List of top Mathematics Questions asked in OJEE

Consider the function
\[ f(x) = \begin{cases} \frac{\log(1+3x) - \log(1-2x)}{x}, & x \neq 0 \\ k, & x = 0 \end{cases} \] If \( f \) is continuous at \( x = 0 \), then the value of \( k \) must be

The solution of the differential equation \( \frac{d^2 y}{dx^2} + y = 0 \) with \( y(0) = 1, y\left( \frac{\pi}{2} \right) = 2 \) is

The general solution of the differential equation \( \frac{dy}{dx} = \frac{y}{x} + \tan \frac{y}{x} \) is

Curve generated by a point on the circumference of a circle which rolls along a straight line is termed:

The solution of the differential equation \( \frac{dy}{dx} = \frac{x + y}{x} \) satisfying \( y(1) = 1 \) is

The solution of the differential equation \( y \, dx + (x + x^2 y) \, dy = 0 \) is

The solution of the differential equation \( \frac{d^2 y}{dx^2} - 3 \frac{dy}{dx} + 2y = 0 \) is given by

If the vectors \( 2\hat{i} - 3\hat{j} + \hat{k} \) and \( 3\hat{i} - 4\hat{j} - \hat{k} \) form three concurrent edges of a parallelepiped, then the volume of the parallelepiped is

Let \( \vec{x} \) and \( \vec{y} \) be two unit vectors and \( \theta \) is the angle between them. Then \( \vec{x} + \vec{y} \) is a unit vector if

The distance between the lines \( 3x - 4y + 2 = 0 \) and \( 3x - 4y - 8 = 0 \) is

If the line \( y = mx \) does not intersect the circle \( (x + 10)^2 + (y + 10)^2 = 180 \), then a possible value of \( m \) is

For complex numbers \( z \), if \( |z| = 1 \), then the value of \( \frac{z-1}{z+1} \) is

If \( (1+x)^n = C_0 + C_1 x + C_2 x^2 + \dots + C_n x^n \), then \( C_0 + \frac{C_1}{2} + \frac{C_2}{3} + \dots + \frac{C_{10}}{11} \) is

If \( z = \cos\theta + i \sin\theta \), then the value of \( z^{100} + \frac{1}{z^{100}} \) is

The number of 3 digit numbers that can be formed with \( S = \{0,1,2,3,\dots,8\} \) when repetitions are allowed is

From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. The number of ways this can be done is

The value of \[ \int \sin(\log x) \, dx + \int \cos(\log x) \, dx \] \text{is equal to}

The number of terms in the expansion of \( (2x + 3y + 5z)^5 \) is

Consider the following statements: Statement I: \( 5 + 8 = 12 \) or 11 is a prime. Statement II: Sun is a planet or 9 is a prime. Which of the following is true?

The value of \[ \lim_{x \to \infty} \left( e^x + e^{-x} - e^x \right) \] \text{is equal to}

The standard deviation of the observations 1; 2; 3; 4; 4; 5; 5; 5; 8 is

The points on the curve \( y = 2x^3 + 3x^2 - 8x \) where the tangents are parallel to the line \( y = 4x + 3 \) are

The position vectors of the vertices of a triangle are \( 4\hat{i} + 5\hat{j} + \hat{k} \), \( 2\hat{i} + 4\hat{j} - \hat{k} \) and \( 3\hat{i} + 6\hat{j} - 3\hat{k} \). Then the triangle is

Local maximum and local minimum values of \( f(x) = (x-1)^2(x+2) \) are attained respectively at

The equation of the normal to the curve \( y = x + \frac{1}{x} \) at the point where \( x = 2 \) is