Recent questions tagged 2005

If $y=3x$ is a tangent to a circle with center $(1,1),$then the other tangent drawn through $(0,0)$ to the circle is:

asked Nov 12, 2013 by meena.p

1 answer

If $x-y+1=0$ meets the circle $x^2+y^2+y-1=0$ at A and B , then the equation of the circle with AB as diameter is :

asked Nov 12, 2013 by meena.p

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The equation of the circle whose diameter is the common chord of the circles $x^2+y^2+2x+3y+2=0$ and $x^2+y^2+2x-3y-4=0$ is :

asked Nov 12, 2013 by meena.p

1 answer

The point collinear with $(1,-2,-3)$ and $(2,0,0)$ among the following is :

asked Nov 12, 2013 by meena.p

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The direction cosines of the line passing through $P(2,3,-1) $ and the orgin are :

asked Nov 12, 2013 by meena.p

1 answer

The product of the perpendicular distances from the origin on the pair of straight lines $12x^2+25xy+12y^2+10x+11y+z=0$ is :

asked Nov 12, 2013 by meena.p

1 answer

The area of the triangle formed by the pair of straight lines $(ax+by)^2-3(bx-ay)^2=0$ and $ax+by+c=0$, is :

asked Nov 12, 2013 by meena.p

1 answer

The equation of the straight line perpendicular to $5x-2y=7$ and passing through the point of intersection of the lines $2x+3y=1$ and $3x+4y=6$ is :

asked Nov 12, 2013 by meena.p

1 answer

If PM is the perpendicular from $P(2,3)$ onto the line $x+y=3, then the co-ordinates of M are :

asked Nov 12, 2013 by meena.p

1 answer

The area (in square units) of the triangle formed by the lines $x=0,y=0$ and $3x+4y=12,$ is :

asked Nov 12, 2013 by meena.p

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If a point P moves such that its distances from the point $A(1,1)$ and the line $x+y+z=0$ are equal, then locus of P is :

asked Nov 12, 2013 by meena.p

1 answer

For a binomial variate X with $n=6,$ if $P(X=2)=9\;P(X=4),$ then its variance is :

asked Nov 12, 2013 by meena.p

1 answer

If the range of a random variable X is $\{0,1,2,3,4.......\}$ with $P(X =k)= \large\frac{(k+1)a}{3^k}$ for $ k \leq 0,$ then a is equal to :

asked Nov 12, 2013 by meena.p

1 answer

Box A contains 2 black and 3 red balls, white Box contains 3 black and 4 red balls. Out of these two boxes one is selected at random ; and the probability of choosing Box A is double that of Box B. If a red ball is drawn from the selected box, then the probability that it has come from Box B, is :

asked Nov 12, 2013 by meena.p

2 answers

A number n is chosen at random from $S=\{1,2,3,.....,50\}$.Let $A= \bigg \{ n \in S:n +\large\frac{50}{n} $$ > 27 \bigg\}$$,B= (n \in S:n$ is a Prime) and $C=\{n \in S:n \;is\; a\; square \}$. Then correct order of their probabilities is :

asked Nov 12, 2013 by meena.p

1 answer

A coin and six faced die, both unbiassed, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die, is :

asked Nov 12, 2013 by meena.p

1 answer

Observe the following statements:A: Three vectors are coplanar if one of them is expressible as a linear combination of the other two. R: Any three coplanar vectors are linearly dependent . Then which of the following is true?

asked Nov 12, 2013 by meena.p

1 answer

Observe the following lists :

asked Nov 12, 2013 by meena.p

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I : Two non-zero , non-collinear vectors are linearly independent. II. Any three coplanar vectors are linearly dependent .Which of the above statements is /are true?

asked Nov 12, 2013 by meena.p

1 answer

If $\overrightarrow {a}$ and $\overrightarrow{b}$ are unit vectors, then the vector $(\overrightarrow a+\overrightarrow b) \times (\overrightarrow{a} \times \overrightarrow{b})$ is parallel to the vector:

asked Nov 12, 2013 by meena.p

1 answer

If the vector $\overrightarrow{a} =2 \hat i+3 \hat j+6 \hat k$ and $\overrightarrow {b}$ are collinear and $|\overrightarrow {b}|=21,$ then $\overrightarrow {b}$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

A tower, of x meters high, has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant y meters from the foot of the tower. Then the length of the flagstaff(in meters), is :

asked Nov 12, 2013 by meena.p

1 answer

Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\large\frac{\pi}{3}$. Then the perimeter of the triangle is :

asked Nov 12, 2013 by meena.p

2 answers

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

asked Nov 12, 2013 by meena.p

1 answer

In a $\Delta ABC, a (\cos ^2 B+\cos^2 C)+ \cos A(c \cos C+b \cos B)$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

$2 \tan h^{-1} \large\frac{1}{2}$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

$\sin^{-1} \large\frac{4}{5}$$+2 \tan ^{-1} \large\frac{1}{3}$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

If $\cos 2x =(\sqrt 2 +1) \bigg(\cos x - \large\frac{1}{\sqrt 2}\bigg), \cos x \neq \large\frac{1}{2}$ then $x \in :$

asked Nov 12, 2013 by meena.p

1 answer

$A+B=C=> \cos ^2 A +\cos ^2 B+\cos ^2 C- 2 \cos A \cos B \cos C $ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

If $A+C=2B$ then $\large\frac{\cos C- \cos A}{\sin A- \sin C}$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

If $ \large\frac{\tan 3A}{\tan A}$$=a$ then $\large\frac{\sin 3A}{\sin A}$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

The extreme values of $4 \cos (x^2) \cos \bigg( \large\frac{\pi}{3}$$+x^2\bigg) - \cos \bigg(\large\frac{\pi}{3}$$-x^2\bigg)$ over R, are :

asked Nov 12, 2013 by meena.p

1 answer

If $\cos \theta-4 \sin \theta=1$ then $\sin \theta+4 \cos \theta$ is equal to :

asked Nov 11, 2013 by meena.p

0 answers

If $\alpha$ is a non-real root of $x^6=1$, then $\large\frac{\alpha ^5+ \alpha ^3+ \alpha +1}{\alpha ^2+1}$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

If $\alpha_1, \alpha_2, \alpha_3$ respectively denote the moduli of the complex number $-i, \large\frac{1}{3} $$ (1+i)$ and $-1+i$, then their increasing order is :

asked Nov 11, 2013 by meena.p

1 answer

If $A= \begin {bmatrix} -1 & 0 \\ 0 & 2 \end {bmatrix}$ then $A^3-A^2$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

adj $\begin {bmatrix} 1 & 0 & 2 \\ -1 & 1 &-2 \\ 0 & 2 & 1 \end {bmatrix}=\begin {bmatrix} 5 & a & -2 \\ 1 & 1 &0 \\ -2 & -2 & b \end {bmatrix}$ then $[a \quad b]$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

If $m [-3 \quad 4]+n [ 4 \quad -3]=[10 \quad -11]$ then $3m+7n$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

If $\alpha, \beta, \gamma$ are the roots of $x^3+2x^2-3x-1=0$, then $\alpha^{-2}+\beta^{-2}+\gamma^{-2}=$

asked Nov 11, 2013 by meena.p

1 answer

The roots of the equation $x^3-3x-2=0$ are :

asked Nov 11, 2013 by meena.p

1 answer

$E_1: a+b+c=0$, if 1 is a root of $ax^2+bx+c=0$ .$E_2:b^2-a^2=2ac,$ if $\sin \theta, \cos \theta$ are the roots of $ax^2+bx+c=0$ Which of the following is true?

asked Nov 11, 2013 by meena.p

1 answer

If x is real, then the minimum value of $\large\frac{x^2-x+1}{x^2+x+1}$, is :

asked Nov 11, 2013 by meena.p

1 answer

If $|a| < 1,b= \sum \limits_{k=1} ^{ \infty} \; \large\frac{a^k}{k}$ then a is equal to :

asked Nov 11, 2013 by meena.p

1 answer

$\sum \limits _{n=1}^{\infty} \large\frac{2n^2+n+1}{n !}$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

If $\large\frac{x^3}{(2x-1)(x+2)(x-3)}$$=A+\large\frac{B}{2x-1}+\frac{C}{x+2}+\frac{D}{x-3}$ then A is equal to :

asked Nov 11, 2013 by meena.p

1 answer

If $|x| < \large\frac{1}{2}$, then the coefficient of 'x' in the expansion of $\large\frac{1+2x}{(1-2x)^2}$ is :

asked Nov 11, 2013 by meena.p

1 answer

The coefficient of $x^3y^4z^5$ in the expansion of $(xy+yz+xz)^6$ is :

asked Nov 11, 2013 by meena.p

1 answer

If $(1+x)^{15}=a_0 +a_1 x +.....+ a_{15} x^{15},$ then $\sum \limits_{r=1}^{15} r \large\frac{a_r}{a_{r_1}}$ is equal to :

asked Nov 11, 2013 by meena.p

1 answer

A three digit number n is such that the last two digits of it are equal and differ from the first. Then number of such n's is :

asked Nov 11, 2013 by meena.p

1 answer

$\{ n(n+1)(2n+1): n \in Z \} \in $

asked Nov 11, 2013 by meena.p

1 answer

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