List of top Mathematics Questions

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

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

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

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

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

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

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

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

The order of the differential equation \( \frac{d}{dz}\left[\left(\frac{dy}{dz}\right)^3\right]=0 \) is

\( 0.2 + 0.22 + 0.022 + \cdots \) up to \( n \) terms is equal to

The solution set of the system of inequalities \( 5-4x \leq -7 \) or \( 5-4x \geq 7,\ x \in R \) is

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

The solution of \( (x+\log y)dy+ydx=0 \) when \( y(0)=1 \) is

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = \(0.007x^3 - 0.003x^2 + 15x + 400\). The marginal cost when 10 items are produced is:

Find the value of \( x \) in the equation \( 2x + 3 = 7x - 8 \).

Evaluate the following integrals: \[ \int \frac{(x^4 + 1)}{x(2x + 1)^2} \, dx \] and \[ \int \frac{1}{x^4 + 5x^2 + 6} \, dx \]

The domain of the function \( f(x) = \left(\sqrt{8x - x^2 - 7}\right)^{\frac{3}{2}} \) is:

If \(x = \frac{1 + \cos 2\theta}{\tan \theta - \sec \theta}\) and \(y = \frac{\tan \theta + \sec \theta}{\sec^2 \theta}\), then \(\frac{y}{x}\) is equal to: