List of top Mathematics Questions

If \( A = \begin{pmatrix} 0 & 1 & -2 -1 & 0 & 3 2 & -3 & 0 \end{pmatrix} \), then \( A^{-1} \)

Area of the region bounded by the curve \( y = \sin\left(\frac{x}{2}\right) \) between \( -4\pi \) and \( 0 \) is

\( \int \log x^2 \, dx = \)

Distance of the point \( (-2,3) \) from the line \( 12x - 5y - 2 = 0 \) is \( \frac{41}{k} \). Then the value of \( k \) is

Equation of a circle whose area is 154 sq units and having \(2x-3y+12=0\) and \(x+4y-5=0\) as diameters is

Let \(A\) and \(B\) be two events such that one of the two events must occur. Given that the chance of occurrence of \(A\) is \( \frac{2}{3} \) the chance of occurrence of \(B\), then odds in favour of \(B\) is

If \(y=\sqrt{\frac{x}{a}}+\sqrt{\frac{a}{x}}\), then \(2xy\frac{dy}{dx}\) is equal to

Codes used in vehicle identification consists of two distinct English alphabets followed by two distinct digits from 1 to 9. How many of them end with an even number.

If \( A = \begin{pmatrix} 1 & -2 4 & 5 \end{pmatrix} \); \( f(t) = t^2 - 3t + 7 \) then \( f(A) + \begin{pmatrix 3 & 6 -12 & -9 \end{pmatrix} = \)}

For two matrices \(A\) and \(B\), given that \( A^{-1} = \frac{1}{8}B \) then inverse of \( (8A) \) is

\( \int \tan^2\left(5-\frac{x}{2}\right) dx = \)

A person writes four letters and addresses four envelopes. If the letters are placed in the envelopes at random, then the probability that not all letters are placed in the right envelope is

\( \int \frac{1}{\sqrt{9+8x-x^2}}\,dx = \varphi(x) + c \), then \( \varphi(x) = \)

The sum of three numbers is 6. Twice the third number, when added to the first number gives 7. On adding the sum of the second and third numbers to thrice the first number, we get 12. The above situation can be represented in matrix form as \( AX = B \). Then \( | \text{adj } A | \) is equal to

Let \( M \) be the set of all \( 2 \times 2 \) matrices with entries from the set \( R \) of real numbers. Then the function \( f : M \to R \) defined by \( f(A) = |A| \) for every \( A \in M \) is

If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( a \neq 0 \) and \( \vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c}) \), \( |\vec{a}| = |\vec{c}| = 1 \), \( |\vec{b}| = 4 \) and \( |\vec{b} \times \vec{c}| = \sqrt{15} \), if \( \vec{b} - 2\vec{c} = \lambda \vec{a} \) then \( \lambda^2 \) equals:

The general solution of the differential equation \( (x-y)dy=(x+y)dx \) is

P is a point on the line joining the points \( (3,5,-1) \) and \( (6,3,-2) \). If \( y \)-coordinate of point P is 2, then \( x \)-coordinate will be

A line \(L_1\) passes through the points \( (h,k), (1,2) \) and \( (-3,4) \). The points \( (4,3) \) and \( (h,k) \) lie on the line \(L_2\). Given \(L_1 \perp L_2\), then \( (k-h) \) equals to

The least value of \( a \) such that the function \( x^2 + ax + 1 \) is increasing on \([1,2]\) is

The digits of a three-digit number taken in an order are in geometric progression. If one is added to the middle digit, they form an arithmetic progression. If 594 is subtracted from the number, then a new number with the same digits in reverse order is formed. The original number is divisible by

\( -\frac{2\pi}{5} \) is the principal value of

Three fair dice are thrown. What is the probability of getting a total of 15 given that they exhibit three different numbers that are in arithmetic progression?

The variance of 25 observations is 8. If each observation is multiplied by 3, then the new variance of the resulting observations is

Find the value of \( \displaystyle \lim_{h \to 0} \frac{(a+h)^2 \sin(a+h) - a^2 \sin a}{h} \)