Recent questions tagged past papers

If $x = \theta - \frac{1}{\theta}$ and $y = \theta + \frac{1}{\theta}$, then $\frac{dy}{dx}$ is equal to :

asked Dec 19, 2018 by pady_1

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The derivative of $\sin^{-1}x$ w.r. to $\cos^{-1} \sqrt{1-x^2}$ is :

asked Dec 19, 2018 by pady_1

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$\frac{d}{dx} \{ \cos^{-1} x + \sin^{-1} \sqrt{1-x^2} \}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $y = f(x) = \frac{2x-1}{x-2}$, then $f(y)$ is equal to :

asked Dec 19, 2018 by pady_1

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$\displaystyle\lim_{x \to \infty} \frac{2x + 7 \sin x } {4x + 3 \cos x} $ is equal to :

asked Dec 19, 2018 by pady_1

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In a group $(G,o)$ the elements $a$ and $b$ are such that $a^3 = e = b^3$ when $e$ is the identity element, then $a^7 ob^{-4}$ is equal to :

asked Dec 19, 2018 by pady_1

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For the set $G = \{ -1, 1\}$ be a group the binary operation is equal to :

asked Dec 19, 2018 by pady_1

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If $a, \; b$ are elements of group, then $(aob)^{-1}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\begin{bmatrix} x & y^3 \\ 2 & 0 \end{bmatrix} = \begin{bmatrix} 1 & 8 \\ 2 & 0 \end{bmatrix}$, then $\begin{bmatrix} x&y\\ 2 & 0 \end{bmatrix}^{-1}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $x \neq 0$ and $\begin{vmatrix}1 & x & 2x \\ 1 & 3x & 5x \\ 1 & 3 & 4 \end{vmatrix}=0$, then $x$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If the matrix $\begin{bmatrix} \cos \theta & \sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$ is singular, then $\theta$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The real part of $\begin{vmatrix} \cos \alpha + i \sin \alpha & \cos \beta + i \sin \beta \\ \sin \beta + i \cos \beta & \sin \alpha + i \cos \alpha \end{vmatrix}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $A(\alpha) = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}$, then $A(\alpha), \; A(\beta)$ is equal to :

asked Dec 19, 2018 by pady_1

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The maximum value of $c + 2bx - x^2$ is equal to :

asked Dec 19, 2018 by pady_1

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If $2x - 7 - 5x^2$ has maximum value at $x=a$, then $a$ is equal to :

asked Dec 19, 2018 by pady_1

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The coefficient of the middle term in the expansion of $(1+x)^{40}$ is equal to :

asked Dec 19, 2018 by pady_1

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The coefficient of the $8^{th}$ term in expansion of $(1+x)^{10}$ is equal to :

asked Dec 19, 2018 by pady_1

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The term independent of $x$ in expansion of $\begin{pmatrix} x^2 - \frac{1}{x} \end{pmatrix}^6$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\frac{1}{(1-2x)(1+3x)} = \frac{A}{1-2x} + \frac{B}{1+3x}$, then $2B$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$f : R \to R$, defined by $f(x)=\sin x$ and $g : R \to R$, defined by $g(x) = x^2, \; (fog) (x)$ is equal to :

asked Dec 19, 2018 by pady_1

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$\log_8 128$ is equal to :

asked Dec 19, 2018 by pady_1

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If $x=27$ and $y=\log_3 4$, then $x^y$ is equal to :

asked Dec 19, 2018 by pady_1

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If $x=7 + 4\sqrt{3}$ and $xy=1$, then $\frac{1}{x^2} + \frac{1}{y^2}$ is equal to :

asked Dec 19, 2018 by pady_1

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The least value of $n$ that satisfies $^{n-1}C_3 + ^{n-1}C_4 >^nC_3$ is :

asked Dec 19, 2018 by pady_1

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If $^nP_7 = 42 \;^nP_5$, then $n$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $f : R \to R$ is defined by $f(x) = 3x-2$, then $fof(x) +2$ is equal to :

asked Dec 19, 2018 by pady_1

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If the mean of 9 binomial distribution is 6, then its variance is :

asked Dec 19, 2018 by pady_1

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In a poisson distribution, if $P(X=0) = P(X=1)=k$, then the value of $k$ is :

asked Dec 19, 2018 by pady_1

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A random variable $X$ has following distribution <br> <br> the value of $c$ is :

asked Dec 19, 2018 by pady_1

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A single letter is selected at random from the word "PROBABILITY". The probability that it is a vowel, is :

asked Dec 19, 2018 by pady_1

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One of the two events A and B must occur. If $P(A) = \frac{2}{3} P(B)$, odd in favour of B are

asked Dec 19, 2018 by pady_1

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The probability of getting a total score of 7 when two unbiased dice are thrown simultaneously, is :

asked Dec 19, 2018 by pady_1

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If the area of parallelogram, whose adjacent sides are $3 \hat{i} + 4 \hat{j}-\lambda \hat{k}$ and $2\hat{j} - 4 \hat{k}$ is $\sqrt{436}$ sq unit and $\lambda=0$, then $\lambda$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

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If $\overrightarrow{a} = -\hat{i} + 2 \hat{j} + 3 \hat{k},\;\overrightarrow{b} = \hat{i}-2\hat{j}+\hat{k}, \; \overrightarrow{c} = 4 \hat{i} - 3 \hat{j} - 2 \hat{k}$ and $\overrightarrow{a} + \lambda \overrightarrow{b}$ is perpendicular to $\overrightarrow{c}$, then $\lambda$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $\overrightarrow{a} = 3 \hat{i} - 2 \hat{j} + \hat{k}$ and $\overrightarrow{b} = \hat{i} + 2 \hat{j} + 5 \hat{k}$, then the unit vectors along $\overrightarrow{a} - \overrightarrow{b}$ is :

asked Dec 19, 2018 by pady_1

0 answers

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors and $|\overrightarrow{a} \times \overrightarrow{b}|=1$, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is :

asked Dec 19, 2018 by pady_1

0 answers

If $|\overrightarrow{a}| = 3, \; |\overrightarrow{b}| = 4$ and $|\overrightarrow{a} + \overrightarrow{b}| = 1$, then $|\overrightarrow{a} - \overrightarrow{b}|$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If the position vectors of $\overrightarrow{A} $ and $\overrightarrow{B}$ are $3 \hat{i} - 2 \hat{j} + \hat{k}$ and $2 \hat{i} + 4\hat{j} - 3\hat{k}$, then $|\overrightarrow{AB}|$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$(\hat{i} - \hat{j}) \times (\hat{j} - \hat{k}). (\hat{k} - \hat{i})$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $\overrightarrow{a} $ and $\overrightarrow{b}$ are unit vectors such that $|\overrightarrow{a} \times \overrightarrow{b}| = \overrightarrow{a}.\overrightarrow{b}$, then $|\overrightarrow{a} + \overrightarrow{b}|^2$ is equal to :

asked Dec 19, 2018 by pady_1

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The equation $\frac{1}{r} = \frac{1}{8} +\frac{3}{8} \cos \theta$ represents $a/an$ :

asked Dec 19, 2018 by pady_1

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The eccentricity of hyperbola $4x^2 - 9y^2 = 2ax + b^2$ is :

asked Dec 19, 2018 by pady_1

0 answers

The pole of line $x=\frac{a}{e}$ w.r. to ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} =1$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The focus of parabola $y^2-4y -8x-4=0$ is :

asked Dec 19, 2018 by pady_1

1 answer

If $2y = 5x+k$ is tangent to parabola $y = 6x$, then $k$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The vertex of the parabola $x^2+12x - 9y=0$ is :

asked Dec 19, 2018 by pady_1

0 answers

The slope of radical axis of the circles $x^2 + y^2 + 3x + 4y-5=0$ and $x^2+y^2 - 5x+5y+6=0$, is :

asked Dec 19, 2018 by pady_1

0 answers

If the circle $x^2 +y^2 +2x -2y+4=0$ cuts the circle $x^2 +y^2 + 4x + 2fy+2=0$ orthogonally, then $f$ is equal to :

asked Dec 19, 2018 by pady_1

1 answer

The equation of polar of $(-2,3)$ w.r.to $x^2 + y^2 - 4x-6y+5=0$, is :

asked Dec 19, 2018 by pady_1

0 answers

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