Recent questions tagged past papers

The value of $(127)^{1/3}$ upto 4 decimal places, is :

asked Dec 19, 2018 by pady_1

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The point on the curve $y^2 = 4x$ which is the nearest to the point $(2, 1)$ is :

asked Dec 19, 2018 by pady_1

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The maximum value of $fx) = 2x^3 - 21x^2 + 36 x + 20$, in the interval $0 \leq x \leq 2$, is

asked Dec 19, 2018 by pady_1

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The solution of the differential equation $\frac{dy}{dx} - \frac{2xy}{1+x^2}=0$ is :

asked Dec 19, 2018 by pady_1

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$y = x^2 \sin 2x$, then $n^{th}$ derivative of $y ( n = 4m)$ is :

asked Dec 19, 2018 by pady_1

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$\frac{d}{dx} (x^x)$ is equal to :

asked Dec 19, 2018 by pady_1

1 answer

Derivative of $\sin^2x$ with respect to $(\log x)^2$ is:

asked Dec 19, 2018 by pady_1

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$\frac{d}{dx} (\cos x*)$ is equal to :

asked Dec 19, 2018 by pady_1

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If $f(x) = \frac{\sin x }{x}, \; x \neq 0$, if $f(x)$ is to be continuous at $x=0$, then $f(0)$ is equal to :

asked Dec 19, 2018 by pady_1

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One of the focii of hyperbola is origin and the corresponding directrix is $3x + 4y + 1=0$. The eccentricity of the hyperbola is $\sqrt{5}$. The equation to the hyperbola is :

asked Dec 19, 2018 by pady_1

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The eccentricity of ellipse $9x^2 + 4y^2 = 36$ is :

asked Dec 19, 2018 by pady_1

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The pole of the line $2x + 3y- 4=0$ with respect to the parabola $y^2 = 4x$ is :

asked Dec 19, 2018 by pady_1

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The equation of the directrix to the parabola $y^2 -2x - 6y -5 = 0$ is

asked Dec 19, 2018 by pady_1

1 answer

The equation of the normal to the circle $x^2 + y^2 - 2x - 2y - 2 = 0$ at the point $(3,1)$ on it is :

asked Dec 19, 2018 by pady_1

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The length of the tangent from (6, 8) to the circle $x^2 + y^2 = 4$ is :

asked Dec 19, 2018 by pady_1

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If $(1,2), \; (4, 3)$ are the limiting points of a system of coaxial circles, then the radical axis of the system is :

asked Dec 19, 2018 by pady_1

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The radical axis of cirlces $x^2 + y^2 - 6x -4y - 44=0$ and $x^2 +y^2- 14 x - 5y-24=0$ is :

asked Dec 19, 2018 by pady_1

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The pole of line $8x-2y=11$ with respect to the circle $2x^2 + 2y^2 = 11$ is :

asked Dec 19, 2018 by pady_1

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The locus of point of intersection of perpendicular tangents to the circle $x^2+y^2=a^2$ is:

asked Dec 19, 2018 by pady_1

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The equation of a circle with centre $(4, 1)$ and having $3x + 4y - 1 =0$ as tangent is

asked Dec 19, 2018 by pady_1

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If $z = \sin^{-1} \{ \frac{x+y}{\sqrt{x} + \sqrt{y} } \}$, then $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $x^xy^yz^z$ = constant, then $\frac{dz}{dx}$ is equal to :

asked Dec 19, 2018 by pady_1

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If the operation $$ is defined on $R$, the set of all real numbers, as $ab = ab +1 \; \forall\; a, b \in R$ then $a * (b *c) $ is equal to :

asked Dec 19, 2018 by pady_1

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Let $Q_1 = Q - \{1 \}$ the set of all rationals except 1, $$ is the operation defined on $Q_1$, as $a b = a + b - ab \; \forall a, b \in Q_1$. The inverse of 2 is :

asked Dec 19, 2018 by pady_1

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The inverse of the matrix $\begin{bmatrix} 2 & 1 \\ 1 & 3 \end{bmatrix}$ is :

asked Dec 19, 2018 by pady_1

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If $a+b+c=0$, then one root of $\begin{vmatrix} a-x & c & b \\ c & b-x& a \\ b & a & c-x \end{vmatrix}=0$ is :

asked Dec 19, 2018 by pady_1

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If the system of equations $3x-2y+z=0 $ $\lambda x - 14 y +15z =0$ $x+2y-3z=0$ have non-zero solution, then $\lambda$ is equal to

asked Dec 19, 2018 by pady_1

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The minimum value of $x^2-8x+17, \; x \in R$ is :

