43030 + Interview Questions in Mathematics Page 130 InterviewSolution

6451.	If f(x)=x2a+x, then which of the following is/are true?
Answer» If $f (x) = \frac{x^{2}}{a + x},$ then which of the following is/are true?

Discussion

6452.	Evaluate the following limits:limx→0cosax-cosbxcoscx-1
Answer» Evaluate the following limits: $\lim_{x \to 0} \frac{\cos a x - \cos b x}{\cos c x - 1}$

Discussion

6453.	Solve the following system of inequalities graphically: x + y ≤ 9, y > x, x ≥ 0
Answer» Solve the following system of inequalities graphically: x + y ≤ 9, y > x, x ≥ 0

Discussion

6454.	If AD is the median of ∆ABC, using vectors, prove that AB2+AC2=2AD2+CD2.
Answer» If AD is the median of ∆ABC, using vectors, prove that ${AB}^{2} + {AC}^{2} = 2 ({AD}^{2} + {CD}^{2})$ .

Discussion

6455.	d/dx of 1+tanx/1-tanx
Answer» d/dx of 1+tanx/1-tanx

Discussion

6456.	If the equations of two diameters of a circle arc 2x + y = 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle.
Answer» If the equations of two diameters of a circle arc 2x + y = 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle.

Discussion

6457.	Differentiate thefunction with respect to x.
Answer» Differentiate the function with respect to x.

6457.

Differentiate thefunction with respect to x.

Answer»

Differentiate the
function with respect to x.

Discussion

6458.	The range of f(x) = sgn(ex) isOptions:{0}Wrong {–1}Should have chosen {1}{0, 1
Answer» The range of f(x) = sgn(ex) is Options: {0} Wrong {–1} Should have chosen {1} {0, 1

Discussion

6459.	If 2 sec 2α=tan β+cot β, then one of the values ofα+β is
Answer» If $2 s e c 2 α = t a n β + c o t β,$ then one of the values of $α + β$ is

Discussion

6460.	Match List I with the List II and select the correct answer using the code given below the lists : List I List II(A)f(x)=sin−1(sinx+cosx2)(P)Domain is R(B)g(x)=sin−1(2πtan−1x)(Q)Range contains only one integer (C)h(x)=tan−1(2π(2tan−1x−sin−1x+cot−1x−cos−1x))(R)Odd function (D)j(x)=tan−1(x3+x)(S)No vertical tangent Which of the following is a WRONG combination?
Answer» Match $List I$ with the $List II$ and select the correct answer using the code given below the lists : $\begin{matrix} List I & List II (A) & f (x) = {sin}^{- 1} (\frac{sin x + cos x}{2}) & (P) & Domain is R (B) & g (x) = {sin}^{- 1} (\frac{2}{π} {tan}^{- 1} x) & (Q) & Range contains only one integer (C) & h (x) = {tan}^{- 1} (\frac{2}{π} (2 {tan}^{- 1} x - {sin}^{- 1} x + {cot}^{- 1} x - {cos}^{- 1} x)) & (R) & Odd function (D) & j (x) = {tan}^{- 1} (x^{3} + x) & (S) & No vertical tangent \end{matrix}$ Which of the following is a WRONG combination?

Discussion

6461.	The function f(x)=xsinx satisfies the following equation:f ''(x) + f(x) + tcos x = 0The value of t is -2
Answer» The function $f (x) = x s i n x$ satisfies the following equation: f ''(x) + f(x) + tcos x = 0 The value of t is -2

Discussion

6462.	The symmetric equation of lines 3x + 2y + z - 5 = 0 and x + y - 2z - 3 = 0, is
Answer» The symmetric equation of lines 3x + 2y + z - 5 = 0 and x + y - 2z - 3 = 0, is

Discussion

6463.	Let f(x)=max{3,x2,1x2} for 12≤x≤2. Then the value of the integral 2∫1/2f(x)dx is
Answer» $Let f (x) = max {3, x^{2}, \frac{1}{x^{2}}} for \frac{1}{2} \leq x \leq 2.$ Then the value of the integral $2 \int 1 / 2 f (x) d x$ is

Discussion

6464.	If A and B are mutually exclusive events then
Answer» If A and B are mutually exclusive events then

Discussion

6465.	DERIVE THE FOLLOWING :V= ROOT OVER u^2 + g^2t^2 - 2u sintheta gt
Answer» DERIVE THE FOLLOWING : V= ROOT OVER u^2 + g^2t^2 - 2u sintheta gt

Discussion

6466.	An ordinary cubical die has four blank faces, one face marked 2 and another marked 3. Then the probability of obtaining 12 in 5 throws is
Answer» An ordinary cubical die has four blank faces, one face marked 2 and another marked 3. Then the probability of obtaining 12 in 5 throws is

Discussion

6467.	A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.
Answer» A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.

Discussion

6468.	The value of tan x+cot π+x+cot π2+x+cot 2π-x is ______________ .
Answer» The value of tan $x + \cot (π + x) + \cot (\frac{π}{2} + x) + \cot (2 π - x)$ is ______________ .

Discussion

6469.	If A + B + C = π then tan2A2 + tan2B2 + tan2C2 is always
Answer» If A + B + C = $π$ then $t a n^{2} \frac{A}{2}$ + $t a n^{2} \frac{B}{2}$ + $t a n^{2} \frac{C}{2}$ is always

Discussion

6470.	Two numbers are selected at random (without replacement) from the first six positive integers. Let X denotes the larger of the two numbers obtained. Find E(X).
Answer» Two numbers are selected at random (without replacement) from the first six positive integers. Let X denotes the larger of the two numbers obtained. Find E(X).

Discussion

6471.	If sin y = x sin (a+y). Prive that dy/dx=sin^2(a+y)/sin a
Answer» If sin y = x sin (a+y). Prive that dy/dx=sin^2(a+y)/sin a

Discussion

6472.	Show by using mean value theorem and taking f(x)=logx that 1-a/b < logb/a < b/a -1
Answer» Show by using mean value theorem and taking f(x)=logx that 1-a/b < logb/a < b/a -1

Discussion

6473.	If the 9th term of an AP be zero, then the ratio of its 29th and 19 th term is
Answer» If the 9th term of an AP be zero, then the ratio of its 29th and 19 th term is

Discussion

6474.	Write any three decimal numbers between 1.25 and 1.75.
Answer» Write any three decimal numbers between 1.25 and 1.75.

Discussion

6475.	Let A = (3, –4), B = (1, 2) and P = (2λ – 1, 2λ + 1). If the sum PA + PB is minimum, then the value of λ is
Answer» Let A = (3, –4), B = (1, 2) and P = (2λ – 1, 2λ + 1). If the sum PA + PB is minimum, then the value of λ is

Discussion

6476.	sin3x(cos4x+3cos2x+1)tan−1(secx+cosx)dx=
Answer» $\frac{s i n^{3} x}{(c o s^{4} x + 3 c o s^{2} x + 1) t a n^{- 1} (s e c x + c o s x)} d x =$

Discussion

6477.	If A = [cos θsin θ−sin θcos θ], then for any natural number n, find the value of Det(A").
Answer» If A = $[\begin{matrix} c o s θ & s i n θ - s i n θ & c o s θ \end{matrix}]$ , then for any natural number n, find the value of Det(A").

Discussion

6478.	Seven different lectures are to be delivered in 7 periods of a class on a particular day. Out of 7 lecturers, A,B and C are three of them. If the number of ways in which a routine for the day can be made such that A delivers his lecture before B and B before C is N, then the value of (N120) is
Answer» Seven different lectures are to be delivered in $7$ periods of a class on a particular day. Out of $7$ lecturers, $A, B$ and $C$ are three of them. If the number of ways in which a routine for the day can be made such that $A$ delivers his lecture before $B$ and $B$ before $C$ is $N,$ then the value of $(\frac{N}{120})$ is

Discussion

6479.	18. 5x 3 2 3x 5
Answer» 18. 5x 3 2 3x 5

Discussion

6480.	If x+y+z=0, then the value of ∣∣∣∣xaybzcyczaxbzbxcya∣∣∣∣ is equal to
Answer» If $x + y + z = 0,$ then the value of $∣ ∣∣ ∣ \begin{matrix} x a & y b & z c y c & z a & x b z b & x c & y a \end{matrix} ∣ ∣∣ ∣$ is equal to

Discussion

6481.	If f(x)=x + tan x and f is inverse of g, then g' (x) is equal to
Answer» If f(x)=x + tan x and f is inverse of g, then g' (x) is equal to

Discussion

6482.	Show that the tangent of an angle between the lines xa+yb=1 and xa-yb=1 is 2aba2-b2
Answer» Show that the tangent of an angle between the lines $\frac{x}{a} + \frac{y}{b} = 1 and \frac{x}{a} - \frac{y}{b} = 1 is \frac{2 a b}{a^{2} - b^{2}}$

Discussion

6483.	Find the sum to n terms of the A.P., whose kthterm is 5k + 1.
Answer» Find the sum to n terms of the A.P., whose k^thterm is 5k + 1.

Discussion

6484.	( √2 + 3√5 ) - ( 4√9 - 3√2 )
Answer» ( √2 + 3√5 ) - ( 4√9 - 3√2 )

Discussion

6485.	If the point (3, 5) lies on the graph of the equation 3y = ax + 9, the value of a is ___.
Answer» If the point (3, 5) lies on the graph of the equation 3y = ax + 9, the value of a is ___ .

6485.

If the point (3, 5) lies on the graph of the equation 3y = ax + 9, the value of a is ___.

Answer»

If the point (3, 5) lies on the graph of the equation 3y = ax + 9, the value of a is

___

.

Discussion

6486.	A is a matrix of order n and k is a constant, then adj(kA) is
Answer» A is a matrix of order n and k is a constant, then adj(kA) is

Discussion

6487.	The number of roots of the equation, (81)sin2x+(81)cos2x=30 in the interval [0,π] is equal to:
Answer» The number of roots of the equation, $(81)^{{sin}^{2} x} + (81)^{{cos}^{2} x} = 30$ in the interval $[0, π]$ is equal to:

Discussion

6488.	∫022xxdx
Answer» $\int_{0}^{2} 2 x [x] d x$

Discussion

6489.	A square ABCD of diagonal 2a is folded along the diagonal 2a so that the planes DAC and BAC are at right angle. The shortest distance between DC and AB is [Kurukshetra CEE 1998]
Answer» A square ABCD of diagonal 2a is folded along the diagonal 2a so that the planes DAC and BAC are at right angle. The shortest distance between DC and AB is [Kurukshetra CEE 1998]

Discussion

6490.	If the line x+αy+1=0 is perpendicular to the line 2x−βy+1=0 and parallel to the line x−(β−3)y−1=0, then the value of α+β is
Answer» If the line $x + α y + 1 = 0$ is perpendicular to the line $2 x - β y + 1 = 0$ and parallel to the line $x - (β - 3) y - 1 = 0,$ then the value of $α + β$ is

Discussion

6491.	A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the container. If the volume of the material used to make the container is minimum when the inner radius of the container is 10 mm, then the value of V250π is
Answer» A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of $V {mm}^{3},$ has a $2$ mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness $2$ mm and is of radius equal to the outer radius of the container. If the volume of the material used to make the container is minimum when the inner radius of the container is $10$ mm, then the value of $\frac{V}{250 π}$ is

Discussion

6492.	ntLet A = [-1,1]. Check whether f: A --> A is one-one or onto or both in f(x) = x/2.n
Answer» ntLet A = [-1,1]. Check whether f: A --> A is one-one or onto or both in f(x) = x/2.n

Discussion

6493.	Given an example of a relation. Which is (ii) Transitive but neither reflexive nor symmetric.
Answer» Given an example of a relation. Which is (ii) Transitive but neither reflexive nor symmetric.

Discussion

6494.	Find the roots of the following equations :1x+4−1x−7=1130,x≠−4,7
Answer» Find the roots of the following equations : $\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30}, x \neq - 4, 7$

Discussion

6495.	Let I=∫exe4x+e2x+1dx,J=∫e−xe−4x+e−2x+1dx. Then, for an arbitrary constant C, the value for J−I equals
Answer» Let $I = \int \frac{e^{x}}{e^{4 x} + e^{2 x} + 1} d x, J = \int \frac{e^{- x}}{e^{- 4 x} + e^{- 2 x} + 1} d x .$ Then, for an arbitrary constant $C$ , the value for $J - I$ equals

Discussion

6496.	If x23+y-11=105, find the value of x.
Answer» If $x [\begin{matrix} 2 \\ 3 \end{matrix}] + y [\begin{matrix} - 1 \\ 1 \end{matrix}] = [\begin{matrix} 10 \\ 5 \end{matrix}]$ , find the value of x.

Discussion

6497.	18. The general solution of the differential equation e* dy + (y e2x) dx 0 is(A) xexC(C) ye2C
Answer» 18. The general solution of the differential equation e* dy + (y e2x) dx 0 is(A) xexC(C) ye2C

Discussion

6498.	5. x—y$ll
Answer» 5. x—y$ll

Discussion

6499.	The number of solution(s) of the equation 2cos2x−2√2cosx+tan2x−2tanx+2=0 where x∈[−4π,4π] is
Answer» The number of solution(s) of the equation $2 {cos}^{2} x - 2 \sqrt{2} cos x + {tan}^{2} x - 2 tan x + 2 = 0$ where $x \in [- 4 π, 4 π]$ is

Discussion

6500.	If f(x)=∫5x8+7x6(x2+1+2x7)2dx, (x≥0), and f(0)=0, then the value of f(1) is :
Answer» If $f (x) = \int \frac{5 x^{8} + 7 x^{6}}{{(x^{2} + 1 + 2 x^{7})}^{2}} d x, (x \geq 0)$ , and $f (0) = 0$ , then the value of $f (1)$ is :

Discussion

Explore topic-wise InterviewSolutions in .

If f(x)=x2a+x, then which of the following is/are true?

Evaluate the following limits:limx→0cosax-cosbxcoscx-1

Solve the following system of inequalities graphically: x + y ≤ 9, y &gt; x, x ≥ 0

If AD is the median of ∆ABC, using vectors, prove that AB2+AC2=2AD2+CD2.

d/dx of 1+tanx/1-tanx

If the equations of two diameters of a circle arc 2x + y = 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle.

Differentiate thefunction with respect to x.

The range of f(x) = sgn(ex) isOptions:{0}Wrong {–1}Should have chosen {1}{0, 1

If 2 sec 2α=tan β+cot β, then one of the values ofα+β is

The function f(x)=xsinx satisfies the following equation:f ''(x) + f(x) + tcos x = 0The value of t is -2

The symmetric equation of lines 3x + 2y + z - 5 = 0 and x + y - 2z - 3 = 0, is

Let f(x)=max{3,x2,1x2} for 12≤x≤2. Then the value of the integral 2∫1/2f(x)dx is

If A and B are mutually exclusive events then

DERIVE THE FOLLOWING :V= ROOT OVER u^2 + g^2t^2 - 2u sintheta gt

An ordinary cubical die has four blank faces, one face marked 2 and another marked 3. Then the probability of obtaining 12 in 5 throws is

A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.

The value of tan x+cot π+x+cot π2+x+cot 2π-x is ______________ .

If A + B + C = π then tan2A2 + tan2B2 + tan2C2 is always

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denotes the larger of the two numbers obtained. Find E(X).

If sin y = x sin (a+y). Prive that dy/dx=sin^2(a+y)/sin a

Show by using mean value theorem and taking f(x)=logx that 1-a/b &lt; logb/a &lt; b/a -1

If the 9th term of an AP be zero, then the ratio of its 29th and 19 th term is

Write any three decimal numbers between 1.25 and 1.75.

Let A = (3, –4), B = (1, 2) and P = (2λ – 1, 2λ + 1). If the sum PA + PB is minimum, then the value of λ is

sin3x(cos4x+3cos2x+1)tan−1(secx+cosx)dx=

If A = [cos θsin θ−sin θcos θ], then for any natural number n, find the value of Det(A").

Seven different lectures are to be delivered in 7 periods of a class on a particular day. Out of 7 lecturers, A,B and C are three of them. If the number of ways in which a routine for the day can be made such that A delivers his lecture before B and B before C is N, then the value of (N120) is

18. 5x 3 2 3x 5

If x+y+z=0, then the value of ∣∣∣∣xaybzcyczaxbzbxcya∣∣∣∣ is equal to

If f(x)=x + tan x and f is inverse of g, then g' (x) is equal to

Show that the tangent of an angle between the lines xa+yb=1 and xa-yb=1 is 2aba2-b2

Find the sum to n terms of the A.P., whose kthterm is 5k + 1.

( √2 + 3√5 ) - ( 4√9 - 3√2 )

If the point (3, 5) lies on the graph of the equation 3y = ax + 9, the value of a is ___.

A is a matrix of order n and k is a constant, then adj(kA) is

The number of roots of the equation, (81)sin2x+(81)cos2x=30 in the interval [0,π] is equal to:

∫022xxdx

A square ABCD of diagonal 2a is folded along the diagonal 2a so that the planes DAC and BAC are at right angle. The shortest distance between DC and AB is [Kurukshetra CEE 1998]

If the line x+αy+1=0 is perpendicular to the line 2x−βy+1=0 and parallel to the line x−(β−3)y−1=0, then the value of α+β is

ntLet A = [-1,1]. Check whether f: A --> A is one-one or onto or both in f(x) = x/2.n

Given an example of a relation. Which is (ii) Transitive but neither reflexive nor symmetric.

Find the roots of the following equations :1x+4−1x−7=1130,x≠−4,7

Let I=∫exe4x+e2x+1dx,J=∫e−xe−4x+e−2x+1dx. Then, for an arbitrary constant C, the value for J−I equals

If x23+y-11=105, find the value of x.

18. The general solution of the differential equation e* dy + (y e2x) dx 0 is(A) xexC(C) ye2C

5. x—y$ll

The number of solution(s) of the equation 2cos2x−2√2cosx+tan2x−2tanx+2=0 where x∈[−4π,4π] is

If f(x)=∫5x8+7x6(x2+1+2x7)2dx, (x≥0), and f(0)=0, then the value of f(1) is :

Solve the following system of inequalities graphically: x + y ≤ 9, y > x, x ≥ 0

Show by using mean value theorem and taking f(x)=logx that 1-a/b < logb/a < b/a -1