BSc CSIT Entrance Mathematics Questions with Answers

If $|y-3|\le7$, then

Answer: $-4\le y\le10$

For any two non-empty sets A and B, $A-B=$

Answer: $A\cap \bar B$

If $f(x)=1-x$ then $f$ of $f(x)$ is

Answer: $x$

The function $f(x)=x+2x^3$ is

Answer: odd

The sum of the infinite series $1-\frac12+\frac14-\frac18\dots$ is

Answer: $\frac23$

If $A=\begin{pmatrix}1&x+2\2x+2&3\end{pmatrix}$ is symmetric then $x=$

Answer: 0

If $w$ is the cube root of unity, then $\begin{vmatrix}1&w&w^2\w&w^2&1\w^2&1&w\end{vmatrix}=$

Answer: 0

The imaginary part of $\frac{2i^2}{(1+i)^2}$ is

Answer: 1

The value of $k$ for which one root of the equation $px^2-qx+k=0$ is reciprocal of the other is

Answer: p

If $|x-5|=7$, then $x=$

Answer: ${12,-2}$

If $f(x)=3x-2$ for $x\in R$, then $f^{-1}(7)=$

Answer: 3

The range of the function $f(x)=\sqrt{x-3}$ is

Answer: $[0,\infty)$

The function $f(x)=x^4+5$ is symmetrical about

Answer: y-axis

If a, b, c, d... are in G.S., then $1/a, 1/b, 1/c, 1/d$ are in

Answer: G.S.

If $A=\begin{pmatrix}2&5\3&7\end{pmatrix}$, then $A^{-1}=$

Answer: $\begin{pmatrix}-7&5\3&-2\end{pmatrix}$

If A is a square matrix, then the matrix $A+A^T$ is

Answer: symmetric

If one root of a quadratic equation is $\frac{1}{3+\sqrt5}$, then the quadratic equation is

Answer: $4x^2-6x+1=0$

The least positive integer $k$ which will reduce $\left(\frac{i-1}{i+1}\right)^k$ to a real number is

Answer: 2

A sentence $x+7=5$ is

Answer: not a statement

If $P$ and $Q$ are nonempty sets and $P\subset Q$ then

Answer: $\overline{Q}\subset\overline{P}$

If $|x-3|=7$ then

Answer: {10, -4}

$\sqrt{-1}$ is

Answer: a complex number

The range of the function $f(x)=\sqrt{9-x^{2}}$ is

Answer: [0,3]

If x, y and z are in A.P. then

Answer: x + z = 2y

The determinant of the matrix $A=[-3]$ is

Answer: -3

If $x-iy=(5+2i)^{2}$ then $(x,y)$ is

Answer: (21, -20)

Let $U$ be the universal set, and $A$ and $B$ be two sets. If $n(U)=100$, $n(A)=35$, $n(B)=60$ and $n(A\cup B)=80$, then the value of $n(A\cap B)$ is

Answer: $15$

If $A=[-3,1]$ and $B=[-2,4]$, then $A-B$ is

Answer: $[-3,-2)$

A sentence which is a true statement is

Answer: Mount Everest is in Nepal.

Let a function $f:N\to N$ be defined by $f(x)=2x$ for all $x\in N$. Then $f$ is

Answer: one to one

If $a,b,c$ are in A.P., $b,c,d$ are in G.P. and $c,d,e$ are in H.P., then $a,c,e$ are in

Answer: G.P.

If $A=[-7]$, then the value of $\det A$ is

Answer: $-7$

The system of equations $3x-2y=1$ and $6x-4y=2$ is

Answer: consistent and dependent

The sum of the three cube roots of unity is

Answer: $0$

Let $A$ and $B$ be two sets. Then $\overline{A\cup B}=$

Answer: $\bar A\cap\bar B$

The inverse of the matrix $\begin{pmatrix}2&3\3&5\end{pmatrix}$ is

Answer: $\begin{pmatrix}5&-3\-3&2\end{pmatrix}$

The remainder of $x^3-2x^2+5x+10$ when divided by $x+1$ is

Answer: $2$

The coefficient of $x^2$ in $\left(x^2+\frac{a^2}{x^2}\right)^3$ is

Answer: $3a^2$

How many numbers of three different digits less than $500$ can be formed from the integers $1,2,3,4,5$?

