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

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On the sphere $ (x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 25 $, find the point $ M_0 $ to the plane $ 3x - 4z + 19 $.

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The limit \[ \lim_{x \to 0} \frac{1 - \cos 2x}{x \tan 4x} \]

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If $ A(2,3) $ and $ B(-2,1) $ are two vertices of a triangle and the third vertex moves on the line $ 2x + 3y = 9 $, then the locus of the centroid of the new set of observations will be the triangle is

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\[ \lim_{x \to 0} \frac{\ln \cos 2x}{\sin 2x} \]

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Let $ f(x) = ax^3 + 5x^2 - bx + 1 $. If when divided by $ x - 1 $ it leaves a remainder of 5, and $ f(x) $ is divisible by $ 3x - 1 $, then

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If the SD of a set of observations is 8 and each observation is divided by -2, then the SD of the new set of observation will be:

Choose the most appropriate option. \[ \lim_{x \to 1} \sin(x - 1) \cdot \tan\left( \frac{\pi}{x} \right) \]

The set of values of $ x $ satisfying the system of inequalities $ 5x + 2 < 3x + 8 $ and $ \frac{x^2}{x-1} < 4 $ is:

Three points are chosen randomly and independently on a circle. What is the probability that all three pairwise distances between the points are less than the radius of the circle?

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

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

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

If the tangent at (1,1) on $ y^2 = x(2 - x^2) $ meets the curve again at P, then P 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

The equation of a straight line passing through the point of intersection of $ x - y + 1 = 0 $ and $ 3x + y - 5 = 0 $ and perpendicular to one of them, 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

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