Recent questions tagged past papers

$20^{2-3x^2} = (40\sqrt{5})^{3x^2-2}$, then $x$ is equal to :

asked Dec 11, 2018 by pady_1

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If $\alpha, \beta$ are the roots of the equation $x^2 + bx + c =0$ and $\alpha + h, \; \beta+h$ are the roots of the equation $x^2 + qx + r =0$, then $h$ is equal to :

asked Dec 11, 2018 by pady_1

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$|x| <1$, the coefficient of $x^3$ in the expansion of $\log (1+x+x^2)$ in ascending powers of $x$, is :

asked Dec 11, 2018 by pady_1

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$\frac{2}{2!} + \frac{2+4}{3!} + \frac{2+4+6}{4!}$ + ...$ is equal to:

asked Dec 11, 2018 by pady_1

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If $\frac{x-4}{x^2-5x-2k} = \frac{2}{x-2} - \frac{1}{x+k'}$ then $k$ is equal to :

asked Dec 11, 2018 by pady_1

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If $(1+x)^n = C_0 + C_1x + C_2x^2 + ....+ C_nx^n$, then $C_0+2C_1 + 3C_2 + ....+(n+1)C_n$ is equal to :

asked Dec 11, 2018 by pady_1

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The co-efficient of $x^4$ in the expansion of $\frac{(1-3x)^2}{(1-2x)}$ is equal to :

asked Dec 11, 2018 by pady_1

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$1+\frac{1}{4} + \frac{1.3}{4.8} + \frac{1.3.5}{4.8.12} + ...$ is equal to :

asked Dec 11, 2018 by pady_1

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Using the digits $0, 2, 4, 6, 8$ not more than once in any number, the number of 5 digited numbers that can be formed, is :

asked Dec 11, 2018 by pady_1

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The number of ways in which 5 boys and 4 girls sit around a circular tables. So that no two girls sit together is :

asked Dec 11, 2018 by pady_1

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If $y = A \cos nx + B \sin nx$, then $y_2 = n^2y$ is equal to :

asked Dec 11, 2018 by pady_1

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If $2^3 + 4^3 + 6^3 + ....+(2n)^3 = hn^2 (n+1)^2$, then $h$ is equal to :

asked Dec 11, 2018 by pady_1

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If $x =\log_{0.1} 0.001, \; y = \log_9 81 $, then $\sqrt{x -2\sqrt{y}}$ is equal to :

asked Dec 11, 2018 by pady_1

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$\frac{\sqrt{8 +\sqrt{28} } + \sqrt{8 - \sqrt{28}}}{\sqrt{8 +\sqrt{28} } - \sqrt{8 - \sqrt{28}}} $ is equal to :

asked Dec 11, 2018 by pady_1

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Two functions $f : R \to R, \; g: R \to R$ are defined as follows $ f(x) = \begin{cases} 0 , & \quad \text{x } \text{ is rational}\\ 1, & \quad \text{x} \text{ is irrational} \end{cases}$ $ g(x) = \begin{cases} -1 , & \quad \text{x } \text{ is rational}\\ 0, & \quad \text{x} \text{ is irrational} \end{cases}$ Then $(fog) (\pi) + (gof)(e)$ is equal to :

asked Dec 11, 2018 by pady_1

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Let $f : R \to R$ is defined by $ f(x) = \begin{cases} x+2, & x \leq -1 \\ x^2 , & -1 < x <1 \\ 2-x, & x \geq 1 \end{cases}$ Then the value of $f(-1.75) + f(0.5) + f(1.5)$ is :

asked Dec 11, 2018 by pady_1

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Let $Z$ denote the set of integers define $f : Z \to Z $ by $ f(x) = \begin{cases} \frac{x}{2}, & \quad \text{x} \text{ is even}\\ 0, & \quad \text{x} \text{ is odd} \end{cases}$ then $f$ is :

asked Dec 11, 2018 by pady_1

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$f(x) = (20 - x^4)^{1/4}$ for $0 < x < \sqrt{5}$, then $f(f(1/2))$ is equal to :

asked Dec 11, 2018 by pady_1

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If $\tan \theta + \cot \theta = 2$, then $\sin \theta$ is equal to :

asked Dec 11, 2018 by pady_1

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The solution of $\frac{dy}{dx} +y =e^x$ is :

asked Dec 11, 2018 by pady_1

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The solution of $x^2 +y^2 \frac{dy}{dx}=4$ is :

asked Dec 11, 2018 by pady_1

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The family of curves in which the sub-tangent at any point to any curve is double the abscissa is given by :

