Recent questions tagged past papers

In the expression of $\begin{pmatrix} x^4 - \frac{1}{x^3} \end{pmatrix}^{15}$ coefficient of $x^{32}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $a \neq b, \; b, \; c$ satisfy $\begin{vmatrix} a & 2b & 2c \\ 3 & b & c \\ 4 & a & b \end{vmatrix} = 0$ then $b^2$ is equal to :

asked Dec 19, 2018 by pady_1

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If $d$ is the determinant of a square matrix $A$ of order $m$, then the determinant of its adjoint, is :

asked Dec 19, 2018 by pady_1

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If $A=\begin{bmatrix} 1&3\\2&1 \end{bmatrix}$, then the determinant of $A^2-2A$ is :

asked Dec 19, 2018 by pady_1

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If $A$ and $B$ are two square matrices such that $B= -A^{-1}BA$, then $(A+B)^2$ is equal to :

asked Dec 19, 2018 by pady_1

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$\begin{align}\frac{\frac{1}{2}. \frac{2}{2}}{1^3} + \frac{\frac{2}{2}. \frac{3}{2}}{1^3+2^3} + \frac{\frac{3}{2}.\frac{4}{2}}{1^3+2^3+3^3}+...+n \end{align}$ terms :

asked Dec 19, 2018 by pady_1

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Summation $\displaystyle\sum_{k=1}^{n} \;k \begin{bmatrix}1 +\frac{1}{n} \end{bmatrix}^{k-1}$ is equal to :

asked Dec 19, 2018 by pady_1

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The set $\{x \in R : x -2 + x^2 =0 \}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\alpha , \beta$ are the roots of the equation $9x^2+6x+1=0$, then the equation with the roots are $\frac{1}{\alpha}$, $\frac{1}{\beta}$, is real to :

asked Dec 19, 2018 by pady_1

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The equation formed by decreasing each root of $ax^2+bx + c = 0$ by $1$ is $2x^2 + bx+ 2=0$, then :

asked Dec 19, 2018 by pady_1

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If $3+i$ is a root of $x^2+ax+b=0$, then $a$ is equal to :

asked Dec 19, 2018 by pady_1

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In the argand plane the area in square units of the triangle formed by the points $1+i, \; 1-i, \; 2i$ is :

asked Dec 19, 2018 by pady_1

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If $1, \omega, \omega^2$ are the roots of unity, then $(a+b)^3 + (a \omega + b \omega^2)^3 + (a \omega^2 +b \omega)^3$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\theta$ is real, the modulus of $\frac{1}{(1+\cos \theta) + i \sin \theta}$ is :

asked Dec 19, 2018 by pady_1

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The locus of the $z$ in the argand plane for which $|z+1|^2 + |z-1|^2 = 4$, is a :

asked Dec 19, 2018 by pady_1

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If $\frac{n^2 +5}{(n^2+2)^2} = \frac{1}{(n^2+2) }+ \frac{k}{(n^2+2)^{2'}}$ then $k$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If the coefficient of $r^{th}$ term and $(r+1)^{th}$ term in the expansion of $(1+x)^{3n}$ are in the ratio $1 :2$, then $r$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The coefficient of $x^{-n}$ in $(1+x)^n (1+\frac{1}{x})^n$ is :

asked Dec 19, 2018 by pady_1

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If $C_0, \; C_1, \; C_2, ....$ are binomial coefficients, then $C_1 + C_2 +C_3 + C_4 + ..... + C_r +.... + C_n$ is equal to:

asked Dec 19, 2018 by pady_1

0 answers

If $a_k = \frac{1}{k(k+1)} $ for $k = 1, 2, 3,...n$, then $\begin{bmatrix} \displaystyle\sum_{k=1}^{n} a_k \end{bmatrix}^2$ is equal to :

asked Dec 19, 2018 by pady_1

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The number of quadratic expressions with the coefficient drawn from the set $\{0, 1, 2, 3\}$ is :

asked Dec 19, 2018 by pady_1

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The number of ways in which 13 gold coins can be distributed among three persons such that each one gets at least two gold coins is :

asked Dec 19, 2018 by pady_1

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If $^nC_3 : ^{n-1}C_4= 8:5$, then $n$ is equal to :

asked Dec 19, 2018 by pady_1

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If $5^x = (0.5)^y = 1000$, then $\frac{1}{x} - \frac{1}{y}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $x = \frac{2}{3 +\sqrt{7}}$ then $(x-3)^2$ is equal to :

asked Dec 19, 2018 by pady_1

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If $f : R \to R$ is defined by $g : R \to R$ are defined by $f(x) = 2x + 3$ and $g(x) = x^2 + 7$, then the values of $x$ for which $f(g(x)) = 25$, are :

asked Dec 19, 2018 by pady_1

0 answers

If $F : R \to R$ is defined by $f(x) = 2x + |x|$ then $f(2x) + f(-x) - f(x)$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

