Recent questions tagged 2000

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

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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

0 answers

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

0 answers

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

0 answers

$\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

0 answers

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

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

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

Area of the triangle formed by the normal to the curve $x = e^{\sin v} $ at $(1, 0)$ with the co-ordinate axes is :

asked Dec 19, 2018 by pady_1

0 answers

The minimum value of $x^x$ is :

asked Dec 19, 2018 by pady_1

0 answers

If $l^2 + m^2 = 1$, then the maximum value of $l+m$ is :

asked Dec 19, 2018 by pady_1

0 answers

The angle between the curves $y^2=4x, \; x^2 = 4y$ at $(4,4)$, is :

asked Dec 19, 2018 by pady_1

0 answers

The distance moved by the particle in time $t$ is given by $s = t^3 - 12t^2 + 6t +8$. At the instant when its acceleration is zero, the velocity is :

asked Dec 19, 2018 by pady_1

0 answers

If $xy=(x+y)^n$ and $\frac{dy}{dx} = \frac{y}{x}$, then $n$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$\frac{d}{dx} \{ \cos^{-1} (\frac{4x^3}{27} - x ) \}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $y=2^{2x}$, then $\frac{dy}{dx} $ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If the function $f(x) = \begin{cases} \frac{\sin 3x}{x}, & \quad x \neq 0\\ \frac{k}{2} & \quad x=0 \end{cases}$ continuous at $x=0$, then $k$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$\displaystyle\lim_{x \to 0} \frac{\log_e (1+x)}{3^x-1}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$\displaystyle\lim_{\theta \to \pi/2} \frac{1-\sin \theta}{\cos (\frac{\pi}{2} - \theta)}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The radius of the circle $r^2 - 2\sqrt{2}r (\cos \theta + \sin \theta) -5 = 0$ is :

asked Dec 19, 2018 by pady_1

0 answers

The curve represented by $x=2 (\cos t + \sin t), \;y = 5(\cos t - \sin t)$ is :

asked Dec 19, 2018 by pady_1

0 answers

The prouct of the length of perpendiculars from the foci on any tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is :

asked Dec 19, 2018 by pady_1

0 answers

The eccentricity of the ellipse $5x^2 + 9y^2 = 1$ is :

asked Dec 19, 2018 by pady_1

0 answers

The line $4x +6y+9=0$, touches the parabola $y^2 =4x$ at the point :

asked Dec 19, 2018 by pady_1

1 answer

The vertex of the parabola $x^2+ 8x + 12y+4=0$ is :

asked Dec 19, 2018 by pady_1

0 answers

If $(m_v \frac{1}{m_i}), \; i = 1, 2,3,4$ are noncyclic points, then the value of $m_1m_2m_3m_4$ is :

asked Dec 19, 2018 by pady_1

0 answers

If $(1,2)$ is a limiting point of a co-axial system of circles containing the circle $x^2 + y^2 + x - 5y + 9 =0$, then the equation of radical axis is :

asked Dec 19, 2018 by pady_1

1 answer

The number of common tangents that can be drawn to the circles $x^2 + y^2=1$ and $x^2 + y^2 -2x - 6y + 6 =0$, is :

asked Dec 19, 2018 by pady_1

0 answers

Two circles of equal radii cut orthogonally, if their centres are (2, 3) and (5, 6), then r is equal to:

asked Dec 19, 2018 by pady_1

0 answers

The slope $m$ of a tangent through the point $(7,1)$ to the circle $x^2+y^2=25$, satisfy the equation :

asked Dec 19, 2018 by pady_1

0 answers

The centre of circle which touch the y-axis at $(0,3)$ and making an intercept of $2$ units on the positive $x$-axis is :

asked Dec 19, 2018 by pady_1

0 answers

If the equation $\lambda x^2 - 5xy + 6y^2 + x - 3y =0$, represents a pair of straight lines, then their point of intersection is :

asked Dec 19, 2018 by pady_1

0 answers

The equaion of pair of lines through the point $(a,b)$ parallel to co-ordinate axes is :

asked Dec 19, 2018 by pady_1

0 answers

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