43030 + Interview Questions in Mathematics Page 85 InterviewSolution

4201.	In a ΔABC,a(b cosC −c cos B) is equal to -
Answer» In a $Δ A B C, a (b c o s C - c c o s B)$ is equal to -

Discussion

4202.	If the H.M. of two distinct numbers a and b is an−1+bn−1an−2+bn−2, then the value of n is
Answer» If the H.M. of two distinct numbers $a$ and $b$ is $\frac{a^{n - 1} + b^{n - 1}}{a^{n - 2} + b^{n - 2}}$ , then the value of $n$ is

Discussion

4203.	Using integration, find the area of the region in the first quadrant enclosed by the X-axis, the line y=x and the circle x2+y2=32.
Answer» Using integration, find the area of the region in the first quadrant enclosed by the $X$ -axis, the line $y = x$ and the circle $x^{2} + y^{2} = 32$ .

Discussion

4204.	If 3x – 4y + 12 = 0 and 3x + 2y – 6 = 0, then area of triangle formed by the given lines and x-axis is (in sq. units)
Answer» If 3x – 4y + 12 = 0 and 3x + 2y – 6 = 0, then area of triangle formed by the given lines and x-axis is (in sq. units)

Discussion

4205.	The minimum value of the function 6x+3x+6−x+3−x+2 is
Answer» The minimum value of the function $6^{x} + 3^{x} + 6^{- x} + 3^{- x} + 2$ is

Discussion

4206.	Cos 9A=sinA and 9A
Answer» Cos 9A=sinA and 9A<90^°,then value of tanA?

Discussion

4207.	The distance between two parallel planes 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is
Answer» The distance between two parallel planes 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is

Discussion

4208.	If the line x-3y+k =0 touches the parabola 3y2=4x then the value of k is
Answer» If the line x-3y+k =0 touches the parabola $3 y^{2} = 4 x$ then the value of k is

Discussion

4209.	If A(1,2,3),B(2,10,1),Q are collinear points and Qx=−1 then Qz=
Answer» If $A (1, 2, 3), B (2, 10, 1), Q$ are collinear points and $Q_{x} = - 1$ then $Q_{z} =$

Discussion

4210.	The set of values of x satisfying the inequation (2−π2)(cot−1x−3)+tan−1x(cot−1x−3)>0 is
Answer» The set of values of $x$ satisfying the inequation $(2 - \frac{π}{2}) ({cot}^{- 1} x - 3) + {tan}^{- 1} x ({cot}^{- 1} x - 3) > 0$ is

Discussion

4211.	If the variance of the terms in an increasing A.P., b1,b2,b3, ....., b11 is 90, then the common difference of this A.P. is
Answer» If the variance of the terms in an increasing A.P., $b_{1}, b_{2}, b_{3}, . . . . ., b_{11}$ is 90, then the common difference of this A.P. is

Discussion

4212.	Resul†an t R of two vectors A and B is normal to vector A and its magnitude is same as vector A. Angle between vectorA and vector
Answer» Resul†an t R of two vectors A and B is normal to vector A and its magnitude is same as vector A. Angle between vectorA and vector

Discussion

4213.	Let f:R→R be defined as f(x)=(\|x−1\|+\|4x−11\|)[x2−2x−2], where [.] denotes the greatest integer function. Then the number of points of discontinuity of f(x) in (12,52) is
Answer» Let $f : R \to R$ be defined as $f (x) = (\| x - 1 \| + \| 4 x - 11 \|) [x^{2} - 2 x - 2],$ where $[.]$ denotes the greatest integer function. Then the number of points of discontinuity of $f (x)$ in $(\frac{1}{2}, \frac{5}{2})$ is

Discussion

4214.	An ant moves 3 units along the positive direction of the X-axis from the origin and reaches a point P, then moves 4 units from P along the negative direction of the Y-axis and reaches a point Q. What are the coordinates of points P and Q?
Answer» An ant moves 3 units along the positive direction of the X-axis from the origin and reaches a point P, then moves 4 units from P along the negative direction of the Y-axis and reaches a point Q. What are the coordinates of points P and Q?