Answer: $48$

The irrational number is

Answer: $\pi$

If P and Q are non-empty sets and $P \subset Q \subset U$, then $P \cap Q =$

Answer: $P$

A sentence which is not a statement is

Answer: $x > 2$

If $|x-3|=5$ then $x =$

Answer: ${8,-2}$

If the graph of $y=a^x$ contains the point $(3,64)$ then the base $a$ is

Answer: $4$

If $f(x)=x-5$ for $x\in R$ then $f^{-1}(x)=$

Answer: $x+5$

If $3^{rd}$, $5^{th}$ and $7^{th}$ terms of a G.P. are $p,q,r$ respectively, then

Answer: $pr=q^2$

The value of $p$ for which $3p+4,\ 6p-2$ and $2p+7$ are in A.P. is

Answer: $\frac{15}{7}$

If $A=[a_{ij}]$, where $a_{ij}=i+j$, then the $2\times2$ matrix $A$ is

Answer: $\begin{pmatrix}2&3\3&4\end{pmatrix}$

The value of $x$ for the determinant $\begin{vmatrix}x+1&3\0&1\end{vmatrix}=0$ is

Answer: $-1$

The system of equations $2x+3y=5,\ 2x+3y=7$ has

Answer: no solution

If $\omega$ is the cube root of unity of a complex number then $(1-\omega)(1-\omega^2)=$

Answer: $3$

$\sqrt{-3}\sqrt{-5}=$

Answer: $-\sqrt{15}$

A quadratic equation whose roots are $2,-3$ is

Answer: $x^2+x-6=0$

If $f(0)=1, f(1)=2, f(2)=5, f(3)=10$, then $f(-1)=$

Answer: $2$

If $A\subseteq B$, then

Answer: $B^c\subseteq A^c$

If $\log_a(ab)=x$, then $\log_b(ab)=$

Answer: $\frac{x}{x-1}$

If $A=\begin{pmatrix}\frac{1}{3}&2\0&2x-3\end{pmatrix}$, $B=\begin{pmatrix}3&6\0&-1\end{pmatrix}$, $AB=I$, then $x=$

Answer: $1$

If $A^2-A+I=0$, then $A^{-1}=$

Answer: $I-A$

The sum of 3 numbers of G.P. is 38 and their product is 1728. The middle term is

Answer: 12

Fourth roots of unity are

Answer: $\pm1,\pm i$

The multiplicative inverse of $\frac{2+3i}{3-i}$ is

Answer: $\frac{3}{13}-\frac{11i}{13}$

If the roots of $\frac{a}{x-a}+\frac{b}{x-b}=1$ are numerically equal and opposite in sign, then

Answer: $a+b=0$

The remainder when $(kx^2+x-1)$ is divided by $(x+2k)$ is

Answer: $(4k^3-2k-1)$

If $a/b$, $a,b\in\mathbb{R}$, is equal to zero, then

Answer: $a=0,\ b\neq0$

If $x\ge5$ then $x$ may be

Answer: $6$

If $|x-2|=5$ then the value of $x$ is

Answer: ${-3,7}$

The range of the relation $R={(1,2),(2,3),(3,4)}$ is

Answer: ${2,3,4}$

If $y=a^x$ is the exponential function passing through $(4,81)$, then the base $a$ is

Answer: $3$

The sum to infinity of the G.P. $\frac14,\frac1{16},\frac1{64},\dots$ is

Answer: $\frac13$

The value of $a$ so that $8a+4$, $6a-2$ and $3a+7$ will form an A.P. is

Answer: $15$

The quadratic equation whose roots are $3$ and $4$ is

Answer: $x^2-7x+12=0$

$p/q$, $p,q\in R$, is undefined if

Answer: $p\ne 0,\ q=0$

$[a,b]=$

Answer: ${x: a\le x\le b}$

If $f:R\to R$ is defined by $f(x)=\sqrt{4-x^2}$ then $f(-3)$ is

Answer: Undefined

If $|x|=1$ then $x$ is

Answer: ${-1,1}$

If $\log_2(x-7)=1$, then $x$ is

Answer: $9$

If $k+2,\ 4k-6,\ 3k-2$ are in AP then $k$ is

Answer: $3$

The sum to infinity of $1-\frac12+\frac14-\frac18+\cdots$ is

Answer: $2/3$

If $A=\begin{pmatrix}1\2\3\end{pmatrix}$ and $B=(1\ \ 2\ \ 3)$ then $AB$ is

Answer: $\begin{pmatrix}1&2&3\2&4&6\3&6&9\end{pmatrix}$

The value of $\begin{vmatrix}0&2&3\1&2&3\4&8&12\end{vmatrix}$ is

Answer: $0$

The matrix $\begin{pmatrix}1&2&3\2&0&4\3&4&5\end{pmatrix}$ is

Answer: Symmetric

$[2(\cos15^\circ+i\sin15^\circ)]^6=$

Answer: $64i$

$(1+\omega+\omega^2)^3+(1+\omega-\omega^2)^3=$

Answer: $-8$

The quadratic equation whose roots are $-3$ and $2$ is

Answer: $x^2+x-6=0$

Which one is not a logical statement:

Answer: I am sick.