Let $X$ and $Y$ be subsets of $R$ which is the set of all real numbers, the function $F : X \to Y$ defined by $F(x) = x^2$ for $x \in X$ is one-one but not onto if $R^+$ is the set of all $+ve$ real numbers, then :

asked Dec 19, 2018 by pady_1

0 answers

If $(1+x)^n = C_0 + C_1 x+ ... C_n x^n$, then the value of $\displaystyle\sum_{r=0}^{n} \; \displaystyle\sum_{s=0}^{n} \; C_r C_s$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

Let $x, \; y, \; z$ be three positive numbers. The progression in which $\sqrt{x}, \; \sqrt{y}, \; \sqrt{z}$ can be three terms (not necessarily consecutive), is :

asked Dec 19, 2018 by pady_1

0 answers

The probability distribution of a random variable $X$ is given below, then $k$ is equal to : <br>

asked Dec 19, 2018 by pady_1

0 answers

The probabilities of two events $A$ and $B$ are $0.25$ and $0.40$ respectively and $ P ( A \cap B) = 0.15$. The probabilities that neither $A$ nor $B$ occurs is :

asked Dec 19, 2018 by pady_1

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Probability of choosing a number divisible by 6 or 8 from among 1 to 90 is :

asked Dec 19, 2018 by pady_1

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$(\overrightarrow{b} \times \overrightarrow{c} ) \times (\overrightarrow{c} \times \overrightarrow{a} )$ is equal to:

asked Dec 19, 2018 by pady_1

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If $\overrightarrow{a} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k} , \; \overrightarrow{b} = \hat{i} + \hat{j} +\hat{k}$ and $\overrightarrow{c} = 4 \hat{i} + 2 \hat {j} + 3 \hat{k}$, then $|\overrightarrow{a} \times (\overrightarrow{b} \times \overrightarrow{c} )|$

asked Dec 19, 2018 by pady_1

0 answers

If $\theta$ is the angle between the vectors $2 \hat{i} + 2 \hat{j} + 4 \hat{k}$ and $3 \hat{i} + \hat{j} + 2 \hat{k}$, then $\sin \theta$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If two out of the three vectors are unit vectors. $\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} = 0$ and $2(\overrightarrow{a} . \overrightarrow{b} + \overrightarrow{b} . \overrightarrow{c} + \overrightarrow{c} . \overrightarrow{a} ) + 3 = 0$, then the third vector is of length :

asked Dec 19, 2018 by pady_1

0 answers

If $\theta$ is an acute angle and the vector $(\sin \theta) \hat{i} + (\cos \theta) \hat{j}$ is perpendicular to the vector $\hat{i}- \sqrt{3} \hat{j}$ ,then $\theta$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $OACB$ is a parallelogram with $\overrightarrow{OC} = \overrightarrow{a} $ and $\overrightarrow{AB} = \overrightarrow{b}$, then $\overrightarrow{OA}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The equation of the curve passing through the origin and satisfying the differential equation $\frac{dy}{dx} = (x-y)^2 $, is :

asked Dec 19, 2018 by pady_1

0 answers

If $c$ is a parameter, then the differential equation whose solution is $y = c^2 + \frac{c}{x'}$ is :

asked Dec 19, 2018 by pady_1

2 answers

The area in square units bounded by the curves $y = x^3,\; y = x^2$ and the ordinates $x=1, \; x=2$ is equal to

asked Dec 19, 2018 by pady_1

0 answers

The area (in square units) of the region bounded by the curve $x^2 = 4y$, the line $x=2$ and the $x$-axis is equal to :

asked Dec 19, 2018 by pady_1

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$\displaystyle\lim_{x \to 0} \frac{a^x - b^x}{x} $ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $f(x)$ is integrable on $(0,a)$ then $\begin{align} \int_0^a \frac{f(x)}{(x) + f(a-x) } dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$, then $A+B$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$\begin{align} \int e^{x \log a}. e^x \;dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

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$\begin{align} \int \frac{\sin^6x}{\cos^8 x}dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$\begin{align} \int e^x (1+\cot x + \cot^2 x)dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$u = \cos^{-1} (\frac{x+y}{\sqrt{x} + \sqrt{y}})$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

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