List of top Mathematics Questions

If \( \alpha = \frac{\pi}{4} \), find \( (\sin \alpha + \sin \beta)^2 + (\cos \alpha + \cos \beta)^2 \).

Number of words that can be formed starting and ending with the same letter from the word BANANA.

Number of ways 3 boys and 4 girls can be arranged such that there is one girl between any 2 boys and one boy between any 2 girls.

If \(y = 4\sqrt{x}\) then \(\frac{d^2y}{dx^2} =\)

Find the value of \( \tan(105^\circ) \) using compound angle identities.

The converse of the statement \( ((\sim p) \land q) \rightarrow r \) is:

If \(A\) is a \(3\times3\) matrix such that \(|A| = 4\) and \(B = \text{adj}\,A\), find the value of \(|B|\).

Consider two matrices \(A=\begin{bmatrix}3 & -4 1 & -1\end{bmatrix}\) and \(B=\begin{bmatrix}6 & -13 5 & -10\end{bmatrix}\). If the following matrix equation holds true: \[ \left((A^{-1})^2 + B\right)\begin{bmatrix}x y\end{bmatrix} = \begin{bmatrix}0 0\end{bmatrix} \] Find the values of \(x\) and \(y\).

Evaluate the following indefinite integral: \[ \int \sin(\log x)\,dx \]

Arrange the following words in a meaningful order: 1. Hectogram, 2. Milligram, 3. Decagram, 4. Tonne, 5. Decigram

Find the unit vector perpendicular to both \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + 2\hat{j} - 3\hat{k} \).

Prove that: \(\frac{\sec^3 \theta}{\sec^2 \theta - 1} + \frac{\csc^3 \theta}{\csc^2 \theta - 1} = \sec \theta \cdot \csc \theta (\sec \theta + \csc \theta)\)

If \( y = \sin^{-1}(3x - 4x^3) \), find \( \dfrac{dy}{dx}. \)

What is the order of the differential equation \( \dfrac{d^2 y}{dx^2} + \left(\dfrac{dy}{dx}\right)^3 = 0 \)?

Find the slope of the normal to the curve \(y = 2x^2 + 3\sin x\) at \(x = 0\).

Evaluate \( \int \log x \, dx \).

If the line \( 2x - 3y + c = 0 \) passes through the focus of the parabola \( x^2 = -8y \), then the value of \( c \) is equal to:

A straight line passing through (6,1,3) meets the line \( \frac{x-1}{2} = \frac{y}{1} = \frac{z-2}{3} \) at Q. If the lines are perpendicular to each other, then the coordinates of Q are:

The three vertices of a triangle are \( (0,0), (3,1) \) and \( (1,3) \). If this triangle is inscribed in a circle, then the equation of the circle is:

Let \( U \) be the universal set and let \( A \) and \( B \) be any two subsets of \( U \). If \( n(U) = 25, n(A) = 14, n(A \cap B) = 6 \) and \( n(A \cup B) = 20 \), then \( n(B') \) is equal to:

Five digit number is formed using the digits 0, 1, 2, 3, 4, and 5 without repetitions. Number of five digit numbers which are divisible by 10 is:

The 25th term of 9, 3, 1, \( \frac{1}{3} \), \( \frac{1}{9} \), ... is:

Find the area of the region bounded by the curve \(y^2 = 4x\) and the line \(x = 3\).

Evaluate the integral: \( \displaystyle \int \frac{4x^2 \cot^{-1}(x^3)}{1+x^6}\,dx \) (where \(C\) is a constant of integration).

A trader has three different types of oils of volume \(870 \text{ l}\), \(812 \text{ l}\) and \(638 \text{ l}\). Find the least number of containers of equal size required to store all the oil without getting mixed.