Discussion

4215.	Let f(x) = ax²+bx+c, where a,b,c are integers. Suppose f(a) = 0, 40 < f(6) < 50, 60 < f(7) < 70 and 1000t < f(50) < 1000(t+1) for some integer t. Then the value of t is A. 2B. 3C. 4D. 5 or more
Answer» Let f(x) = ax²+bx+c, where a,b,c are integers. Suppose f(a) = 0, 40 < f(6) < 50, 60 < f(7) < 70 and 1000t < f(50) < 1000(t+1) for some integer t. Then the value of t is A. 2 B. 3 C. 4 D. 5 or more

Discussion

4216.	Write the solution set of the inequation ∣∣1x−2∣∣<4
Answer» Write the solution set of the inequation $∣ ∣ \frac{1}{x} - 2 ∣ ∣ < 4$

Discussion

4217.	If z1,z2 and z3 are complex numbers such that\|z1\|=\|z2\|=\|z3\|=∣∣1z1+1z2+1z3∣∣=1,then \|z1+z2+z3\|
Answer» If $z_{1}, z_{2} a n d z_{3}$ are complex numbers such that \| $z_{1}$ \|=\| $z_{2}$ \|=\| $z_{3}$ \|= $∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ = 1$ , then \| $z_{1}$ + $z_{2}$ + $z_{3}$ \|

4217.

If z1,z2 and z3 are complex numbers such that|z1|=|z2|=|z3|=∣∣1z1+1z2+1z3∣∣=1,then |z1+z2+z3|

Answer»

If $z_{1}, z_{2} a n d z_{3}$ are complex numbers such that

| $z_{1}$ |=| $z_{2}$ |=| $z_{3}$ |= $∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ = 1$ ,

then | $z_{1}$ + $z_{2}$ + $z_{3}$ |

Discussion

4218.	20. Let f(x)=1/x and g(x)=1/x then
Answer» 20. Let f(x)=1/x and g(x)=1/x then

Discussion

4219.	Statements: W S, K ® Z, U + W, S $ K Conclusions: I. U K II. Z S
Answer» Statements: W S, K $®$ Z, U + W, S $ K Conclusions: I. U K II. Z S

4219.

Statements: W S, K ® Z, U + W, S $ K Conclusions: I. U K II. Z S

Answer»

Statements: W S, K $®$ Z, U + W, S $ K

Conclusions:

I. U K

II. Z S

Discussion

4220.	Let f(x)=xα+3xβ with α>1,β>1. If the value of a for which the area of the region bounded by y=f(x) and straight lines x=0,x=1 and y=f(a) is minimum is λ, then value of 3.5λ is
Answer» Let $f (x) = x^{α} + 3 x^{β}$ with $α > 1, β > 1$ . If the value of $a$ for which the area of the region bounded by $y = f (x)$ and straight lines $x = 0, x = 1 and y = f (a)$ is minimum is $λ$ , then value of $3.5 λ$ is

Discussion

4221.	The negation of ∼ s∨(∼ r∨s) is
Answer» The negation of $\sim s \lor (\sim r \lor s)$ is

Discussion

4222.	In △ABC,1−tan A2 tan B2=[Roorkee 1973]
Answer» In $△ A B C, 1 - t a n \frac{A}{2} t a n \frac{B}{2} =$ [Roorkee 1973]

Discussion

4223.	A student appears for tests I,II and III. The student is successful only if he passes either in tests I and II or tests I and III(not all the 3).The probabilities of the student passing in tests I,II,III are p,q and 13 respectively. The probability that the student is successful is 16 and the relation between p and q is 1k=pq+p. Then the value of k is:
Answer» A student appears for tests $I, I I$ and $I I I$ . The student is successful only if he passes either in tests $I$ and $I I$ or tests $I$ and $I I I$ (not all the $3$ ). The probabilities of the student passing in tests $I, I I, I I I$ are $p, q$ and $\frac{1}{3}$ respectively. The probability that the student is successful is $\frac{1}{6}$ and the relation between $p$ and $q$ is $\frac{1}{k} = p q + p$ . Then the value of $k$ is:

Discussion

4224.	If a+b=90 where a,b>0,then maximum value of sin A +sin b is equal to
Answer» If a+b=90 where a,b>0,then maximum value of sin A +sin b is equal to

Discussion

4225.	the equation of the curve , slope of whose †an gent at any point (h,k) is 2k/h and which passes through the point (1,1) i
Answer» the equation of the curve , slope of whose †an gent at any point (h,k) is 2k/h and which passes through the point (1,1) i

Discussion

4226.	Find∫3√sin2(x)cos14(x)dx
Answer» Find $\int \sqrt[3]{\frac{s i n^{2} (x)}{c o s^{14} (x)}} d x$

Discussion

4227.	Nonzero vectors →a,→b,→c satisfy →a.→b =0, (→b−→a).(→b+→c) = 0 and 2 \|→b+→c\|=\|→b−→a\|. If = →a=μ→b+4→c then μ = ______ ___
Answer» Nonzero vectors $\to a, \to b, \to c$ satisfy $\to a . \to b$ =0, $(\to b - \to a) . (\to b + \to c)$ = 0 and 2 $\| \to b + \to c \| = \| \to b - \to a \|$ . If = $\to a = μ \to b + 4 \to c$ then $μ$ = ______ ___

4227.

Nonzero vectors →a,→b,→c satisfy →a.→b =0, (→b−→a).(→b+→c) = 0 and 2 |→b+→c|=|→b−→a|. If = →a=μ→b+4→c then μ = ____ _

Answer»

Nonzero vectors $\to a, \to b, \to c$ satisfy $\to a . \to b$ =0, $(\to b - \to a) . (\to b + \to c)$ = 0 and 2 $| \to b + \to c | = | \to b - \to a |$ .

If = $\to a = μ \to b + 4 \to c$ then $μ$ = ______

___

Discussion

4228.	11. Vector a,b,c are coplannar then the value of [a+2b b+2c c+2a] is?
Answer» 11. Vector a,b,c are coplannar then the value of [a+2b b+2c c+2a] is?

Discussion

4229.	If A is a matrix of order m x n then the order of AT where, AT is the transpose of A is
Answer» If A is a matrix of order m x n then the order of $A^{T}$ where, $A^{T}$ is the transpose of A is

Discussion

4230.	Let y=sin−1(sin8)−tan−1(tan10)+cos−1(cos12)−sec−1(sec9)+cot−1(cot6)−cosec–1(cosec 7). If y simplifies to aπ+b, then the value of a−b is
Answer» Let $y = {sin}^{- 1} (sin 8) - {tan}^{- 1} (tan 10) + {cos}^{- 1} (cos 12) - {sec}^{- 1} (sec 9) + {cot}^{- 1} (cot 6) - {cosec}^{- 1} (cosec 7) .$ If $y$ simplifies to $a π + b,$ then the value of $a - b$ is

Discussion

4231.	In a bank, principal increases continuously at the rate of r % per year. Find the value of r if Rs 100 doubles itself in 10 years (log e 2 = 0.6931).
Answer» In a bank, principal increases continuously at the rate of r % per year. Find the value of r if Rs 100 doubles itself in 10 years (log e 2 = 0.6931).

Discussion

4232.	Differentiate the function xx+xa+ax+aa, for some fixed constants a>0 and x>0 w.r.t.x.
Answer» Differentiate the function $x^{x} + x^{a} + a^{x} + a^{a}$ , for some fixed constants $a > 0 and x > 0$ w.r.t. $x$ .

Discussion

4233.	If 2x3+ax2+bx+4=0,a,b>0 has 3 real roots and the minimum value of a+b is m(x1/3+41/3), then the value of m+x is
Answer» If $2 x^{3} + a x^{2} + b x + 4 = 0, a, b > 0$ has $3$ real roots and the minimum value of $a + b$ is $m (x^{1 / 3} + 4^{1 / 3})$ , then the value of $m + x$ is

Discussion

4234.	The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them, is(a) 16C11(b) 16C5(c) 16C6(d) 20C9
Answer» The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them, is (a) ¹⁶C₁₁ (b) ¹⁶C₅ (c) ¹⁶C₆ (d) ²⁰C₉

Discussion

4235.	limx→∞(a1/x+b1/x+c1/x3)x= (where a,b,c are positive real numbers)
Answer» $lim x \to \infty {(\frac{a^{1 / x} + b^{1 / x} + c^{1 / x}}{3})}^{x} =$ (where $a, b, c$ are positive real numbers)

Discussion

4236.	Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX-plane.
Answer» Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX-plane.

Discussion

4237.	A=⎡⎢⎣152314223⎤⎥⎦ .The following elementary transformations are applied on the matrix A in the given order. What will be the resultant matrix?
Answer» $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 5 & 2 3 & 1 & 4 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦$ .The following elementary transformations are applied on the matrix A in the given order. What will be the resultant matrix?

Discussion

4238.	301224-79
Answer» 301224-79

Discussion

4239.	If I=∫dtt43+t, then which of the following is/are equal to I:(where C is integration constant)
Answer» If $I = \int \frac{d t}{t^{\frac{4}{3}} + t}$ , then which of the following is/are equal to $I$ : (where $C$ is integration constant)

Discussion

4240.	Let z,w be complex numbers such that ¯z+i¯w=0 and argzw=π. Then argz equals
Answer» Let $z, w$ be complex numbers such that $¯ z + i ¯ w = 0$ and $arg z w = π$ . Then $arg z$ equals

Discussion

4241.	Find and , if .
Answer» Find and , if .

Discussion

4242.	Equation of hyperbola whose axes are parallel to coordinate axis with e=√2 and having distance between the foci as 1 unit is :
Answer» Equation of hyperbola whose axes are parallel to coordinate axis with $e = \sqrt{2}$ and having distance between the foci as $1$ unit is :

Discussion

4243.	Explain spin multiplicity
Answer» Explain spin multiplicity

Discussion

4244.	The solution of differential equation xdydx+2y=x2 is......
Answer» The solution of differential equation $x \frac{d y}{d x} + 2 y = x^{2}$ is......

Discussion

4245.	Match List I with the List II and select the correct answer using the code given below the lists : List IList II(A)Radius of the largest circle which passes through the focus of the parabola y2=4x and is completely(P)16 contained in it, is(B)If the shortest distance between the curves y2=4x and y2=2x–6 is d , then d2 is (Q)5(C)Let AB be a focal chord of y2=12x with focus S. The harmonic mean of lengths of segments AS(R)6 and BS is (D)Tangents drawn from P meet the parabola y2=16x at A and B. If these two tangents are (S)4 perpendicular, then the least value of √AB is Which of the following is CORRECT ?
Answer» Match $List I$ with the $List II$ and select the correct answer using the code given below the lists : $\begin{matrix} List I & List II (A) & Radius of the largest circle which passes through the focus of the parabola y^{2} = 4 x and is completely & (P) & 16 contained in it, is (B) & If the shortest distance between the curves y^{2} = 4 x and y^{2} = 2 x - 6 is d, then d^{2} is & (Q) & 5 (C) & Let A B be a focal chord of y^{2} = 12 x with focus S . The harmonic mean of lengths of segments A S & (R) & 6 and B S is (D) & Tangents drawn from P meet the parabola y^{2} = 16 x at A and B . If these two tangents are & (S) & 4 perpendicular, then the least value of \sqrt{A B} is \end{matrix}$ Which of the following is CORRECT ?

Discussion

4246.	integral of sin^n x
Answer» integral of sin^n x

Discussion

4247.	13+x=3, then x =(a) 73(b) 23(c) 43(d) 83Disclaimer: There is a misprint in the question, 1x is written instead of x.
Answer» $\frac{1}{3} + x = 3$ , then x = (a) $\frac{7}{3}$ (b) $\frac{2}{3}$ (c) $\frac{4}{3}$ (d) $\frac{8}{3}$ Disclaimer: There is a misprint in the question, $\frac{1}{x}$ is written instead of x.

Discussion

4248.	99. Has not it got two points of inflection as second derivative has discriminent greater than zero
Answer» 99. Has not it got two points of inflection as second derivative has discriminent greater than zero

Discussion

4249.	the seet of values of x satiesfying (x^2 - x -1) (x^2 - x - 7) < -5 is (a,b) uniton (c,d) then a+b+c+d is equal to
Answer» the seet of values of x satiesfying (x^2 - x -1) (x^2 - x - 7) < -5 is (a,b) uniton (c,d) then a+b+c+d is equal to

Discussion

4250.	Let f be a twice differentiable function defined on R such that f(0)=1, f′(0)=2 and f′(x)≠0 for all x∈R. If ∣∣∣f(x)f′(x)f′(x)f′′(x)∣∣∣=0, for all x∈R, then the value of f(1) lies in the interval
Answer» Let $f$ be a twice differentiable function defined on $R$ such that $f (0) = 1,$ $f^{'} (0) = 2$ and $f^{'} (x) \neq 0$ for all $x \in R .$ If $∣ ∣ ∣ \begin{matrix} f (x) & f^{'} (x) f^{'} (x) & f^{''} (x) \end{matrix} ∣ ∣ ∣ = 0,$ for all $x \in R,$ then the value of $f (1)$ lies in the interval

Discussion

Explore topic-wise InterviewSolutions in .

In a ΔABC,a(b cosC −c cos B) is equal to -

If the H.M. of two distinct numbers a and b is an−1+bn−1an−2+bn−2, then the value of n is

Using integration, find the area of the region in the first quadrant enclosed by the X-axis, the line y=x and the circle x2+y2=32.

If 3x – 4y + 12 = 0 and 3x + 2y – 6 = 0, then area of triangle formed by the given lines and x-axis is (in sq. units)

The minimum value of the function 6x+3x+6−x+3−x+2 is

Cos 9A=sinA and 9A

The distance between two parallel planes 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is

If the line x-3y+k =0 touches the parabola 3y2=4x then the value of k is

If A(1,2,3),B(2,10,1),Q are collinear points and Qx=−1 then Qz=

The set of values of x satisfying the inequation (2−π2)(cot−1x−3)+tan−1x(cot−1x−3)&gt;0 is

If the variance of the terms in an increasing A.P., b1,b2,b3, ....., b11 is 90, then the common difference of this A.P. is

Resul†an t R of two vectors A and B is normal to vector A and its magnitude is same as vector A. Angle between vectorA and vector

Let f:R→R be defined as f(x)=(|x−1|+|4x−11|)[x2−2x−2], where [.] denotes the greatest integer function. Then the number of points of discontinuity of f(x) in (12,52) is

An ant moves 3 units along the positive direction of the X-axis from the origin and reaches a point P, then moves 4 units from P along the negative direction of the Y-axis and reaches a point Q. What are the coordinates of points P and Q?

Let f(x) = ax²+bx+c, where a,b,c are integers. Suppose f(a) = 0, 40 < f(6) < 50, 60 < f(7) < 70 and 1000t < f(50) < 1000(t+1) for some integer t. Then the value of t is A. 2B. 3C. 4D. 5 or more

Write the solution set of the inequation ∣∣1x−2∣∣&lt;4

If z1,z2 and z3 are complex numbers such that|z1|=|z2|=|z3|=∣∣1z1+1z2+1z3∣∣=1,then |z1+z2+z3|

20. Let f(x)=1/x and g(x)=1/x then

Statements: W S, K ® Z, U + W, S $ K Conclusions: I. U K II. Z S

Let f(x)=xα+3xβ with α&gt;1,β&gt;1. If the value of a for which the area of the region bounded by y=f(x) and straight lines x=0,x=1 and y=f(a) is minimum is λ, then value of 3.5λ is

The negation of ∼ s∨(∼ r∨s) is

In △ABC,1−tan A2 tan B2=[Roorkee 1973]

If a+b=90 where a,b>0,then maximum value of sin A +sin b is equal to

the equation of the curve , slope of whose †an gent at any point (h,k) is 2k/h and which passes through the point (1,1) i

Find∫3√sin2(x)cos14(x)dx

Nonzero vectors →a,→b,→c satisfy →a.→b =0, (→b−→a).(→b+→c) = 0 and 2 |→b+→c|=|→b−→a|. If = →a=μ→b+4→c then μ = ______ ___

11. Vector a,b,c are coplannar then the value of [a+2b b+2c c+2a] is?

If A is a matrix of order m x n then the order of AT where, AT is the transpose of A is

Let y=sin−1(sin8)−tan−1(tan10)+cos−1(cos12)−sec−1(sec9)+cot−1(cot6)−cosec–1(cosec 7). If y simplifies to aπ+b, then the value of a−b is

In a bank, principal increases continuously at the rate of r % per year. Find the value of r if Rs 100 doubles itself in 10 years (log­ e 2 = 0.6931).

Differentiate the function xx+xa+ax+aa, for some fixed constants a&gt;0 and x&gt;0 w.r.t.x.

If 2x3+ax2+bx+4=0,a,b&gt;0 has 3 real roots and the minimum value of a+b is m(x1/3+41/3), then the value of m+x is

The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them, is(a) 16C11(b) 16C5(c) 16C6(d) 20C9

limx→∞(a1/x+b1/x+c1/x3)x= (where a,b,c are positive real numbers)

Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX-plane.

A=⎡⎢⎣152314223⎤⎥⎦ .The following elementary transformations are applied on the matrix A in the given order. What will be the resultant matrix?

301224-79

If I=∫dtt43+t, then which of the following is/are equal to I:(where C is integration constant)

Let z,w be complex numbers such that ¯z+i¯w=0 and argzw=π. Then argz equals

Find and , if .

Equation of hyperbola whose axes are parallel to coordinate axis with e=√2 and having distance between the foci as 1 unit is :

Explain spin multiplicity

The solution of differential equation xdydx+2y=x2 is......

integral of sin^n x

13+x=3, then x =(a) 73(b) 23(c) 43(d) 83Disclaimer: There is a misprint in the question, 1x is written instead of x.

99. Has not it got two points of inflection as second derivative has discriminent greater than zero

the seet of values of x satiesfying (x^2 - x -1) (x^2 - x - 7) < -5 is (a,b) uniton (c,d) then a+b+c+d is equal to

Let f be a twice differentiable function defined on R such that f(0)=1, f′(0)=2 and f′(x)≠0 for all x∈R. If ∣∣∣f(x)f′(x)f′(x)f′′(x)∣∣∣=0, for all x∈R, then the value of f(1) lies in the interval

The set of values of x satisfying the inequation (2−π2)(cot−1x−3)+tan−1x(cot−1x−3)>0 is

Write the solution set of the inequation ∣∣1x−2∣∣<4

Let f(x)=xα+3xβ with α>1,β>1. If the value of a for which the area of the region bounded by y=f(x) and straight lines x=0,x=1 and y=f(a) is minimum is λ, then value of 3.5λ is

Nonzero vectors →a,→b,→c satisfy →a.→b =0, (→b−→a).(→b+→c) = 0 and 2 |→b+→c|=|→b−→a|. If = →a=μ→b+4→c then μ = ____ _

In a bank, principal increases continuously at the rate of r % per year. Find the value of r if Rs 100 doubles itself in 10 years (log e 2 = 0.6931).

Differentiate the function xx+xa+ax+aa, for some fixed constants a>0 and x>0 w.r.t.x.

If 2x3+ax2+bx+4=0,a,b>0 has 3 real roots and the minimum value of a+b is m(x1/3+41/3), then the value of m+x is