List of top Mathematics Questions asked in MET

The radical centre of the system of circles, \[ x^2 + y^2 + 4x + 7 = 0,\quad 2(x^2 + y^2) + 3x + 5y + 9 = 0 \] and \(x^2 + y^2 + y = 0\) is
Roots of equation \(x^3 - 6x + 1 = 0\) lie in the interval
If one regression coefficient is less than unity, then the other will be:
Let \[ f(x) = \begin{vmatrix} \sin 3x & 1 & 2\left(\cos \frac{3x}{2} + \sin \frac{3x}{2}\right)^2 \cos 3x & -1 & 2\left(\cos \frac{3x}{2} - \sin \frac{3x}{2}\right)^2 \tan 3x & 4 & 1 + 2\tan 3x \end{vmatrix} \] Then \(f(x)\) is equal to
Condition for line \(lx + my + n = 0\) to be a normal to \(\frac{x^2}{25} + \frac{y^2}{9} = 1\):
The least value of \(a\), for which the function \[ \frac{4}{\sin x} + \frac{1}{1-\sin x} = a \] has at least one solution in the interval \(\left(0,\frac{\pi}{2}\right)\), is:
Three concurrent edges of a parallelepiped are given by \[ \vec{a} = 2\hat{i} - 3\hat{j} + \hat{k},\quad \vec{b} = \hat{i} - \hat{j} + 2\hat{k},\quad \vec{c} = 2\hat{i} + \hat{j} - \hat{k}. \] The volume of the parallelepiped is:
Let \(f(x)\) be differentiable on the interval \((0,\infty)\) such that \(f(1)=1\) and \[ \lim_{t \to x} \frac{t^2 f(x) - x^2 f(t)}{t - x} = 1 \quad \text{for each } x>0. \] Then, \(f(x)\) is equal to
The locus of centre of circles which cut orthogonally the circle \(x^2 + y^2 - 4x + 8 = 0\) and touches \(x + 1 = 0\), is
Probability of getting sum 7 or 9 when two dice are thrown is:
The coefficient of \(x^4\) in \((1 + x + x^3 + x^4)^{10}\) is
If \[ \int \sin^2 t \tan^{-1}\sqrt{\frac{1-x}{1+x}}\,dx = A\sin^{-1}x + B\sqrt{1-x^2} + C, \] then \(A+B\) is equal to
If point \(D\) divides base \(BC\) of \(\triangle ABC\) in ratio \(m:n\), then value of \(mBD^2 + nCD^2 + (m+n)AD^2\) is:
Equation of tangent to the circle \(x^2 + y^2 - 2x - 2y + 1 = 0\) perpendicular to \(y = x\) is given by
A man is standing on the horizontal plane. The angle of elevation of top of the pole is \(\alpha\). If he walks a distance double the height of the pole, then the elevation of the pole is \(2\alpha\). The value of \(\alpha\) is
If \( f(x) = \begin{cases} \frac{\sin |x|}{x}, & \text{for } [x] \ne 0 \\ 0, & \text{for } [x] = 0 \end{cases} \) where, \([x]\) denotes the greatest integer less than or equal to \(x\), then \(\lim_{x \to 0} f(x)\) is equal to
If \( f(x) > 0 \; \forall x \in \mathbb{R} \), \( f'(3) = 0 \) and \( g(x) = f(\tan^2 x - 2\tan x + 4) \), \( 0 < x < \frac{\pi}{2} \), then \( g(x) \) is increasing in
Equation of a plane passing through \((-1,1,1)\) and \((1,-1,1)\) and perpendicular to \(x + 2y + 2z - 5 = 0\) is
The value of the angle between two straight lines is \(y = (2 - \sqrt{3})x + 5\) and \(y = (2 + \sqrt{3})x - 7\) is
If \(A\) and \(B\) are two such events that \(P(A \cup B) = P(A \cap B)\), then which of the following is true?
If \(f(x) = \begin{cases} x, & 0 \le x \le 1 \\ 2x - 1, & 1<x \end{cases}\), then
If \(I_n = \int \sin^n x dx\), then \(nI_n - (n - 1)I_{n-2}\) equals
The remainder obtained when \(5^{124}\) is divided by 124 is
The adjoining graph
If \(x\) follows a binomial distribution with parameters \(n = 100\) and \(p = \frac{1}{3}\), then \(P(X = r)\) is maximum when \(r\) equals