If $|x-2|=5$, then $x$ is in

Answer: ${-3,7}$

$A-B=$

Answer: $\bar B-\bar A$

If $f(x)=2x-3$, then $f^{-1}(x)=$

Answer: $\frac{x+3}{2}$

The fourth, seventh and tenth terms of a G.P. are $l,m,n$ respectively, then

Answer: $ln=m^2$

The $n$th term of the series $1\cdot3+3\cdot5+5\cdot7+\cdots$ is

Answer: $4n^2-1$

If $A=\begin{pmatrix}k&1&0\2&0&k\0&2&-1\end{pmatrix}$ and $|A|=0$, then $k=$

Answer: $\pm1$

The value of $x$ for which $A=\begin{bmatrix}6&x-2\3&x\end{bmatrix}$ has no inverse is

Answer: $-2$

If the system of equations has zero solutions only, then the solution is

Answer: trivial

$(1+i)^6+(1-i)^6=$

Answer: $0$

$\left(\frac{2i}{1+i}\right)^2=$

Answer: $2i$

If one root of $5x^2+2x-k=0$ is the reciprocal of the other, then $k=$

Answer: $-5$

If $a, b \in R$, $a/b$ is indeterminate if

Answer: $a=0, b=0$

$(-\infty,\infty)=$

Answer: ${x: -\infty < x < \infty}$

The statement is

Answer: Bagmati is a River.

If $(2x-1,-3)=(3,y+3)$, then

Answer: $x=2, y=-6$

If $f:R\to R$ is defined by $f(x)=x$ and $g:R\to R$ is defined by $g(x)=x$, then $(f\circ g)(x)$ is

Answer: $x$

If $2p$, $p+8$, $3p+1$ are in A.P., then $p$ is

Answer: 5

If $A$, $G$ and $H$ are the arithmetic mean, geometric mean and harmonic mean respectively, then

Answer: $G^{2}=AH$

If $A=(-1\ 0\ 2)$ and $B=\begin{pmatrix}2\3\4\end{pmatrix}$, then $AB$ is

Answer: $(6)$

The value of the determinant $\begin{vmatrix}1&2&0\2&4&1\3&6&2\end{vmatrix}$ is

Answer: 0

The adjoint of the matrix $\begin{pmatrix}a&b\c&d\end{pmatrix}$ is

Answer: $\begin{pmatrix}d&-b\-c&a\end{pmatrix}$

The real part of $\frac{(1+i)^{2}}{2-i}$ is

Answer: $-2/5$

If $\omega$ be the cube root of unity then $(1+\omega+\omega^{2})(1+\omega-\omega^{2})=$

Answer: 0

The value of $k$ for which the equation $x^{2}+2(k+2)x+9k=0$ has equal roots are

Answer: 4, 1

If $|x-3|=4$ then $x$ is

Answer: $7$ and $-1$

If ${x-x^2=9}$ and $2x=6$, then

Answer: null set

If $f:\mathbb{R}\to\mathbb{R}$ is defined by $f(x)=x^2+3$, then $f^{-1}(4)$ is

Answer: ${-1,1}$

The value of $\log_2\sqrt2+\log_3\sqrt3+\log_4\sqrt4$ is

Answer: $\frac{3}{2}$

If $a^2,b^2,c^2$ are in H.P. then

Answer: $2a^2c^2=b^2(a^2+c^2)$

If $A=\begin{pmatrix}1&2\2&3\end{pmatrix}$ and $A^2-nA-I=0$, then the value of $n$ is

Answer: $4$

If $A=\begin{pmatrix}1&0&1\0&1&1\1&0&0\end{pmatrix}$, then $A$ is

Answer: Nonsingular

The system of equations $2x+y=5$; $4x+2y=8$ is

Answer: Inconsistent and independent

The value of $i^7+\frac{1}{i^4}$ is

Answer: $-i+1$

The value of $\frac{x+wy+w^2z}{y+wz+w^2x}$, where $w$ is the cube root of unity, is

Answer: $w$

If the roots of $x^2+4x+k=0$ are equal then $k$ is

Answer: $4$

If A and B are any two sets, then $A-(A-B)$ is equal to

Answer: $A\cap B$

The range of the function $y=\sqrt{a^2-x^2}$, $a>0$ is equal to

Answer: $[0,a]$

What is the value of $\log_a\sqrt{a^3\sqrt{a^2}}$ ?

Answer: $2$

If $A=\begin{pmatrix}0&1\-1&0\end{pmatrix}$, then $A^{100}$ is equal to

Answer: $1$

If $a^x=b^y=c^z$ and $a,b,c$ are in G.P., then $x,y,z$ are in

Answer: H.P.

The function $f(x)=x-\frac{1}{x^2}$, $x\in R$, $x\neq0$ is defined for

Answer: $(-\infty,0)\cup(0,\infty)$

For what value of $k$ will the equation $5x^2-kx+45=0$ have equal roots?

Answer: $\pm30$

The quadratic equation whose one root is $2+\sqrt3$ is

Answer: $x^2-4x+1=0$

The absolute value of the complex number $(1+i)^{-1}$ is

Answer: $\frac{1}{\sqrt2}$

If $z=\cos\theta+i\sin\theta$, then $z^n+\frac{1}{z^n}$ is equal to

Answer: $2\cos n\theta$

The $n^{th}$ term of the series $2+6+12+20+\dots$ is

Answer: $n(n+1)$

If $|x|<1$ and $y=x+x^2+x^3+x^4+\dots+\infty$, then $x$ is equal to

Answer: $\frac{y}{1+y}$

What is the value of $\begin{vmatrix}1&\omega&\omega^2\\omega&\omega^2&1\\omega^2&1&\omega\end{vmatrix}$, where $\omega$ is an imaginary cube root of unity?

Answer: $0$

Let $A=[-3,2]$ and $B=[2,3]$. Then $A-B$ is equal to

Answer: $[-3,2)$

If $f(x)=\sqrt{4-x^2}$, then $f(2)$ is

Answer: $0$

If $|x|=2$, then the solution set is

Answer: ${-2,2}$

If A, B and C are non-empty sets and $A\subset B$, then $A\cap B$ is

Answer: $A$

The smallest prime number is

Answer: 2

The value of $x$ for $\sum_{i=1}^{2}(xi-4)=13$ is

Answer: 7

The matrix $A=\begin{pmatrix}1&3\3&2\end{pmatrix}$ is

Answer: symmetric

The value of $\begin{vmatrix}0&1&2\0&1&2\1&2&3\end{vmatrix}$ is

Answer: 0

The value of $(1-\omega)(1-\omega^2)$, where $\omega$ is the cube root of unity, is

Answer: 3

The magnitude of $2-3i$ is

Answer: $\sqrt{13}$

1 and 2 are the roots of

Answer: $x^2-3x+2=0$

$\lim_{x\to0}\frac{\sin2x+4x}{x}=$

Answer: 6

If $y=e^{\log(\sin x^2)}$, then $\frac{dy}{dx}=$

Answer: $2xy\cot x^2$

The function $x^3-12x+8$ has maximum at $x=$

Answer: $-2$

$\int_1^2\frac{\cos(\log x)}{x}dx=$

Answer: $\sin(\log2)$

$\lim_{x\to0}\frac{\tan x+4x}{x}=$

Answer: 5

If $y=\log_e e^{\sin(3x^2)}$, then $\frac{dy}{dx}=$

Answer: $6x\cos3x^2$

The points of inflection of the curve $x^4-6x^2+8x$ are:

Answer: $1,-1$

$\int_0^{\pi/2}\cos x,e^{\sin x},dx=$

Answer: $e-1$

$\lim_{x\to3}\frac{x^{3}-27}{x-3}=$

Answer: 27

The value of $x$ for which $\frac{dy}{dx}=0$, for $y=x^{3}-3x^{2}$ are

Answer: 0,2

If $y=e^{\log x^{2}}$ then $\frac{dy}{dx}=$

Answer: 2x

The point of inflection of $y=x^{3}-x^{2}$ is

Answer: 1/3

$\int_0^1 3x^{2}e^{x^{3}}dx=$

Answer: e-1

Area bounded by x-axis and the curve $y=x^{2}$ and the lines $x=0$ and $x=4$ is

Answer: 64/3

If $f(x)=x^{2}+5$, then the approximate value of $f'(2)$ with $x=0.1$ is

Answer: 4.1

The function $f(x)=12-3x$ on $R$ is

Answer: decreasing

The value of $\lim_{x\to0}\frac{\sin x^{\circ}}{x}$ is

Answer: $\frac{\pi}{180}$

The derivative of $e^{\sqrt{x}}$ is

Answer: $\frac{e^{\sqrt{x}}}{2\sqrt{x}}$

The value of $\int\frac{x}{1+x},dx$ is

Answer: $x-\ln(1+x)$

The value of $\int_0^2 3(1+x)^2,dx$ is equal to

Answer: $26$

If $\lim_{x\to a}\frac{x^3-a^3}{x-a}=27$ then $a=$

Answer: $\pm3$

If $y=\frac{x^2}{p^2}+\frac{p^2}{x^2}$, then $\frac{dy}{dx}$ at $x=p$ is

Answer: $0$

$\int\left(3\sqrt{x}+\sin x+2e^{2x}\right)dx=$

Answer: $2x^{\frac32}-\cos x+e^{2x}$

Area bounded by the x-axis and the curve $y=3x^2$ and the lines $x=2$ and $x=4$ is

Answer: $56$

The critical points for $f(x)=x^4-6x^2+8x$ are

Answer: $1,-2$

$\lim_{x\to\infty}\frac{x(x+1)}{x^2}=$

Answer: $1$

$\lim_{x\to\pi/4}\frac{\sec^2x-2}{\tan x-1}=$

Answer: $2$

$\frac{dy}{dx}$ of $t=x^2$, $y=\frac1t$ is

Answer: $-\frac{2}{x^3}$

The derivative of $x^2$ with respect to $-x^2$ is

Answer: $-1$

$\lim_{x\to\infty}\frac{3x^2+2x-5}{6x^2+4x-7}=$

Answer: $\frac12$

$\lim_{x\to0}\frac{1-\cos ax}{x^2}=$

Answer: $\frac{a^2}{2}$

If $x=t+\sin t$, $y=1-\cos t$ then $dy/dx$ is

Answer: $\tan\frac t2$

The derivative of $\cos x$ with respect to $\sin x$ is

Answer: $-\tan x$

The point of inflection of $y=x^3-12x^2$ is

Answer: $4$

$\int\frac{dx}{\sin^2x}=$

Answer: $-\cot x+C$

$\int_0^1\frac{dx}{1+x^2}=$

Answer: $\frac\pi4$

$\lim_{x\to2}\frac{x-2}{\sqrt{x^{2}-4}}$

Answer: 0

$\lim_{x\to0}\frac{1-\cos ax}{x^{2}}$

Answer: $\frac{a^{2}}{2}$

The value of $x$ for which the function $y=x^{3}-x^{2}$ has $\frac{dy}{dx}=0$

Answer: 0, 2/3

The point of inflection for $y=x^{2}-2x$ is

Answer: does not exist

$\int_0^{1}\frac{2x,dx}{\sqrt{1-x^{2}}}$

Answer: 2

$\int x\sin x,dx=$

Answer: $\sin x-x\cos x+C$

The area bounded by the x-axis and the curve $y=3x^{2}$ and the ordinates $x=3$ and $x=4$ is

Answer: 37

The value of $\lim_{x\to2}\frac{x^5-2^5}{x-2}$ is

Answer: $80$

The value of $\lim_{x\to0}\frac{3x+4\tan2x}{x}$ is

Answer: $11$

The derivative of $y=b^x$ is

Answer: $b^x\ln|b|$

The derivative of $y=\cos(\cos\sqrt x)$ is

Answer: $\frac{\sin(\cos\sqrt x)\sin\sqrt x}{2\sqrt x}$

The value of $x$ for which the derivative of $x^2+2x+2$ is zero is

Answer: $-1$

The point of inflection of the curve $x^3+3x^2-9x+2$ is

Answer: $-1$

$\int\frac{dx}{1-\cos x}=$

Answer: $-\cot\frac x2$

$\int_0^{\pi/2}\frac{\cos x}{1+\sin x},dx=$

Answer: $\ln|2|$

$\lim_{x\to2}\frac{x^3-2^3}{x-2}$ is

Answer: 12

$\lim_{x\to0}\frac{\tan x-5x}{x}$ is equal to

Answer: -4

The function $f(x)=\begin{cases}x+2,&x\ge2\2x,&x<2\end{cases}$ is continuous at

Answer: $x=2$

If the derivative of $x^2+3x$ is 1, the value of $x$ is

Answer: -1

If $x=2t+1$ and $y=t^2$, then $\frac{dy}{dt}$ is

Answer: $2t$

The point of inflection for the curve $x^3+4x$ is

Answer: 0

$2\int_0^1 x,dx$ is equal to

Answer: 1

$\int\cos x,dx$ is equal to

Answer: $\sin x$

A first degree equation in $x$ and $y$ always represents a

Answer: Straight line

The point on the x-axis at distance of 5 units from the line $3x+4y=8$

Answer: (11,0)

If the angle between the lines represented by $kx^2+xy-y^2=0$ is $90^\circ$, then $k=$

Answer: 1

The distance of a point (3,5,9) from yz plane is

Answer: 3

The points on the y-axis at distance of $\sqrt2$ units from the line $x+y=1$, are

Answer: $(0,-1)$ and $(0,3)$

The equation $kx^2+xy-y^2+2x-y=0$ represents a pair of lines if $k=$

Answer: 2

Equation of a line perpendicular to the line $2x+3y+5=0$ is

Answer: $3x-2y+7=0$

The two lines represented by $ax^{2}+4xy+2y^{2}=0$ are perpendicular to each other for $a=$

Answer: -2

Equation of tangent at $(3,4)$ to the circle $x^{2}+y^{2}=25$ is

Answer: $3x+4y=25$

The acute angle between the lines $x-3y-6=0$ and $2x-y+5=0$ is

Answer: $\frac{\pi}{4}$

The coordinates of the focus of the parabola $y^2=8x$ are

Answer: $(2,0)$

The center of the circle $x^2+y^2-2ax-2ay+a^2=0$ is

Answer: $(a,a)$

The straight lines represented by $3x^2+2xy+ky^2=0$ are perpendicular to each other if $k=$

Answer: $-3$

Equation of tangent to the circle $x^2+y^2=5$ at $(2,1)$ is

Answer: $2x+y=5$

The value of $k$ for which the line pair $x^2+kxy+2y^2+3x+5y+2=0$ represents a straight line is

Answer: $3$

The number of common tangents that can be drawn to the two circles when they touch externally is

Answer: three

The point of contact of the circle $x^2+y^2-10x=0$ with the chord $y=2x$ are

Answer: (2, 4), (0, 0)

The angle between the lines represented by $2x^2+7xy+3y^2=0$ is

Answer: $\frac{\pi}{4}$

The perpendicular distance from $(-1,-2)$ to the line $3x+4y+12=0$ is

Answer: $\frac15$

If the lines represented by $kx^2+(2-k)xy-3y^2=0$ are perpendicular, then $k=$

Answer: $3$

The equation of the tangent to the circle $x^2+y^2=5$ at $(2,1)$ is

Answer: $2x+y=5$

The lines $kx+3y+5=0$ and $5x-2y-6=0$ are perpendicular to each other for $k=$

Answer: $6/5$

The lines represented by $5x^2+3xy+ky^2=0$ are perpendicular to each other for $k=$

Answer: $-5$

The equation of the tangent to the circle $x^2+y^2=2$ at $(1,1)$ is

Answer: $x+y=2$

The equation $x^2-2xy+y^2+3x-2=0$ represents:

Answer: parabola

The area of the triangle with vertices $(1,-1),(-1,1)$ and $(-1,-1)$ is

Answer: $2$

The distance between the point $(1,2)$ and the line $3x+4y-7=0$ is

Answer: $4/5$

The two lines represented by $ax^{2}+2hxy+by^{2}=0$ are coincident if

Answer: $h^{2}=ab$

The equation of the tangent to the circle $x^{2}+y^{2}=5$ at $(2,1)$ is

Answer: $2x+y=5$

The two lines $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ are identical if

Answer: $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

The two lines $2x^2-2xy+ky^2=0$ are perpendicular to each other if $k$ is

Answer: $-2$

The equation of the circle touching the positive x-axis and y-axis with radius $2$ units is

Answer: $x^2+y^2-4x-4y+4=0$

If the line $3x+4y=k$ is tangent to the circle $x^2+y^2=25$ at $(3,4)$ then $k$ is

Answer: $25$

The distance between the parallel lines $y-2x=4$ and $6x-3y=5$ is

Answer: $\frac{17}{\sqrt{45}}$

Radius of the circle $x^2+y^2-3x+2y-\frac34=0$ is

Answer: $2$

The single equation representing the pair of lines $y=x$ and $y=-x$ is

Answer: $y^2-x^2=0$

The curve $y^2=4x$ is symmetric about

Answer: X axis

The length of the perpendicular from $(0,0)$ to the line $x+y+1=0$ is

Answer: $\frac{1}{\sqrt2}$

The angle between the lines $2x^2+xy-2y^2=0$ is

Answer: $90^0$

Center of the circle $x^2+y^2-2x-4y+1=0$ is

Answer: $(1,2)$

Equation of tangent of the circle $x^2+y^2=13$ at $(2,3)$ is

Answer: $2x+3y=13$

What is the derivative of sin x with respect to x?

Answer: cos x

What is the value of lim(x->0) (sin x)/x?

Answer: 1

The determinant of the 2x2 identity matrix is

Answer: 1

The sum 2 + 4 + 6 + ... + 2n equals

Answer: n(n+1)

Two fair dice are rolled. What is the probability that the sum is 7?

Answer: 1/6

The value of i^2, where i is the imaginary unit, is

Answer: -1

The slope of the line y = 3x + 2 is

Answer: 3

What is the integral of x dx?

Answer: x^2/2 + C

If f(x) = x^2 - 3x + 2, what are the roots of f(x) = 0?

Answer: 1 and 2

The derivative of sin(x)cos(x) with respect to x is:

Answer: cos(2x)

If A = [[1,2],[3,4]], what is det(A)?

Answer: -2

The value of lim(x->0) (sin x)/x is:

Answer: 1

How many ways can 5 distinct books be arranged on a shelf?

Answer: 120

The equation of a circle with center (2,-3) and radius 5 is:

Answer: (x-2)^2+(y+3)^2=25

If tan(theta) = 1, and theta is in the first quadrant, theta equals:

Answer: 45 degrees

The sum of first n natural numbers is given by:

Answer: n(n+1)/2

If vectors a = 2i + 3j and b = i - j, what is a.b (dot product)?

Answer: -1

The number of ways to select 3 items from 5 distinct items (combination) is:

Answer: 10

If log(2) = 0.301, then log(8) is approximately:

Answer: 0.903

The modulus of the complex number 3+4i is:

Answer: 5

The slope of the line perpendicular to y = 2x + 3 is:

Answer: -1/2

The derivative of e^(2x) with respect to x is:

Answer: 2e^(2x)

What is the value of i^4 (where i is the imaginary unit)?

Answer: 1

If a matrix A is 2x3 and matrix B is 3x4, what are the dimensions of AB?

Answer: 2x4

The mean of the numbers 4, 8, 6, 10, 12 is:

Answer: 8

The angle between two vectors a and b is 90 degrees. What is a.b?

Answer: 0

The equation x^2 + y^2 - 4x + 6y - 12 = 0 represents a circle. What is its radius?

