List of top Mathematics Questions asked in MET

In a trapezoid of the vector \( \vec{BC} = \lambda \vec{AD} \). We will, then find that \( \vec{P} = \vec{AC} + \vec{BD} \) is collinear with \( \vec{AD} \). If \( \vec{P} = \mu \vec{AD} \), then

A and B are two points on one bank of a straight river and C, D are two other points on the other bank... AB=a, $\angle CAD=α, \angle DAB=β, \angle CBA=γ$, then CD is equal to

In a triangle, if $r₁ > r₂ > r₃$ then

In a \( \Delta ABC \), \( \angle B = 90^\circ \), then \( \tan^2\left(\frac{A}{2}\right) \) is

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

$2 \tan^-1(\csc \tan^-1x - \tan \cot^-1x)$ is equal to

The sum of all the solutions of the equation $\cos x · \cos(\frac\pi3+x) · \cos(\frac\pi3-x) = \frac14, x \in [0, 6π]$ is

The value of $\cos \frac2π15 · \cos \frac4\pi15 · \cos \frac8\pi15 · \cos \frac16\pi15$ is equal to

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 period of function $f(x)=| \sin 4x | + | \cos 4x |$ is

The equation $|z+i|-|z-i|=k$ represents a hyperbola, if

If $n₁, n₂$ are positive integers, then $(1+i)ⁿ₁+(1+i³)ⁿ₁+(1+i⁵)ⁿ₂+(1+i⁷)ⁿ₂$ is a real number if and only if

Let a, b, c be real numbers with $a ≠ 0$ and let $α, β$ be the roots of the equation $ax²+bx+c=0$, then $a³x²+abcx+c³=0$ has roots

If A is an orthogonal matrix, then determinant of A is

For positive numbers x, y, z the numerical value of the determinant $$ is

If the matrix $A = $ has rank 3, then

If A is a skew-symmetric matrix, then trace of A is

If a, b, c are three distinct positive real numbers, the number of real roots of $ax²+2b|x|-c=0$ is

If $α, β, γ$ are such that $α+β+γ=2$, $α²+β²+γ²=6$, $α³+β³+γ³=8$, then $α⁴+β⁴+γ⁴$ is

The number of values of the triplet (a, b, c) for which $a \cos 2x + b \sin² x + c = 0$ is satisfied by all real x, is

If $a>1$ roots of the equation $(1-a)x²+3ax-1=0$ are

The constant term in the expansion of $(1+x)ᵐ(1+\frac1x)ⁿ$ is ________.

The number of terms in the expansion of $(\sqrt5+\sqrt[4]11)¹24$ which are integers is equal to ________.

The greatest coefficient in the expansion of $(1+x)²n$ is ________.

The term independent of \( x \) in the expansion of \( \left[ \sqrt{\frac{x}{3}} + \sqrt{\frac{3}{2}} x^2 \right]^{10} \) is ________.