List of top Mathematics Questions

If the angle between the curves \( y = e^{(x+4)} \) and \( x^2 y = 1 \) at the point \( (1, 1) \) is \( \theta \), then \[ \sin \theta + \cos \theta = \dots \]
If a line is moving between the coordinate axes such that the sum of the intercepts made by it on the coordinate axes is always 12, then the equation of that line which forms a triangle of maximum area with the coordinate axes is:
If the points of contact of the tangents drawn from \( (0,0) \) to the curve \( y = x^2 + 3x + 4 \) are \( (\alpha, \beta) \) and \( (\gamma, \delta) \), then \( \beta + \delta = \):
Evaluate the integral \( \int x^3 (\log x)^2 dx \):
If \[ \int \frac{1}{x(\log x)^2 + 4\log x - 1} \, dx = A \log [ \log x + B ] + K \] where \( K \) is the constant of integration, then \[ \int \frac{1}{x(\log x)^2 + 4\log x - 1} \, dx = A \log [ \log x + C ] + K. \]
If \( f(x) = \int_0^x \left[ (a+1)(t+1)^2 - (a-1)(t^2 + t + 1) \right] dt \), then a possible positive value of \( a \), for which \( f'(x) = 0 \) has equal roots, is:
The area (in sq. units) of the region bounded by the curves \( y = 4 \cos x \) and \( y = -|\cos x| \) from \( x = -\frac{\pi}{2} \) to \( x = \frac{\pi}{2} \) is:
If \[ x^a \frac{dy}{dx} = y^\beta \left( \gamma \log x + \delta y + 1 \right) \] is a homogeneous differential equation, then
The general solution of the differential equation \( \tan x \tan y \, dx + \cos^2 x \csc^2 y \, dy = 0 \) is:
If $\vec{a} = 2\hat{i} - \hat{j} + 3\hat{k}$, $\vec{b} = -3\hat{i} + 5\hat{j} - 4\hat{k}$, $\vec{c} = 6\hat{i} - 4\hat{j} + 5\hat{k}$, then $(\vec{a} \times \vec{b}) \cdot (\vec{b} \times \vec{c}) = $
Which one of the following is false?
Given independent events A, B, and C with rtain intersection probabilities, find $P(A)$, $P(B)$, and $P(C)$.
Probability that missing card is not a spade, given two drawn cards are spades?
If A speaks truth with probability $\frac{4}{5}$ and B with $\frac{3}{4}$, find probability they contradict.
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
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 $f=$
If $(2,3)$ is the vertex and $(3,2)$ is the focus of a parabola, then its equation 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: