List of top Mathematics Questions

A vector \( \vec{A} = i + xj + 3k \) is rotated through an angle and is also doubled in magnitude resulting in \( \vec{B} = 4i + (4x - 2)j + 2k \). An acceptable value of x is
The value of integral \( \int_{-2}^{2} x e^{-2x^2} dx \) is
The area of an equilateral triangle with sides of length \( \alpha \) is
The number of three-letter words, with or without meaning, which can be formed using letters of the word 'VIRUS' without repetition of letters is
Three vectors are as follows: \[ \mathbf{a} = 3\hat{i} - 10\hat{j} + 7\hat{k}, \mathbf{b} = -9\hat{i} + 6\hat{j} - 47\hat{k}, \mathbf{c} = 11\hat{i} - 17\hat{k} \] The value of \((\mathbf{a} + \mathbf{b}) \cdot \mathbf{c}\) is
Choose the most appropriate option. If \(y = a^b x\), then
If the line \( x - 1 = 0 \) is the directrix of the parabola \( y^2 - kx + 8 = 0 \), then one of the values of \( k \) is
Find the distance from the point \( A(2, 3, -1) \) to the given straight lines \( 2x - 2y + z + 3 = 0 \) and \( 3x - 2y + 2z + 17 = 0 \).
Choose the most appropriate option. \(\lim_{x \to 1} x^{(1-x)}\) is equal to:
Evaluate the limit: \[ \lim_{x \to 0} \frac{1 - \cos 4x}{2 \sin^2 x + x \tan 7x} \]
Choose the most appropriate option. \[ \int_{-2}^{2} \frac{3x^7 - 2x^5 + x^3 - 3}{x^4 + 3x^2 + 1} \, dx \]
Find the area of the figure bounded by the parabola \( y^2 = 4x \) and \( x^2 = 4y \).
Evaluate the limit: \[ \lim_{x \to a} \frac{\log{(x^{a-1})}}{x-a} \]
Choose the most appropriate options. Let \( P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \} \) and \( Q = \{ \theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \} \). Then,
Three mutually tangent spheres of radius 1 rest on a horizontal plane. A sphere of radius 2 rests on them. What is the distance from the plane to the top of the larger sphere?
In how many ways can 10 identical objects be put in 8 distinct boxes in such that no box is empty?
In how many ways can 3 blue, 4 white and 2 red balls be distributed into 4 distinct boxes?
Let \( T_n \) denote the number of triangles which can be formed using the vertices of a regular polygon of \( n \) sides. If \( T_{n+1} - T_n = 21 \), then \( n \) equals
If \( \sin \theta + \csc \theta = 2 \), then the value of \( \sin^{10} \theta + \csc^{10} \theta \) is
The standard deviation of a data is 6, when each observation is increased by 1, then the standard deviation of the new data is
If the arithmetic mean of the following data is 7, then \( a + b = \) \[ \begin{array}{|c|c|c|c|c|} \hline x_i & 4 & 6 & 7 & 9 \\ f_i & a & 4 & b & 5 \\ \hline \end{array} \]
Is equal to $$ \left| \begin{matrix} b^2 + c^2 & c^2 + b^2 \\ c^2 & c^2 + a^2 \\ b^2 & a^2 + b^2 \end{matrix} \right| $$ 
Compute the determinant of the \(n \times n\) matrix whose elements are identified by the condition \(a_{ij} = \min(i,j)\), where \(i\) is the row number and \(j\) is the column number.
Let \( n \) be a 5-digit number and let \( q \) and \( r \) be the quotient and remainder respectively, when \( n \) is divided by 100. For how many values of \( n \) is \( q + r \) divisible by 11?
Determine the form of the conic section described by the equation \( x^2 + y^2 + 2xy - 8x + 8y = 0 \)