Answer: 5

If f(x) = 3x^2 + 2x - 1, then f'(1) equals:

Answer: 8

The value of sin^2(theta) + cos^2(theta) is always:

Answer: 1

If a die is rolled once, the probability of getting an even number is:

Answer: 1/2

The general solution of dy/dx = y is:

Answer: y = Ce^x

If $4\cos^2x-1=0$, then for $n\in z$, $x=$

Answer: $n\pi\pm\frac\pi3$

$2\cos^{-1}x=$

Answer: $\cos^{-1}(2x^2-1)$

If $\tan^{-1}2x+\tan^{-1}3x=\pi/4$, then $x=$

Answer: $1/6,-1$

If $\sin^2x=1/2$, then for $n\in Z$, $x=$

Answer: $n\pi\pm\pi/4$

The function $f(x)=\sin x+x$ is

Answer: odd function

If in a triangle ABC, the angles are in A.P. then angle B =

Answer: $60^\circ$

The area of triangle ABC is

Answer: $\frac12 bc\sin A$

If $\operatorname{cosec}x=-1$, then the value of $x$ is

Answer: $(2n+1)\frac{\pi}{2}$

For any real number $x$ with $|x|<1$, the value of $\sin^{-1}x$ is equal to

Answer: $\cos^{-1}\sqrt{1-x^2}$

The period of the function $f(x)=\cos(2x+5)$ is

Answer: $\pi$

If $\sin^{-1}x=\cos^{-1}x$ then $x=$

Answer: $\frac{1}{\sqrt2}$

The solution of $\sin^2x=\frac12$ is

Answer: $n\pi\pm\frac{\pi}{4}$

If $\cos^{-1}x=\cos^{-1}\left(\frac{3}{5}\right)-\sin^{-1}\left(\frac{4}{5}\right)$, then $x=$

Answer: $1$

All values between $0$ to $2\pi$ which satisfy $2\sin^2\theta=3\cos\theta$ is

Answer: $\frac{\pi}{3},\frac{5\pi}{3}$

If $\tan^2x=1$ then $x$ is

Answer: $n\pi\pm\pi/4$

$\sin(2\sin^{-1}x)=$

Answer: $2x\sqrt{1-x^2}$

The value of $\sin\left(\cos^{-1}\frac45\right)$ is

Answer: $3/5$

If $\tan^2x=3$ then $x$ is

Answer: $n\pi\pm\frac\pi3$

The period of the function $f(x)=\sin(2x+5)$ is

Answer: $\pi$

The value of $\sin(\cos^{-1}x)$ is

Answer: $\sqrt{1-x^2}$

If $\csc^2x-2=0$, then $x$ is

Answer: $n\pi\pm\frac{\pi}{4}$

If $\sin 2x=1$, then $x$ is

Answer: $n\pi+(-1)^{n}\frac{\pi}{4}$

The value of $\sin(\tan^{-1}x)$ is

Answer: $\frac{x}{\sqrt{1+x^{2}}}$

If $\cos^2\theta=\frac12$, then $\theta$ is

Answer: $n\pi\pm\frac{\pi}{4}$

$\cos\left(\sin^{-1}\frac35\right)=$

Answer: $\frac45$

$3\cos^{-1}x$ is equal to

Answer: $\cos^{-1}(4x^3-3x)$

Solution of $\tan ax=\cot bx$ is

Answer: $\frac{2n+1}{a+b}\cdot\frac\pi2$

The value of $\tan(\tan^{-1}1)$ is

Answer: 1

The solution of $\cos x=\frac{1}{2}$ is

Answer: $2n\pi\pm\frac{\pi}{3}$

$\lim_{x\to\infty}\frac{ax^2+bx+c}{dx^2+ex+f}=$

Answer: $\frac{a}{d}$

$\lim_{x\to3}\frac{x^n-3^n}{x-3}=27$, and $n$ is a positive integer, then $n=$

Answer: 3

$\frac{d}{dx}\operatorname{cosech}^{-1}x=$

Answer: $\frac{-1}{x\sqrt{x^2+1}}$

If $y=\log_{\sqrt x}x$, then $\frac{dy}{dx}=$

Answer: $0$

$\int\frac{1}{\sqrt{1-x^2}}dx=$

Answer: $\sin^{-1}x+c$

$\int\frac{\cos2x}{\cos x}dx=$

Answer: $2\sin x-\log(\sec x+\tan x)$

$\int a^{\sin x}\cos x,dx=$

Answer: $\frac{a^{\sin x}}{\log a}+c$

The point of inflection of $y=x^3-12x^2$ is

Answer: 4

Area bounded by $y=\sin x$, $x$-axis and the ordinates $x=0$ and $x=2\pi$ is

Answer: 4

$\int_{-1}^{1}\frac{2x}{1+x^2},dx=$

Answer: $0$

$\int\frac{dx}{x(1+\ln x)^2}=$

Answer: $-\frac{1}{1+\ln x}+c$

The area bounded by the x-axis and the curve $y=4x^2$ and the ordinates $x=1$ and $x=4$ is

Answer: $84$

$\lim_{n\to\infty}\frac{1+2+\cdots+n}{n^2}=$

Answer: $\frac12$

$\lim_{x\to0}\frac{5x^2+4x\tan x}{x^2}=$

Answer: $9$

If $y=\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}$ then $\frac{dy}{dx}=$

Answer: $\frac{1}{2y-1}$

If $y=e^{\sqrt{ax^2+b}}$, then $\frac{dy}{dx}=$

Answer: $\frac{ax}{\sqrt{ax^2+b}},e^{\sqrt{ax^2+b}}$

$\int\frac{dx}{1-x^2}=$

Answer: $\frac12\ln\left|\frac{1+x}{1-x}\right|+c$

$\int_1^2\frac{\sin(\ln t)}{t}dt=$

Answer: $1-\cos(\ln2)$

The critical points for $f(x)=x^3-3x$ are:

Answer: $\pm1$

The area bounded by the x-axis and the curve $y=x^3$ and ordinates $x=2$ and $x=4$ is

Answer: $60$ sq. units

$\lim_{x\to0}\frac{a^x-b^x}{x}$ is equal to

Answer: $\log(a/b)$

The derivative of $y=5^x$ with respect to $x$ is equal to

Answer: $5^x\log_e5$

The integral $\int\frac{e^x,dx}{e^x+1}$ is equal to

Answer: $\log(e^x+1)+C$

The derivative of $y=\cos(\cos\sqrt x)$ is

Answer: $\frac{\sin(\cos\sqrt x)\cdot\sin\sqrt x}{2\sqrt x}$

If $\lim_{x\to0^-}f(x)\neq\lim_{x\to0^+}f(x)$, then $f(x)$ is said to have

Answer: jump discontinuity

The area enclosed by the curve $y=3x$, the x-axis and the ordinates $x=0$, $x=4$ is

Answer: $24$

The two vectors $i+3k+j$ and $3i+nk+3j$ are collinear if $n=$

Answer: 9

If the three non zero vectors $\mathbf p,\mathbf q,\mathbf r$ are expressed as $x\mathbf p+y\mathbf q+z\mathbf r=0$ and x, y, z are scalars then the vectors are linearly independent if

Answer: $x=0,y=0,z=0$

The unit vector of $3i+4j$ is

Answer: $\frac15(3i+4j)$

The scalar product of two vectors $3i-4j$ and $3i+4j$ is

Answer: -7

The relation between direction cosines of a line is given by

Answer: $l^2+m^2+n^2=1$

The unit vector in the direction of $\vec i+\vec j-2\vec k$ is

Answer: $\frac{\vec i+\vec j-2\vec k}{\sqrt6}$

Magnitude of the resultant of two forces P and Q will be maximum when both forces act

Answer: in the same direction

A body is thrown vertically upward with a velocity of $40,ms^{-1}$ from the top of a tower, hits the ground after 10 seconds, then the height of the tower is $[g=10,ms^{-2}]$

Answer: 100m

If a force of 10N is inclined 45 degrees to the horizon, then resolved part of the force in vertical direction is

Answer: $5\sqrt2,N$

A ball is projected up an inclined plane with a velocity of $20,m/sec$. If the inclination of the plane to the horizontal is $30^\circ$ and acceleration due to gravity is $10,m/sec^2$, then the length described before coming to rest is

Answer: $40,m$

If two forces P and Q, P > Q, are acting at a point of a body, in the same direction, then the resultant force is

Answer: P + Q

The value of $\begin{vmatrix}2&3&4\5&6&7\10&12&14\end{vmatrix}$ is

Answer: $0$

If $A=(1\ 2\ 3)$ and $B=\begin{pmatrix}1\2\3\end{pmatrix}$ then $AB$ is

Answer: $(14)$

The inverse of the matrix $\begin{bmatrix}-1&1\1&-3\end{bmatrix}$ is

Answer: $\frac12\begin{bmatrix}-3&-1\-1&-1\end{bmatrix}$

If $\omega$ is the cube root of unity then $(1-\omega+\omega^2)^3=$

Answer: $-8$

$\left|\frac{1}{1+i}\right|=$

Answer: $\frac1{\sqrt2}$

A distribution is symmetrical if

Answer: Mean = Median = Mode

While two coins are tossed once, the probability of getting two tails is

Answer: $\frac14$

While two dice are thrown, the probability of getting the sum less than four is

Answer: 1/12

Probability of getting an even number while rolling a dice is

Answer: 1/2

The equation $f(x)=0$ has at least one root in $(a,b)$ where $f(x)$ is continuous in $(a,b)$ if

Answer: $f(a)f(b)<0$

The function $f(x)=x^2+x-4$ defined in $[1,4]$ has

Answer: one root

If the direction cosines of a line are 2, 3, -6, then its direction cosines are;

Answer: $\frac27,\frac37,\frac{-6}{7}$