List of top Mathematics Questions

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 \(A = \{1,2,3,4,5,6,7\}\) 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:

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 \(a^2, b^2, c^2\) 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:

A circle touches both the y-axis and the line \( x + y = 0 \). Then the locus of its center is:

Number of words from the letters of the word BHARAT in which B and H will never come together is:

A thin particle moves from \((0,1)\) and gets reflected upon hitting the x-axis at \((√3,0)\). Then the slope of the reflected line is ?

If the median of the observations \(4,6,7,x,x+2,12,12,13\) arranged in an increasing order is 9,then the variance of these observations is 

In a linear programming problem ,the restrictions under which the objective function is to be optimized are called as?

A six faced fair die is rolled for a large number of times. Then, the mean value of the outcome is 

Let \(a,b,c,d \) be an increasing sequence of real numbers,which are in geometric progression .If \(a+d=112\) and \(b+c=48\) ,then the value of \(\dfrac{a+c+8}{b}\) is 

If\( \dfrac{1+sinx}{1-sinx}=\dfrac{(1+siny)^3}{(1-siny)^3}\) for some real values \(x\) and \(y\) ,then \(\dfrac{sinx}{siny}\)=