Recent questions tagged 2007

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent, then the value of $\lambda$ is

asked Oct 25, 2013 by meena.p

1 answer

The angle between the pair of straight lines formed by joining the points of intersection of $x^2+y^2=4$ and $y=3x+c$ to the origin is a right angle. Then $c^2$ is equal to

asked Oct 25, 2013 by meena.p

1 answer

In the triangle with vertices at $A(6,3),B(-6,3)$ and $C(-6,-3)$ the median through A meets BC at P, the line AC meets the x-axis at Q,while R and S respectively denote the orthocenter and centroid of the triangle. Then the correct matching of the coordinates of points in List -I to List - II is

asked Oct 25, 2013 by meena.p

1 answer

If $A(2,-1)$ and $B(6,5)$ are two points the ratio in which the foot of the perpendicular from (4,1) to AB divides it, is

asked Oct 25, 2013 by meena.p

1 answer

The angle between the line joining the points $(1,-2),(3,2)$ and the line $x+2y-7=0$ is

asked Oct 25, 2013 by meena.p

1 answer

In order to eliminate the first degree terms from the equation $2x^2+4xy+5y^2-4x-22y+7=0,$ the point to which origin is to be shifted, is

asked Oct 25, 2013 by meena.p

1 answer

The probability distribution of a random variable X is given by

asked Oct 25, 2013 by meena.p

1 answer

The mean and standard deviation of a binomial variate x are 4 and $\sqrt 3$ respectively. Then $P( X \geq 1)$ is equal to

asked Oct 25, 2013 by meena.p

1 answer

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is

asked Oct 25, 2013 by meena.p

1 answer

If A and B are mutually exclusive events with $P(B) \neq 1,$ then $P(A | \bar {B})$ is equal to (Here $\bar B$ is the complement of the event B)

asked Oct 25, 2013 by meena.p

1 answer

Four numbers are chosen at random from {1,2,3............,40}. The probability that they are not consecutive, is

asked Oct 25, 2013 by meena.p

1 answer

Let $\overrightarrow {a}=a_1\hat i+a_2 \hat j+a_3 \hat k$ Assertion (A): The identify $|\overrightarrow a \times \hat i |^2+|\overrightarrow a \times \hat j|^2+|\overrightarrow a \times \hat k| ^2=2 | \overrightarrow a |^2$ holds for $\overrightarrow {a}$. Reason (R): $\overrightarrow {a} \times \hat i =a_3 \hat j- a_2 \hat k, \overrightarrow a \times \hat j= a_1 \hat k- a_3 \hat i, \overrightarrow a \times \hat k=a_2 \hat i- a_1 \hat j$ Which of the following is correct ?

asked Oct 25, 2013 by meena.p

1 answer

The volume (in cubic units) of the tetrahedron with edges $\hat i+\hat j+\hat k, \hat i - \hat j+\hat k$ and $\hat i+2 \hat j-\hat k$ is

asked Oct 25, 2013 by meena.p

1 answer

If $\overrightarrow {a}=\hat i+\hat j-\hat k$ and $\overrightarrow{b} =+ \lambda \hat i- 3\hat j+\hat k$ and the orthogonal projection of $\overrightarrow b$ on $\overrightarrow a $ is $\large\frac{4}{3}$$ (\hat i-\hat j-\hat k)$, then $\lambda$ is equal to

asked Oct 25, 2013 by meena.p

1 answer

The ratio in which $\hat i+2 \hat j+5 \hat k$ divides the join of $-2\hat i+3 \hat j+5 \hat k$ and $7 \hat i - \hat k$ is

asked Oct 25, 2013 by meena.p

1 answer

If the points whose position vectors are $2 \hat i+\hat j+\hat k, 6 \hat i-\hat j+2 \hat k$ and $14\hat i-5 \hat j+p \hat k$ are collinear, then the value of p is

asked Oct 25, 2013 by meena.p

1 answer

The angle of elevation of an object from a point P on the level ground is $\alpha$. Moving d meters on the ground towards the object. the angle of elevation is found to be $\beta$. Then the height (in meters) of the object is

asked Oct 25, 2013 by meena.p

2 answers

In $\Delta ABC,$ with usual notation. Observe the two statements given below:(I) $rr_1r_2r_3=\Delta ^2$ (II) $r_1r_2+r_2r_3+r_3r_1=s^2$ Which of the following is correct ?

asked Oct 25, 2013 by meena.p

1 answer

In $\Delta ABC, (a+b+c) \bigg(\tan \large\frac{A}{2}$$+\tan \large\frac{B}{2}\bigg)$ is equal to

asked Oct 25, 2013 by meena.p

1 answer

If two angles of $\Delta ABC$ are $45^{\circ}$ and $60^{\circ}$, then the ratio of the smallest and the greatest sides are

asked Oct 25, 2013 by meena.p

0 answers

$\sec\;h^{-1} (\sin \theta)$ is equal to

asked Oct 24, 2013 by meena.p

0 answers

The value of x, where $ x > 0 $ and $\tan \bigg(\sec^{-1}\bigg(\large\frac{1}{x}\bigg)\bigg)$$=\sin (\tan ^{-1}2)$ is

asked Oct 24, 2013 by meena.p

1 answer

If $a,b,c$ are in AP. $b-a,c-b$ and a are in GP. then $a:b:c$ is

asked Oct 24, 2013 by meena.p

1 answer

$\sin A+ \sin B= \sqrt {3} (\cos B- \cos A)$ => $\sin 3A+ \sin 3B$ is equal to

asked Oct 24, 2013 by meena.p

1 answer

$\large\frac{\tan 80^{\circ} -\tan 10^{\circ}}{\tan 70^{\circ}}$ is equal to

asked Oct 24, 2013 by meena.p

1 answer

If $\cos (A-B)=3/5$ and $\tan A \tan B=2$. then which one of the following is true?

asked Oct 24, 2013 by meena.p

1 answer

If $\theta$ lies in the first quadrant and $5\;\tan \theta=4$, then $\large\frac{5 \sin \theta -3 \cos \theta}{\sin \theta+ 2 \cos \theta}$ is equal to

asked Oct 24, 2013 by meena.p

1 answer

A value of n such that $\bigg(\large\frac{\sqrt 3}{2}+\frac{i}{2}\bigg)^n$$=1$ is

asked Oct 24, 2013 by meena.p

1 answer

The locus of the point $z=x+iy$ satisfying $\bigg|\large\frac{z-2i}{z+2i} \bigg|$$=1$ is

asked Oct 24, 2013 by meena.p

1 answer

If $a=\large\frac{1-i \sqrt 3}{2},$ then the correct matching of List I from List II is

asked Oct 24, 2013 by meena.p

1 answer

The number of non-arrival solutions of the system $x-y+z=0, x+2y-z=0,2x+y+3z=0$ is

asked Oct 24, 2013 by meena.p

1 answer

If A is a square matrix such that $A(adj \;A)=\begin {bmatrix} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end {bmatrix}$, then det (adj A) $ is equal to

asked Oct 24, 2013 by meena.p

1 answer

If $\begin {bmatrix} 1 & 2 & x \\ 4 & -1 & 7\\ 2 & 4 & -6\end{bmatrix}$ is a singular matrix, then x is equal to

asked Oct 24, 2013 by meena.p

1 answer

If $\alpha,\beta,\gamma$ are the roots of $x^3-2x^2+3x-4=0,$ then the value of $\alpha^2\beta^2+\beta^2 \gamma^2+\gamma^2 \alpha^2$ is

asked Oct 24, 2013 by meena.p

1 answer

If 1,2,3 and 4 are the roots of the equation $x^4+ax^3+bx^2+cx+d=0$, then $a+2b+c$ is equal to

asked Oct 24, 2013 by meena.p

1 answer

The set of values of x for which the inequalities $x^2-3x-10 < 0, 10 x - x^2 -16 >0 $ hold simultaneously, is

asked Oct 24, 2013 by meena.p

1 answer

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$ and , if $px^2+qx+r=0$ has roots $\large\frac{1- \alpha}{\alpha}$ and $\large\frac{1-\beta}{\beta}$, then r is equal to

asked Oct 24, 2013 by meena.p

1 answer

$\large\frac{1}{2}-\frac{1}{2, 2^2}+\frac{1}{3.2^3}-\frac{1}{4.2^4}+.........$ is equal to

asked Oct 24, 2013 by meena.p

1 answer

The coefficient of $x^k$ in the expansion of $\large\frac{1-2x-x^2}{e^{-x}}$ is

asked Oct 24, 2013 by meena.p

1 answer

If $\large\frac{3x}{(x-a)(x-b)}=\frac{2}{x-a}+\frac{1}{x-b}$ then $a:b$ is equal to

asked Oct 24, 2013 by meena.p

1 answer

The sum of the series $\large\frac{3}{4.8}-\frac{3.5}{4.8.12}+\frac{3.5.7}{4.8.12.16}-...........$

asked Oct 24, 2013 by meena.p

1 answer

If $a_k$ is the coefficient of $x^k$ in the expansion of $(1+x+x^2)^n$ for $k=0,1,2.......,2n$ then $a_1+2a_2+3a_3+.....+2na_{2n}$ is equal to

asked Oct 24, 2013 by meena.p

1 answer

If a polygon of n sides has 275 diagonals, then n is equal to

asked Oct 24, 2013 by meena.p

1 answer

The number of ways of arranging 8 men and 4 women around a circular table such that no two women can sit together is

asked Oct 24, 2013 by meena.p

1 answer

If $S_n= 1^3+2^3+......+n^3$ and $T_n=1+2......+n$, then

asked Oct 24, 2013 by meena.p

1 answer

If $a^x=b^y=c^z=d^w$, the value of $x \bigg(\large\frac{1}{y}+\frac{1}{z}+\frac{1}{w}\bigg)$ is

asked Oct 24, 2013 by meena.p

1 answer

$\sqrt {2+\sqrt {5}-\sqrt{6-3 \sqrt {5}+\sqrt {14-6 \sqrt{5}}}}$ is equal to

asked Oct 24, 2013 by meena.p

1 answer

If $R \to R$ and $g: R \to R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R,$ where $[x]$ is the greatest integer not exceeding x, then for every $x \in R, f(g(x))$ is equal to

asked Oct 24, 2013 by meena.p

1 answer

If $f: R \to R$ and defined by $f(x)=\large\frac{1}{2-\cos 3x}$ for each $ x \in R$, then the range of f is

asked Oct 24, 2013 by meena.p

1 answer

If Q denotes the set of all rational numbers and $f\bigg(\large\frac{p}{q}\bigg)$$=\sqrt {p^2-q^2}$ for any $\large\frac{P}{q}$$ \in Q$ , then observe the following statements.

asked Oct 24, 2013 by meena.p

1 answer

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