List of top Mathematics Questions asked in Guru Gobind Singh Indraprastha University Common Entrance Test

If \( |a| < 1 \) and \( |b| < 1 \), then the sum of the series \[ a(a + b) + a^2(a^2 + b^2) + a^3(a^3 + b^3) + \cdots \]

The mid-point of the chord $2x + y - 4 = 0$ of the parabola $y^2 = 4x$ is

A line makes the same angle $\theta$ with each of the X and Z-axes. If the angle $\beta$ which it makes with Y-axis is such that $\sin^2 \beta = 3 \sin^2 \theta$, then $\cos^2 \theta$ equals

Let \( x_1 \) and \( x_2 \) be the roots of the equation \[ ax^2 + bx + c = 0 \quad (ac \neq 0) \] Find the value of \[ \frac{1}{x_1} + \frac{1}{x_2} \]

If $n$ is an integer, compute the value of the fraction \[ \frac{(1 + \theta)^n}{(1 - \theta)^{n-2}} \]

Gas is being pumped into a spherical balloon. Then, the rate at of $30 \, \text{ft}^3/\text{min}$ which the radius increases when it reaches the value 15 ft, is

The number of integral values of \( \lambda \) for which the equation \[ x^2 + y^2 - 2\lambda x + 2\lambda y + 14 = 0 \] represents a circle whose radius cannot exceed 6 is:

The solution of the differential equation \[ \frac{d^2y}{dx^2} + 3y = -2x \] is

If the numbers \( a_1, a_2, \ldots, a_n \) are different from zero and form an arithmetic progression, then \[ \frac{1}{a_1} + \frac{1}{a_2} + \frac{1}{a_3} + ... + \frac{1}{a_n} \] is equal to

The number of solutions of the equation \[ 3 \sin^2 x - 7 \sin x + 2 = 0 \] in the interval \( [0, 5\pi] \) is

The value of \[ \int_0^{\frac{\pi}{2}} \sin^7 \theta \cos^4 \theta \, d\theta \] is

The length of the axes of the conic \[ 9x^2 + 4y^2 - 6x + 4y + 1 = 0 \] are

The solution of the differential equation \[ (x^2 - yx^2) \frac{dy}{dx} + y^2 + xy^2 = 0 \] is

The number of real roots of \[ (6 - x)^4 + (8 - x)^4 = 16 \]

The expression \[ \left| (a + 1)^2 \, (b + 1)^2 \, (c + 1)^2 \right| \] is equal to

The function \( f:[0,3] \to [1,29] \) defined by \[ f(x) = 2x^3 - 15x^2 + 36x + 1 \] is