List of top Mathematics Questions

For $z \in C$ if the minimum value of $(| z -3 \sqrt{2}|+| z - p \sqrt{2} i |)$ is $5 \sqrt{2}$, then a value of $p$ is ______
If the vectors \( \vec{p} = (a+1)\hat{i} + a\hat{j} + a\hat{k},\ \vec{q} = a\hat{i} + (a+1)\hat{j} + a\hat{k} \) and \( \vec{r} = a\hat{i} + a\hat{j} + (a+1)\hat{k} \) are coplanar, then the value of \(a\) is _ _ _ _.
If \( A = \begin{bmatrix} 2 & -1 \\ -7 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 4 & 1 \\ 7 & 2 \end{bmatrix} \), then \( B^T A^T \) is:
An unbiased coin is tossed \(n\) times. If the probability of getting 5 heads is equal to the probability of getting 6 heads, then the probability of getting 3 heads is:
If the foot of the perpendicular drawn from the point \((2,0,1)\) on a line passing through \((\alpha,5,1)\) is \(\left(\frac{7}{3}, \frac{5}{3}, \frac{11}{4}\right)\), then \(\alpha\) is equal to _ _ _ _ _ _
If the lines \( \frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4} \) and \( \frac{x-3}{1} = \frac{y-k}{2} = \frac{z}{1} \) intersect, then \(k\) is equal to:
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:
Evaluate the integral: \[ I = \int \frac{x + 3}{(x + 4)^2} e^x \,dx \]
Simplify \( i^{57} + \frac{1}{i^{25}} \) and find its value:
If \( \int \frac{e^x (1 + \sin x)}{1 + \cos x} \, dx = e^x f(x) + C \), then \( f(x) \) is equal to:
The interval in which the function \( f(x) = 4x^2 + x \) is decreasing is: