Recent questions tagged 1999

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

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$(\overrightarrow{a} \times \overrightarrow{b} ) \times (\overrightarrow{b} \times \overrightarrow{c})$ 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

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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

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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

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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

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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

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

asked Dec 19, 2018 by pady_1

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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

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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

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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

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

asked Dec 19, 2018 by pady_1

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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

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The inverse point of $(1, -1)$ with respect to the circle $x^2 + y^2 = 4$ is equal to :

asked Dec 19, 2018 by pady_1

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The parametric equaions $x= \frac{2a(1-t^2)}{1+t^2}$, and $y = \frac{4at}{1+'t^2}$ represents a circle of radius is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If the equation $ax^2 + 5xy - 6y^2 - 10x + 11y + c = 0$ represents two perpendicular lines, then $c$ is equal to :

asked Dec 19, 2018 by pady_1

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The angle between the pair of straight lines $y^2 \cos^2 \theta - xy \cos^2 \theta + x^2 (\sin^2 \theta - 1)=0$, is :

asked Dec 19, 2018 by pady_1

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If $\lambda x^2 + 6xy + 9y^2 +4x + 12y+3=0$ represents a pair of straight lines, then $\lambda$ is equal to :

asked Dec 19, 2018 by pady_1

1 answer

The product of length of perpendiculars from $(-1,2)$ to the pair of lines $2x^2 -5xy + 2y^2 =0$, is :

asked Dec 19, 2018 by pady_1

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The reflection of a point $(6, 8)$ about the line $x=y$, is :

asked Dec 19, 2018 by pady_1

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The equation of lines passing through the intersection of lines $x - 2y + 5=0$ and $3x+2y+7=0$ and perpendicular to $x-y=0$ is :

asked Dec 19, 2018 by pady_1

0 answers

If the straight line $y=4-3x, \; ay = x + 10$ and $2y + bx + 9=0$ represents the three consecutive sides of rectangle, then $ab$ is equal to :

asked Dec 19, 2018 by pady_1

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Equation of a straight line making an intercept of 3 units on the $y$-axis and inclined at $45^{\circ}$ to the $x$-axis, is :

asked Dec 19, 2018 by pady_1

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The ratio in which the line $y=x$ divides the segment joining $(2,3)$ and $(8,6)$ is :

asked Dec 19, 2018 by pady_1

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If the axes are rotated through an angle $30^{\circ}$ about the origin, then the tranformed equation of $x^2 + 2 \sqrt{3} xy - y^2 = 2a^2$, is :

asked Dec 19, 2018 by pady_1

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The locus of the point whose distance from $x$ axis is twice its distance from $y$ axis is :

asked Dec 19, 2018 by pady_1

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If $\frac{3 + 2i \sin \theta}{1- 2i \sin \theta}$ is real, then $\theta$ is equal to :

asked Dec 19, 2018 by pady_1

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The least positive integer $n$ such that $\begin{pmatrix} \frac{1 - i}{1+i} \end{pmatrix}^{2n} = 1$ is :

asked Dec 19, 2018 by pady_1

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$P$ represents $z = x + iy$ in argand plane and $|3z - 1|=3|z-2|$; then locus of $P$ is :

asked Dec 19, 2018 by pady_1

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If $\alpha, \; \beta$ are the cube roots of unity, then $\alpha^5 + \beta^5 + \alpha \beta$ is equal to :

asked Dec 19, 2018 by pady_1

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In a triangle $A = \sqrt{15} - \sqrt{11}, \; B = \sqrt{17} - \sqrt{13}$ then :

asked Dec 19, 2018 by pady_1

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In a triangle $ABC, \; r_1 \cot \frac{A}{2} + r_2 \cot \frac{B}{2} + r_3 \cot \frac{C}{2}$ is equal to :

asked Dec 19, 2018 by pady_1

2 answers

In a $\Delta ABC, \; r \begin{bmatrix} \cot \frac{B}{2} + \cot \frac{C}{2} \end{bmatrix}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The general solution of $\tan^2 \theta = 3$ is :

asked Dec 19, 2018 by pady_1

1 answer

From the top of a building of height $h$ metres the angle of depression of an object on the ground is $\alpha$. The distance of the object from the foot of the building, is :

asked Dec 19, 2018 by pady_1

0 answers

If $|x| = x $, then $\frac{1}{2} \log \begin{pmatrix} \frac{1+x}{1-x} \end{pmatrix}$ is equal to :

asked Dec 19, 2018 by pady_1

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The period of $\sin^3x + \cos^3 x^2$ is :

asked Dec 19, 2018 by pady_1

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The maximum value of $1+8 \sin^2 x^2 \cos^2 x^2$ is :

asked Dec 19, 2018 by pady_1

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$\tan^{-1} (\frac{1}{2}) + \tan^{-1} (\frac{1}{3})$ is equal to :

asked Dec 19, 2018 by pady_1

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$\frac{\sin \theta + \sin 2 \theta}{1 + \cos \theta + 2 \cos \theta}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

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