drawn is red a coin is tossed if it is black a dice thrown find the probability I) of each outcome II) getting head III) getting an even number
Answer» 21. Ball is thrown from a urn containing 1 Red ball and 1 black ball. if the ball drawn is red a coin is tossed if it is black a dice thrown find the probability I) of each outcome II) getting head III) getting an even number

Discussion

4967.	The number of ways of wearing 6 different rings to 5 fingers is
Answer» The number of ways of wearing $6$ different rings to $5$ fingers is

Discussion

4968.	One focus of an Ellipse is (1,0) with centre (0,0). If the length of major axis is 6, its e =
Answer» One focus of an Ellipse is (1,0) with centre (0,0). If the length of major axis is 6, its e =

Discussion

4969.	The number of points at which the function f(x)=1x-x is not continuous is(a) 1(b) 2(c) 3(d) none of these
Answer» The number of points at which the function $f (x) = \frac{1}{x - [x]}$ is not continuous is (a) 1 (b) 2 (c) 3 (d) none of these

Discussion

4970.	If y=sin^3t then find dy/dz
Answer» If y=sin^3t then find dy/dz

Discussion

4971.	∫sin−1x(1−x2)3/4dx
Answer» $\int \frac{s i n^{- 1} x}{(1 - x^{2})^{3 / 4}} d x$

Discussion

4972.	Point A lies on the circle x2+y2=10 and its perpendicular distance from the line L:2x+y=10 is maximum. Then the image of this point about the line L is
Answer» Point $A$ lies on the circle $x^{2} + y^{2} = 10$ and its perpendicular distance from the line $L : 2 x + y = 10$ is maximum. Then the image of this point about the line $L$ is

Discussion

4973.	Mark the correct answer in each of the following:The contrapositive of the statement ~ p ⇒ (p ∧ ~q) is(a) p ⇒ (~ p ∨ q)(b) p ⇒ (p ∧ q)(c) p ⇒ (~ p ∧ q)(d) (~p ∨ q) ⇒ p
Answer» Mark the correct answer in each of the following: The contrapositive of the statement ~ p ⇒ (p ∧ ~q) is (a) p ⇒ (~ p ∨ q) (b) p ⇒ (p ∧ q) (c) p ⇒ (~ p ∧ q) (d) (~p ∨ q) ⇒ p

Discussion

4974.	The value of the determinant Δ=∣∣∣∣cosαcosβcosαsinβ−sinα−sinβcosβ0sinαcosβsinαsinβcosα∣∣∣∣ is
Answer» The value of the determinant $Δ = ∣ ∣∣ ∣ \begin{matrix} cos α cos β & cos α sin β & - sin α - sin β & cos β & 0 sin α cos β & sin α sin β & cos α \end{matrix} ∣ ∣∣ ∣$ is

Discussion

4975.	If x=sec θ+1 and y=tan θ−1, then (x−1)2−(y+1)2 is equal to___
Answer» If $x = s e c θ + 1 a n d y = t a n θ - 1$ , then $(x - 1)^{2} - (y + 1)^{2}$ is equal to ___

Discussion

4976.	Find the area of the region bounded bythe curve y2 = 4x and the line x = 3
Answer» Find the area of the region bounded by the curve y² = 4x and the line x = 3

Discussion

4977.	If the curves x2+py2=1 and qx2+y2=1 are orthogonal to each other then
Answer» If the curves $x^{2} + p y^{2} = 1 a n d q x^{2} + y^{2} = 1$ are orthogonal to each other then

Discussion

4978.	For how many values of ‘x’ in the closed interval [-4, -1] is the matrix ⎡⎢⎣3−1+x23−1x+2x+3−12⎤⎥⎦singular?
Answer» For how many values of ‘x’ in the closed interval [-4, -1] is the matrix $⎡ ⎢ ⎣ \begin{matrix} 3 & - 1 + x & 2 3 & - 1 & x + 2 x + 3 & - 1 & 2 \end{matrix} ⎤ ⎥ ⎦$ singular?

Discussion

4979.	If f(x) = ax2 + bx + c and f(x) – f(x – 1) = 4x + 5,then a + b equals
Answer» If f(x) = ax2 + bx + c and f(x) – f(x – 1) = 4x + 5,then a + b equals

Discussion

4980.	The Fourier transform of t2dx(t)dt is j(KdX(ω)dω−ωd2X(ω)dω2), then the value of K is ________. -2
Answer» The Fourier transform of $t^{2} \frac{d x (t)}{d t}$ is $j (K \frac{d X (ω)}{d ω} - ω \frac{d^{2} X (ω)}{d ω^{2}})$ , then the value of K is ________. -2

Discussion

4981.	The angle of intersection of the curve x2=4y and y2=4x at point (0,0) is
Answer» The angle of intersection of the curve $x^{2} = 4 y$ and $y^{2} = 4 x$ at point (0,0) is

Discussion

4982.	Let △PQR be a right triangle, right angled at R. If tan(P2) and tan(Q2) are the roots of the quadratic equation ax2+bx+c=0, then which of the following is correct ?
Answer» Let $△ P Q R$ be a right triangle, right angled at $R .$ If $tan (\frac{P}{2})$ and $tan (\frac{Q}{2})$ are the roots of the quadratic equation $a x^{2} + b x + c = 0$ , then which of the following is correct ?

Discussion

4983.	Suppose f(x)=⎧⎪⎨⎪⎩sin(π−x)π(π−x), x≠π k, x=π is continuous at x=π then the value of k is
Answer» $Suppose f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{sin (π - x)}{π (π - x)}, x \neq π k, x = π \end{matrix}$ is continuous at $x = π$ then the value of $k$ is

Discussion

4984.	Find the equation of a curve passing through the point (0,-2) given that at any point (x,y) on the curve the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.
Answer» Find the equation of a curve passing through the point (0,-2) given that at any point (x,y) on the curve the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

Discussion

4985.	Find the differential equation of the family of lines passing through the origin.
Answer» Find the differential equation of the family of lines passing through the origin.

Discussion

4986.	The sum of four integers in AP is 24 and their product is 945. Find the numbers.
Answer» The sum of four integers in AP is 24 and their product is 945. Find the numbers.

Discussion

4987.	A and B are two finite sets, such that A has p elements and B has q elements. The number of elements in the power set of A is 48 more than number of elements in the power set of B. Then select the correct statement about p & q.
Answer» $A$ and $B$ are two finite sets, such that $A$ has $p$ elements and $B$ has $q$ elements. The number of elements in the power set of $A$ is $48$ more than number of elements in the power set of $B .$ Then select the correct statement about $p & q .$

Discussion

4988.	The equation of the normal to the circle x2+y2=5 at the point (1,2) is
Answer» The equation of the normal to the circle $x^{2} + y^{2} = 5$ at the point $(1, 2)$ is

Discussion

4989.	The Cartesian coordinates of the point whose polar coordinates are (2,π6), are
Answer» The Cartesian coordinates of the point whose polar coordinates are $(2, \frac{π}{6})$ , are

Discussion

4990.	If A=123, then AAT = __________.
Answer» If $A = [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}],$ then AA^T = __________.

Discussion

4991.	The value of tan 75° – cot75° is(a) 23(b) 2+3(c) 2-3(d) 1
Answer» The value of tan 75° – cot75° is (a) $2 \sqrt{3}$ (b) $2 + \sqrt{3}$ (c) $2 - \sqrt{3}$ (d) 1

Discussion

4992.	Rational function is defined as f(x)/g(x). In this expression domain of f(x) is set of real numbers. Is domain of g(x) also set of real numbers except zero?
Answer» Rational function is defined as f(x)/g(x). In this expression domain of f(x) is set of real numbers. Is domain of g(x) also set of real numbers except zero?

Discussion

4993.	If 2\|x+2\|−\|x+5\|≤4, then x∈
Answer» If $2 \| x + 2 \| - \| x + 5 \| \leq 4$ , then $x \in$

Discussion

4994.	What is system?
Answer» What is system?

Discussion

4995.	Differentiate sec5x w.r.t. x using first principle.
Answer» Differentiate sec5x w.r.t. x using first principle.

Discussion

4996.	If A = {1, 2, 3, 4} and B = {5, 6, 7, 8}, then which function is one-one and onto?
Answer» If A = {1, 2, 3, 4} and B = {5, 6, 7, 8}, then which function is one-one and onto?

Discussion

4997.	Integral 1+cos^2x/1-cos2x.dx
Answer» Integral 1+cos^2x/1-cos2x.dx

Discussion

4998.	A body moves in a straight line under the retardation a bit is given by a is equals to b v square if the initial velocity is 2 metre per second the distance covered in the time T is equals to 2 seconds is
Answer» A body moves in a straight line under the retardation a bit is given by a is equals to b v square if the initial velocity is 2 metre per second the distance covered in the time T is equals to 2 seconds is

Discussion

4999.	The distance of the plane 2x - 3y + 4z = 6 from the origin is equal to
Answer» The distance of the plane 2x - 3y + 4z = 6 from the origin is equal to

Discussion

5000.	If y=sin2x∫1/8sin−1√tdt+∫cos2x1/8cos−1√tdt, where 0≤x≤π/2, then which of the following is correct
Answer» If $y = {sin}^{2} x \int 1 / 8 {sin}^{- 1} \sqrt{t} d t + \int_{1 / 8}^{{cos}^{2} x} {cos}^{- 1} \sqrt{t} d t,$ where $0 \leq x \leq π / 2,$ then which of the following is correct

Discussion

Explore topic-wise InterviewSolutions in .