asked Dec 19, 2018 by pady_1

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If at any point on the curve $y=f(x)$ the length of the subnormal is constant, then the curve will be a / an :

asked Dec 19, 2018 by pady_1

1 answer

If $f(x) = \begin{vmatrix} 2 \cos x & 1 & 0 \\ x - \frac{\pi}{2} & 2 \cos x & 1 \\ 0 & 1 & 2 \cos x \end{vmatrix}$, then $\frac{df}{dx} $ at $x = \frac{\pi}{2}$ is:

asked Dec 19, 2018 by pady_1

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If $x$ and $y$ are strictly positive such that $x+y=1$, then the minimum value of $x \log x + y \log y$ is :

asked Dec 19, 2018 by pady_1

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If $\log y = \tan^{-1}x$, then $(1+x^2) \frac{d^2y}{dx^2} + (2x-1) \frac{dy}{dx}$ is equal to :

asked Dec 19, 2018 by pady_1

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If the side of an equilateral triangle expands at the rate of $2\; cm/sec$, then the rate of increase of its area when the side is 10 cm is (in sq cm) :

asked Dec 19, 2018 by pady_1

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If $\tan y = \frac{2t}{1-t^2}, \; sin x = \frac{2t}{1+t^2}$, then $\frac{dy}{dx}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $y = \sqrt{\cos 2x}$, then $y \frac{d^2y}{dx^2} + 2y^2$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\begin{align}y = e^{{-x}^2} \int_0^x e^{t^2} dt \end{align}$, then $\frac{dy}{dx} + 2xy$ is equal to :

asked Dec 19, 2018 by pady_1

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$\displaystyle\lim_{x \to 0} \frac{\sin ax}{\sin bx} $ is equal to :

asked Dec 19, 2018 by pady_1

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$\displaystyle\lim_{x \to \infty} \begin{vmatrix} \frac{a^{1/x} + b^{1/x} + c^{1/x} }{3} \end{vmatrix}^x$, where $a, b, c$ are real and non-zero is equal to :

asked Dec 19, 2018 by pady_1

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$\displaystyle\lim_{x \to \infty} \frac{1}{\sin^2 x} - \frac{1}{\sin h^2 x}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $f : R \to R$ is continuous such that $f(x+y) = f(x) + f(y), \; \; \forall \; \; x, y \in R$ and $f(1) = 2$, then $f(100)$ is equal to :

asked Dec 19, 2018 by pady_1

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$\displaystyle\lim_{x \to 0} \log \begin{vmatrix} \frac{\log (1+x)}{x} \end{vmatrix}$ is equal to :

asked Dec 19, 2018 by pady_1

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The equaion of the line common to the pairs of lines $(p^2 - q^2)x^2 + (q^2 - r^2) xy + (r^2 - p^2) y^2 = 0$ and $(f-m)x^2 + (m-n)xy + (n-f)y^2 = 0$ is :

asked Dec 19, 2018 by pady_1

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If $a, h, b$ are in A.P., then the triangular area formed by the pair of lines $ax^2 + 2hxy + by^2=0$ and the line $x-y=-2$ (in square units) is :

asked Dec 19, 2018 by pady_1

1 answer

If the pair of lines given by $(x^2+y^2) \sin \alpha = (x \cos \alpha - y \sin \alpha)^2$ are perpendicular to each other, then $\alpha$ is equal to :

asked Dec 19, 2018 by pady_1

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The angle betwen the pair of lines $2(x+2)^2 + 3(x+2)(y+2) - 2(y-2)^2 = 0$ is :

asked Dec 19, 2018 by pady_1

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The equation of the pair of lines through $(1, -1)$ and perpendicular to the pair of lines $x^2 - xy - 2y^2 = 0$ is :

asked Dec 19, 2018 by pady_1

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The perpendicular distance from $(1,2)$ to the straight line $12x + 5y=7$, is :

asked Dec 19, 2018 by pady_1

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Let $a$ and $b$ be non-zero real numbers such that $a \neq b$. Then the equation of the line passing through the origin and the point of intersection of $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{b} + \frac{y}{a} = 1$ is :

asked Dec 19, 2018 by pady_1

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$k$ is non-zero constant. If $k = \frac{a+b}{ab}$, then straight line $\frac{x}{a} + \frac{y}{b} = 1$ passes through the point :

asked Dec 19, 2018 by pady_1

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The angle at which the axes are to be rotated to remove the $xy$ term in the equation $x^2 + 2\sqrt{3}xy = y^2$ is :

asked Dec 19, 2018 by pady_1

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