Recent questions tagged 2008

If $x-a \bigg \{\cos \theta+ \log \tan \bigg(\large\frac{\theta}{2}\bigg)\bigg\}$ and $y= a \sin \theta$ then $\large\frac{dy}{dx}=$

asked Oct 17, 2013 by meena.p

1 answer

If $f(2)=4$ and $f'(2)=1$, then $\lim \limits_{x \to 2} \large\frac{x f(2) -2 f(x)}{x-2}=$

asked Oct 17, 2013 by meena.p

1 answer

If $f: \Re $ is defined by $f(x)= \left\{ \begin{array}{1 1} \frac{\cos 3x- \cos x}{x^2} & \quad for\;x\neq 0 \\ \lambda & \quad for\;x=0 \end{array}. \right. $ and if f is continuous at $x=0,$ then $\lambda=$

asked Oct 17, 2013 by meena.p

1 answer

If $f:\Re \to \Re$ is defined by $f(x) =[x-3]+| x-4 |$ for $ x \in \Re$ then $\lim \limits_{x \to 3^-} f(x)=$

asked Oct 17, 2013 by meena.p

1 answer

$\lim \limits_{x \to 0} \large\frac{(1-e^x) \sin x}{x^2+x^3}=$

asked Oct 17, 2013 by meena.p

1 answer

The radius of the circle with the polar equation $r^2-8r (\sqrt 3 \cos \theta+\sin \theta)+15 -0$ is

asked Oct 17, 2013 by meena.p

1 answer

The distance between the foci of the hyperbola $x^2-3y^2-4x-6y-11=0$ is

asked Oct 17, 2013 by meena.p

1 answer

For an ellipse with eccentricity $\large\frac{1}{2}$ the center is at the orgin. If one directrix is $x=4$, then the equation of the ellipse is

asked Oct 17, 2013 by meena.p

1 answer

If $2x+3y+12=0$ and $x-y+ 4 \lambda=0$ are conjugate with respect to the parabola $y^2=8x$ then $\lambda=$

asked Oct 17, 2013 by meena.p

1 answer

If $\theta$ is the angle between the tangents from $(-1,0)$ to the circle $x^2+y^2-5x+4y-2=0$, then $\theta$

asked Oct 17, 2013 by meena.p

1 answer

The inverse of the point (1,2) with respect to the circle $x^2+y^2-4x-6y+9=0$, is

asked Oct 17, 2013 by meena.p

1 answer

If the lines $2x-3y=5$ and $3x-4y=7$ are two diameters of a circle of radius 7, then the equation of the circle is

asked Oct 17, 2013 by meena.p

1 answer

The angle between the lines whose direction cosines are $\bigg(\large\frac{\sqrt 3}{4},\frac{1}{4},\frac{\sqrt 3}{2}\bigg)$ and $ \bigg(\large\frac{\sqrt 3}{4},\frac{1}{4},\frac{-\sqrt 3}{2} \bigg)$ is

asked Oct 17, 2013 by meena.p

1 answer

In $\Delta ABC$ the mid-points of the sides AB,BC and CA are respectively $(l,0,0),(0,m,0)$ and $(0,0,n).$ Then $\large\frac{AB^2+BC^2+CA^2}{l^2+m^2+n^2}=$

asked Oct 17, 2013 by meena.p

1 answer

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2+y^2=4$ with $x+y=a$. The set containing the value of 'a' is

asked Oct 17, 2013 by meena.p

1 answer

The value of $\lambda$ such that $\lambda x^2-10 xy+12 y^2+5x-16y-3=0$ represents a pair of straight lines, is

asked Oct 17, 2013 by meena.p

1 answer

The value of k such that the lines $2x-3y+k=0,3x-4y-13=0$ and $8x-11y-33=0$ are concurrent , is

asked Oct 17, 2013 by meena.p

1 answer

If l,m,n are in arithmetic progression, then the straight line $lx+my+n=0$ will pass through the point

asked Oct 17, 2013 by meena.p

1 answer

The transformed equation of $3x^2+3y^2,2xy=2$ when the coordinate axes are rotated through an angle of $45^{\circ}$ is

asked Oct 17, 2013 by meena.p

1 answer

If the sum of the distances of a point P from two perpendicular lines in a plane is 1, then the locus of P is a

asked Oct 17, 2013 by meena.p

1 answer

If X is a Poisson variate such that $P(X-1)-P(X=2),$ then $P(X=4)=$

asked Oct 17, 2013 by meena.p

1 answer

The distribution of a random variable X is given below:

asked Oct 17, 2013 by meena.p

1 answer

For $k= 1,2,3$ the box $B_k$ contains k red balls and $(k+1)$ white balls. Let $P(B_1)-\large\frac{1}{2}$$ , P(B_2)-\large\frac{1}{3}$ and $P(B_3)=\large\frac{1}{6}$. A box is selected at random and a ball is drawn from it . If a red ball is drawn, then the probability that it has come from box $B_2$ is

asked Oct 17, 2013 by meena.p

0 answers

Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces ( numbered 1 to 6) and let $E_k=\{(a,b) \in S : ab =k\}\;for\; k \leq 1$ . If $p_k=P(F_k)\; for\; k \leq 1$ then the correct, among the following , is

asked Oct 17, 2013 by meena.p

1 answer

If A and B are independent events of a random experiment such that $P(A \cap B)=\large\frac{1}{6}$ and $P(\bar A \cap \bar B)=\large\frac{1}{3},$ then $P(A)= $ (Here $\bar E$ is the complement of the event E)