If g(x)=x∫1et2 dt then the value of h(x)=x3∫3et2dt equals

A coin is so biased that the probability of falling head when tossed is 14. If the coin is tossed 5 times the probability of obtaining 2 heads and 3 tails, with heads occurring in succession is

Evaluate: √145×142144×2755

7. = 4n — 3; an,

Let E and F be two independent events. The probability that both E and F happen is 1/12 and the probability that neither E nor F happens is 1/2 .Then,

Evaluate ∫∞0sinttdt

Find the no. Of real roots of equation (x-1)(x-2)(x-3)+1=0 in it's domain.

The inverse of the bijective function f(x)=23√x+1−3, is

Minimise Z= −3x + 4ysubjectto.

The range of the function f(x)=7−xPx−3 is

Which of the following is the principal value branch of tan−1x

If x, [x], {x} are in GP(geometric progression) then find the value of x.

Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cm

Let a real valued function is defined as f(x,y)=x2+y2−xy. If x2+4y2=4 and the range of f(x,y) is [a,b], then the value of ab is

If 9∑i=1(xi−5)=9 and 9∑i=1(xi−5)2=45, then the standard deviation of the 9 items x1,x2,⋯,x9 is

21. Ball is thrown from a urn containing 1 Red ball and 1 black ball. if the ball drawn is red a coin is tossed if it is black a dice thrown find the probability I) of each outcome II) getting head III) getting an even number

The number of ways of wearing 6 different rings to 5 fingers is

One focus of an Ellipse is (1,0) with centre (0,0). If the length of major axis is 6, its e =

The number of points at which the function f(x)=1x-x is not continuous is(a) 1(b) 2(c) 3(d) none of these

If y=sin^3t then find dy/dz

∫sin−1x(1−x2)3/4dx

Point A lies on the circle x2+y2=10 and its perpendicular distance from the line L:2x+y=10 is maximum. Then the image of this point about the line L is

Mark the correct answer in each of the following:The contrapositive of the statement ~ p ⇒ (p ∧ ~q) is(a) p ⇒ (~ p ∨ q)(b) p ⇒ (p ∧ q)(c) p ⇒ (~ p ∧ q)(d) (~p ∨ q) ⇒ p

The value of the determinant Δ=∣∣∣∣cosαcosβcosαsinβ−sinα−sinβcosβ0sinαcosβsinαsinβcosα∣∣∣∣ is

If x=sec θ+1 and y=tan θ−1, then (x−1)2−(y+1)2 is equal to___

Find the area of the region bounded bythe curve y2 = 4x and the line x = 3

If the curves x2+py2=1 and qx2+y2=1 are orthogonal to each other then

For how many values of ‘x’ in the closed interval [-4, -1] is the matrix ⎡⎢⎣3−1+x23−1x+2x+3−12⎤⎥⎦singular?

If f(x) = ax2 + bx + c and f(x) – f(x – 1) = 4x + 5,then a + b equals

The Fourier transform of t2dx(t)dt is j(KdX(ω)dω−ωd2X(ω)dω2), then the value of K is ________. -2

The angle of intersection of the curve x2=4y and y2=4x at point (0,0) is

Let △PQR be a right triangle, right angled at R. If tan(P2) and tan(Q2) are the roots of the quadratic equation ax2+bx+c=0, then which of the following is correct ?

Suppose f(x)=⎧⎪⎨⎪⎩sin(π−x)π(π−x), x≠π k, x=π is continuous at x=π then the value of k is

Find the equation of a curve passing through the point (0,-2) given that at any point (x,y) on the curve the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

Find the differential equation of the family of lines passing through the origin.

The sum of four integers in AP is 24 and their product is 945. Find the numbers.

A and B are two finite sets, such that A has p elements and B has q elements. The number of elements in the power set of A is 48 more than number of elements in the power set of B. Then select the correct statement about p &amp; q.

The equation of the normal to the circle x2+y2=5 at the point (1,2) is

The Cartesian coordinates of the point whose polar coordinates are (2,π6), are

If A=123, then AAT = __________.

The value of tan 75° – cot75° is(a) 23(b) 2+3(c) 2-3(d) 1

Rational function is defined as f(x)/g(x). In this expression domain of f(x) is set of real numbers. Is domain of g(x) also set of real numbers except zero?

If 2|x+2|−|x+5|≤4, then x∈

What is system?

Differentiate sec5x w.r.t. x using first principle.

If A = {1, 2, 3, 4} and B = {5, 6, 7, 8}, then which function is one-one and onto?

Integral 1+cos^2x/1-cos2x.dx

A body moves in a straight line under the retardation a bit is given by a is equals to b v square if the initial velocity is 2 metre per second the distance covered in the time T is equals to 2 seconds is

The distance of the plane 2x - 3y + 4z = 6 from the origin is equal to

If y=sin2x∫1/8sin−1√tdt+∫cos2x1/8cos−1√tdt, where 0≤x≤π/2, then which of the following is correct

A and B are two finite sets, such that A has p elements and B has q elements. The number of elements in the power set of A is 48 more than number of elements in the power set of B. Then select the correct statement about p & q.