List of top Questions asked in MET- 2015

I\(_2\) dissolves in KI solution due to formation of

The approximate value of \((1.0002)^{3000}\) is

\((\mathbf{a} \cdot \hat{\mathbf{i}})(\mathbf{a} \times \hat{\mathbf{i}}) + (\mathbf{a} \cdot \hat{\mathbf{j}})(\mathbf{a} \times \hat{\mathbf{j}}) + (\mathbf{a} \cdot \hat{\mathbf{k}})(\mathbf{a} \times \hat{\mathbf{k}})\) is equal to

If \(A = \{(x,y): x^2 + y^2 = 25\}\) and \(B = \{(x,y): x^2 + 9y^2 = 144\}\); then \(A \cap B\) contains

The value of \(c\) prescribed by Lagrange's mean value theorem, when \(f(x) = \sqrt{x^2 - 4}\), \(a = 2\) and \(b = 3\), is

The mean deviation from the mean of the series \(a, a+d, a+2d, .........., a+2nd\), is

If \(f(x) = x e^{x(1-x)}\), then \(f(x)\) is

If \(\omega\) is an imaginary cube root of unity, then the value of \((1+\omega)(1+\omega^2)(1+\omega^3)(1+\omega^4)(1+\omega^5)..........(1+\omega^{3n})\) is

Let \(X\) denotes the number of times heads occur in \(n\) tosses of a fair coin. If \(P(X=4)\), \(P(X=5)\) and \(P(X=6)\) are in AP, then the value of \(n\) is

If there is a term containing \(x^{2r}\) in \(\left(x + \frac{1}{x^2}\right)^{n-3}\), then

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

If \(\cos^{-1}\frac{x}{2} + \cos^{-1}\frac{y}{3} = \theta\), then \(9x^2 - 12xy\cos\theta + 4y^2\) is equal to

If \(\tan(\sec^{-1}x) = \sin\left(\cos^{-1}\frac{1}{\sqrt{5}}\right)\), then \(x\) is equal to

The equation of the tangent to the curve \(y = (2x-1)e^{2(1-x)}\) at the point of its maximum, is

The proposition \((p \rightarrow \neg p) \wedge (\neg p \rightarrow p)\) is

The number of ways in which four letters can be selected from the word 'DEGREE', is

If PQRS is a convex quadrilateral with 3, 4, 5 and 6 points marked on sides PQ, QR, RS and PS respectively. Then, the number of triangles with vertices on different sides is

\(\lim_{x \to -1} \left( \frac{x^4 + x^2 + x + 1}{x^2 - x + 1} \right)^{\frac{1 - \cos(x+1)}{(x+1)^2}}\) is equal to

The term independent of \(x\) in the expansion of \(\left(x - \frac{1}{x}\right)^4 \left(x + \frac{1}{x}\right)^3\), is

If \(A\) is a square matrix such that \(A^2 = A\) and \((I + A)^n = I + \lambda A\), then \(\lambda\) is equal to

The functions \(u = e^x \sin x\) and \(v = e^x \cos x\) satisfy the equation

The derivative of \(\tan^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)\) with respect to \(\tan^{-1}\left(\frac{2x\sqrt{1-x^2}}{1-2x^2}\right)\) at \(x=0\), is

In a \(\triangle ABC\), if \(\begin{vmatrix} 1 & a & b \\ 1 & c & a \\ 1 & b & c \end{vmatrix} = 0\), then \(\sin^2 A + \sin^2 B + \sin^2 C\) is equal to

The area of the region enclosed by the curves \(y = x\), \(x = e\), \(y = \frac{1}{x}\) and the positive X-axis, is

The value of \(\lim_{x \to \infty} \left\{ \frac{a_1^{1/x} + a_2^{1/x} + .......... + a_n^{1/x}}{n} \right\}^x\) is