asked Dec 11, 2018 by pady_1

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The solution of $x \; dx + y \;dy = x^2y\; dy - xy^2\;dx$ is :

asked Dec 11, 2018 by pady_1

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Using the Trapezoidal rule, the approximate value of $\begin{align} \int_1^4 y \;dx \end{align}$

asked Dec 11, 2018 by pady_1

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$\begin{align} \int_{-1}^1 (ax^3 +bx ) dx =0 \end{align}$ for :

asked Dec 11, 2018 by pady_1

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$\begin{align} \int_0^{\pi/2} \sin^8x \cos^2 x \;dx \end{align}$ is equal to :

asked Dec 11, 2018 by pady_1

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$\begin{align} \int \frac{dx}{a^2 \sin^2x +b^2 \cos^2 x} \end{align}$ is equal to :

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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$\begin{align} \int \frac{dx}{\sqrt{x} (x+9)} \end{align}$ is equal to :

asked Dec 11, 2018 by pady_1

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If $u = xy^2 \tan^{-1} (\frac{y}{x})$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ is equal to :

asked Dec 11, 2018 by pady_1

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If $u = e^{x^2 -y^2}$, then :

asked Dec 11, 2018 by pady_1

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The maximum value of $xy$ subject to $x+y =7$ is :

asked Dec 11, 2018 by pady_1

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The area (in square units) of the region bounded by $x^2 = 8y, \; x = 4$ and $x$-axis, is :

asked Dec 11, 2018 by pady_1

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The equation of tangent to the curve $6y = 7 - x^3$ at $(1,1)$ is :

asked Dec 11, 2018 by pady_1

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The minimum value of $(x- \alpha) ( x-\beta)$ is:

asked Dec 11, 2018 by pady_1

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If $f(x) = \frac{x^2}{x+a}$, then $f''(a)$ is equal to :

asked Dec 11, 2018 by pady_1

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If $y_{_k}$ is the $k^{th}$ derivative of $y$ with respect to $'x'$ and $y = \cos (\sin x)$, then $y_{_1} \sin x+y_{_2} \cos x$ is equal to :

asked Dec 11, 2018 by pady_1

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$\frac{d}{dx} \sin^{-1} (3x-4x^3)$ is equal to :

asked Dec 11, 2018 by pady_1

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If $h(x) = x^{x^2}$, then at $x=1$ $\frac{h'(x)}{h(x)}$ is equal to :

asked Dec 11, 2018 by pady_1

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If $f(x) = \frac{x^2 - 10x + 25}{x^2 - 7x + 10}$ and $f$ is continuous at $x=5$, then $f(5)$ is equal to :

asked Dec 11, 2018 by pady_1

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$\displaystyle\lim_{x \to 0} \begin{pmatrix}\frac{x. 10^x - x}{1-\cos x}\end{pmatrix} $ is equal to :

asked Dec 11, 2018 by pady_1

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$\displaystyle\lim_{x \to \infty} \begin{pmatrix}\frac{x+a}{x+b}\end{pmatrix}^{a+b} $ is equal to :

asked Dec 11, 2018 by pady_1

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Evaluate $\begin{align} \int_{-1}^1 f(x) \;dx \end{align}$, where $f(x) = \begin{cases} 1-2x, & x \leq 0 \\ 1+2x, & x \geq 0 \end{cases} $

asked Dec 11, 2018 by pady_1

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Equation of curve in polar co-ordinates is $\frac{l}{r} = 2 \sin^2 \frac{\theta}{2}$, then it represents :

asked Dec 11, 2018 by pady_1

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The equation $16x^2 + y^2 + 8xy - 74x -78 y +212 = 0$ represents :

asked Dec 11, 2018 by pady_1

1 answer

The products of lengths of perpendiculars from any point of hyperbola $x^2 - y^2 =8 $ to its asymptotes; is :

asked Dec 11, 2018 by pady_1

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The eccentricity of ellipse $\frac{x^2}{16} + \frac{y^2}{9}=1$ is:

asked Dec 11, 2018 by pady_1

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If the normal to the parabola $y^2 = 4x$ at $P(1,2)$ meets the parabola again in $Q$, then co-ordinates of $Q$ are :

asked Dec 11, 2018 by pady_1

1 answer

The length of latus rectum of parabola $y^2 + 8x -2y+17=0$ is :

asked Dec 11, 2018 by pady_1

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If the polar of a point on the circle $x^2+y^2=p^2$ with respect to the circle $x^2+y^2=q^2$ touches the circle $x^2+y^2=r^2$, then $p, q, r$ are in:

asked Dec 11, 2018 by pady_1

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