List of practice Questions

If A speaks truth with probability $\frac{4}{5}$ and B with $\frac{3}{4}$, find probability they contradict.
If $X_1, X_2, ..., X_n$ are $n$ independent events such that $P(X_r) = \frac{1}{r+1}$, for $r=1, 2, ..., n$, then the probability that none of the $n$ events occur is
If the mean and varian of a binomial variable $X$ are 2 and 1 respectively, then $P(X>1) = $
The probability that a person chosen at random is left handed is 0.1. Then the probability that in a group of 10 people there is exactly one left-handed person is
If A(2,3) and B(2,-3) are two points, then the equation of the locus of a point $P$ such that $PA + PB = 8$ is
In triangle $\triangle ABC$, $A=(1,2)$ and the equations of medians through $B$ and $C$ are $x+y=5$ and $x=4$. Find area of triangle ABC.
The equation of the line, passing through the point $(a\cos^3\theta, a\sin^3\theta)$ and perpendicular to the line $x\sec\theta - y\csc\theta = a$, is
A ray of light incident along a line meets another line $7x - y + 1 = 0$ at the point $(0,1)$ and is then reflected along the line $y + 2x = 1$. Then the equation of the line of inciden is
If the lines joining the origin to the points of intersection of a line $L$ and $x^2 + y^2 = 4$ are the coordinate axes, then the equation of the line $L$ is
If the chord through $(1,-2)$ cuts the curve $3x^2 - y^2 - 2x + 4y = 0$ at P and Q, then the angle subtended by PQ at the origin is
The transformed equation of $2x^2 + 3y^2 - z^2 - 8x + 18y + 2z + 9 = 0$ when the axes are translated to the point $(2,-3,1)$ is
If a point R$(4,y,z)$ lies on the line joining $P(2,-3,4)$ and $Q(8,0,10)$, then distan of R from origin is
If the foot of the perpendicular drawn from $(0,0,0)$ to a plane is $(1,2,3)$, then the equation of the plane is
The line $3x+y-5=0$ touches a circle S at $(1,2)$. If $(h,k)$ is the ntre of the circle S such that $h^2+hk+k^2=37$ and radius is $\sqrt{10}$, then $k=$
If $x+y-1=0$ and $2x - y + 1=0$ are conjugate lines with respect to the circle $x^2 + y^2 - 4x + 2fy - 1 = 0$, then $f=$
The product of the slopes of the common tangents drawn to the circles $x^2+y^2+2x-2y-2=0$ and $x^2+y^2-2x+2y+1=0$ is
The length of the chord of contact from point $(2,1)$ to the circle $x^2+y^2+4x+2y+1=0$ is
If the circles $x^2+y^2 - 4x + 2fy + 1 = 0$ and $x^2+y^2 + 2gx - 4y - 1 = 0$ cut orthogonally, then $r_1^2 + r_2^2 - 8=$
If $(2,3)$ is the vertex and $(3,2)$ is the focus of a parabola, then its equation is
Let A, A' be the end points of major axis, S, S' be the foci and B, B' be the end points of minor axis of an ellipse E. If $\angle \text{BAB}' = 60^\circ$, then $\angle \text{SBS}' =$
The equation of the pair of asymptotes of the hyperbola $x^2 - 2y^2 - 8x + 8y + 4 = 0$ is
Let the points $P_1(\frac{\pi}{4}), P_2(\frac{3\pi}{4}), P_3(\frac{5\pi}{4}), P_4(\frac{7\pi}{4})$ lie on the hyperbola $\frac{x^2}{9} - \frac{y^2}{16} = 1$. Then they form:
If $f(g(x+y)) = f(g(x)) + f(g(y))$, $g(1)=2$, $f(2)=1$, then $g(f(x))$ is discontinuous on:
The number of metalloids in the following elements are: Si, Mn, B, F, Cu, Ag, K, Sb, As, Na, Ge
The polar of a point with respect to the circle \( x^2 + y^2 - 10x + 12y - 3 = 0 \), which is not a tangent and not a chord of contact, is: