List of top Mathematics Questions asked in MET

The area bounded by the curves \( y = \tan x,\ -\frac{\pi}{3} \le x \le \frac{\pi}{3} \), \( y = \cot x,\ \frac{\pi}{6} \le x \le \frac{\pi}{2} \) and the X-axis is:
The area of the region bounded by the curves \( y = |5 - x| \), \( x = 1 \), \( x = 6 \) and the X-axis is:
If \( \int f(x)\,dx = g(x) \), then \( \int \cos x \, f(\sin x)\,dx \) is equal to:
Set of values of \(x\) lying in \([0,2\pi]\) satisfying the inequality \( |\sin x|>2\sin^2 x \) contains:
Let \( f(x) = \frac{1}{\sqrt{1 + x^2}} \), then:
Let \(A = \{1,2,3,4,5,6,7\}\) and \(B = \{3,6,7,9\}\). Then, the number of elements in the set \(\{ C \subseteq A : C \cap B \neq \phi \}\) is:
If \( \sum_{i=1}^{9} (x_i - 5) = 9 \) and \( \sum_{i=1}^{9} (x_i - 5)^2 = 45 \), then the standard deviation of the 9 items \(x_1, x_2, \ldots, x_9\) is:
The value of \( \lim_{x \to 0} \left(\frac{e^x + 2^x + 4^x}{3}\right)^{\frac{2}{x}} \) is:
If \( f : \mathbb{R} \to \mathbb{R} \) is a differentiable function and \( f(3) = 6 \), then \[ \lim_{x \to 3} \frac{\displaystyle \int_{6}^{f(x)} \frac{2t \, dt}{t - 2}}{x - 3} \text{ is equal to} \]
The differential equation of all circles which pass through the origin and whose centres lie on Y-axis is:
Last two digits in \(9^{50}\) are _ _ _ _ _.
If the coefficients of \(x^3\) and \(x^4\) in the expansion of \((1 + ax + bx^2)(1 - 2x)^{18}\) are both zero, then \((a,b)\) is equal to
If \(a^2, b^2, c^2\) are in A.P., then \(b+c, c+a, a+b\) are in:
The number of words (with or without meaning) that can be formed from all the letters of the word "LETTER" in which vowels never come together is _ _ _ _ _ .
If complex number \(z\) lies in the interior or on the boundary of circle of radius 3 units, then maximum and minimum values of \(|z + 1|\) are:
If the lines \( \frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k} \) and \( \frac{x-1}{2k} = \frac{y-3}{2} = \frac{z-5}{1} \) are coplanar, then \( k \) can have
If \[ \begin{vmatrix} a & a^2 & 1+a^3 b & b^2 & 1+b^3 c & c^2 & 1+c^3 \end{vmatrix} = 0 \] and vectors \( (1,a,a^2), (1,b,b^2), (1,c,c^2) \) are non-coplanar, then the product \( abc \) is ___.
If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is \( p \), then \( 96p \) is equal to ___.
A multiple choice examination has 5 questions. Each question has 4 alternatives of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing is
If the foot of the perpendicular drawn from the point \( (0,2,1) \) on a line passing through \( (a,5,1) \) is \( \left(\frac{5}{3}, \frac{7}{3}, \frac{15}{3}\right) \), then \( a \) is equal to ___.
The area of the region described by \( A = \{(x,y) : x^2 + y^2 \le 1 \text{ and } y^2 \le 1 - x \} \) is
The area of the region bounded by the curves \( y = |x - 2| \), \( x = 1 \), \( x = 3 \) and the x-axis is
If \( \int f(x)\,dx = g(x) \), then \( \int x^9 f(x^5)\,dx \) is equal to
For what value of \( \theta \) lying between \(0\) and \( \pi \) which satisfy inequality \( \sin\theta \cos^3\theta>\sin^3\theta \cos\theta \)
Let \( f(x) = \sqrt{1 + x^2} \), then