List of top Mathematics Questions asked in MET

If \( z = \tan(y + ax) + \sqrt{y} - ax \), then \( z_{xx} - a^2 z_{yy} \) is equal to

\( \int \frac{x^2 + 4x^4 + 16}{dx} \) is equal to

If the solution of the differential equation \( \frac{dy}{dx} = ax + 32y + f \) represents a circle, then the value of \( a \) is

Solution of the differential equation \[ x = 1 + xy \frac{dy}{dx} + \frac{(xy)^2}{2!} \left(\frac{dy}{dx}\right)^2 + \frac{(xy)^3}{3!} \left(\frac{dy}{dx}\right)^3 + \cdots \] is

If \( \cos x = \frac{2\cos y - 1}{2 - \cos y} \), where \( x, y \in (0, \pi) \), then \( \tan \frac{x}{2} \cot \frac{y}{2} \) is equal to:

The value of \[ \sin^{-1}\left[\cos\left(\sin^{-1}\left(\sqrt{\frac{2-\sqrt{3}}{4}}\right) + \cos^{-1}\left(\frac{\sqrt{12}}{4}\right) + \sec^{-1}\left(\sqrt{2}\right)\right)\right] \] is

The approximate value of $\int₁⁵x²dx$ using trapezoidal rule with $n=4$ is

The value of the integral $\int_π/2³π/2[sin~x]dx$, where $[·]$ denotes the greatest integer function, is

The area of the loop of the curve $ay²=x²(a-x)$ is

The point in the interval [0, 2π], where $f(x)=eˣsin~x$ has maximum slope, is

If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then its acceleration is

If $\int f(x)dx=F(x)$, then $\int x³f(x²)dx$ is equal to

If $y=sin(m~sin^-1x)$, then $(1-x²)y^\prime\prime-xy^\prime}$ is equal to

If $f(x)=(ax+b)sin~x+(cx+d)cos~x$, then the values of a, b, c and d such that $f^\prime(x)=x~cos~x$ for all x, are

The locus of the equation $xy+yz=0$ is

If \( f(x) = \begin{cases} b, & 0 \leq x < 1 \\ x + 3, & 1 < x \leq 2 \\ 4, & x = 1 \end{cases} \) , then the value of \( (a, b) \) for which \( f(x) \) cannot be continuous at \( x = 1 \) is

The reflection of the point (2, 1, 3) in the plane $3x-2y-z=9$ is

The direction cosines of any normal to the xy-plane are

If $f(x)=logₓ(log~x)$, then $f^\prime(x)$ at $x=e$ is

The tangent and normal to a rectangular hyperbola $xy=c²$ at a point cut off intercepts $a₁, a₂$ on one axis and $b₁, b₂$ on the other, then $a₁a₂ + b₁b₂$ is equal to

If the equation $lx²+2mxy+ny²=0$ represents a pair of conjugate diameters of the hyperbola $x²/a² - y²/b² = 1$, then

If $e$ is the eccentricity of the hyperbola $x²/a² - y²/b² = 1$ and $θ$ is the angle between the asymptotes, then $\cos(θ/2)$ is equal to

The number of real tangents that can be drawn to the ellipse $3x²+5y²=32$ passing through (3, 5) is

If $(mᵢ, 1/mᵢ)$ are four distinct points on a circle, then