asked Oct 17, 2013 by meena.p

1 answer

Let $\bar a$ be a unit vector, $\bar b= 2 \bar i+\bar j- \bar k$ and $\bar c= \bar i +3 \bar k$. The maximum value of $[\bar a\;\bar b\;\bar c]$ is

asked Oct 17, 2013 by meena.p

1 answer

If $\bar {a} = \bar i + \bar j+ \bar k, \bar b= \bar i- \bar j+ \bar k,\bar c= \bar i+ \bar j- \bar k$ and $\bar d= \bar i- \bar j- \bar k,$ then observe the following lists:

asked Oct 17, 2013 by meena.p

1 answer

If the position vector of $A,B$ and $C$ are respectively $2 \bar i - \bar j +\bar k, \bar i - 3 \bar j - 5 \bar k$ and $ 3 \bar i - 4 \bar j - 4 \bar k$, then $\cos ^2 A=$

asked Oct 17, 2013 by meena.p

1 answer

If the points with position vectors $60 \bar i+ 3 \bar j, 40 \bar i-80 \bar j$ and $a \bar i-52 \bar j$ are collinear, then $a = $

asked Oct 17, 2013 by meena.p

1 answer

The position vectors of P and Q are respectively $\bar {a}$ and $\bar {b}$. If R is a point on $\overleftrightarrow{PQ}$ such that $\overrightarrow{PR}= 5 \overrightarrow{PQ},$ then the position vector of R is :

asked Oct 17, 2013 by meena.p

1 answer

From the top of a hill the angles of depression of the top and the bottom of a pillar are $\alpha$ and $\beta$ respectively. The height (in meters) of the pillar is

asked Oct 17, 2013 by meena.p

1 answer

In a triangle , if $r_1=2 r_2=3 r_3$, then $\large\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$$=$

asked Oct 17, 2013 by meena.p

1 answer

Observe the following statements :(I) In $\Delta ABC, b \; \cos ^2 \large\frac{C}{2}+c \cos ^2 \large\frac{B}{2} =s$ (II) In $\Delta ABC, \cot \large\frac{A}{2}=\frac{b+c}{2}$$ => B =90^{\circ}$ Which of the following is correct?

asked Oct 17, 2013 by meena.p

1 answer

If $\Delta ABC$ if $\large\frac{1}{b+c}+\frac{1}{c+a}=\frac{3}{a+b+c}$ then $C=$

asked Oct 17, 2013 by meena.p

1 answer

$\large\frac{1+ \tan h \Large\frac{x}{2}}{1- \tan h \Large\frac{x}{2}}=$

asked Oct 17, 2013 by meena.p

1 answer

If $\sin ^{-1} \bigg(\large\frac{3}{x}\bigg)$$+ \sin ^{-1} \bigg(\large\frac{4}{x}\bigg)=\large\frac{\pi}{2}$ then $x=$

asked Oct 17, 2013 by meena.p

1 answer

$\{ x \in \Re : \cos 2x+ 2 \cos ^2 x =2 \}=$

asked Oct 17, 2013 by meena.p

1 answer

If $\alpha +\beta+\gamma= 2\theta$, then $cos \theta+ \cos (\theta- \alpha)+ \cos (\theta- \beta)+ \cos (\theta- \gamma)=$

asked Oct 17, 2013 by meena.p

1 answer

If $\tan \theta + \tan \bigg(\theta +\large\frac{\pi}{3}\bigg)$$+\tan \bigg(\theta +\large\frac{2 \pi}{3}\bigg)$$=3$,then which of the following is equal to 1?

asked Oct 17, 2013 by meena.p

0 answers

If $A=35^{\circ},B=15^{\circ}$ and $C=40^{\circ}$, then $tan A. \tan B+\tan B. \tan C+\tan C. \tan A=$

asked Oct 17, 2013 by meena.p

1 answer

$\sqrt 2 - cosec20^{\circ}- \sec 20^{\circ}=$

asked Oct 17, 2013 by meena.p

1 answer

If $m_1,m_2,m_3$ and $m_4$ respectively denote the moduli of the complex numbers $1+4 i,3+i,1-i,$ and $2-3i,$ then the correct one, among the following is

asked Oct 17, 2013 by meena.p

1 answer

If $\Omega$ is a complex cube root of unity, then $\sin\bigg\{(\omega ^{10}+ \omega^{23}) \pi -\large \frac{\pi}{4}\bigg\}=$

asked Oct 17, 2013 by meena.p

1 answer

The points in the set $\bigg\{z \in C: Arg \bigg(\large\frac{Z-2}{Z-6i}\bigg)-\frac{\pi}{2}\bigg\}$ lie on the curve which is (Where C denotes the set of all complex numbers )

asked Oct 17, 2013 by meena.p

1 answer

$\begin {bmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{bmatrix}$

asked Oct 17, 2013 by meena.p

1 answer

The inverse of the matrix $\begin {bmatrix} 7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1 \end{bmatrix} $ is :

asked Oct 17, 2013 by meena.p

1 answer

If $A=\begin {bmatrix} 1 & -2 \\ 4 & 5 \end{bmatrix}$ and $f(t)=t^2-3t+7$, then $f(A)+ \begin {bmatrix} 3 & 6 \\ 12 & -9 \end{bmatrix} = $

asked Oct 17, 2013 by meena.p

0 answers

The sum of the fourth powers of the of the equation $x^3+x+1=0$ is

asked Oct 17, 2013 by meena.p

1 answer

The cubic equation whose roots are thrice to each of the roots of $x^3+2x^2-4x+1=0$ is

asked Oct 16, 2013 by meena.p

1 answer

If $ \alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$, then the quadratic equation whose roots are $\alpha$ and $\beta$ is

asked Oct 16, 2013 by meena.p

1 answer

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