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

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

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

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

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 area bounded by the curves $ y = \cos x $ and $ y = \sin x $ between the ordinates $ x = 0 $ and $ x = \frac{3\pi}{2} $ is

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

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

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

A differentiable function $ f(x) $ has a relative minimum at $ x = 0 $, then the function $ y = f(x) + ax + b $ has a relative minimum at $ x = 0 $ for

The maximum number of points into which 4 circles and 4 straight lines intersect, is

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

Consider line segments of lengths 1, 2, 3, ..., 10, what is the number of triangles that can be formed from them?

How many paths are there from the point A to the point B in the figure below, if no point in a path is to be traversed more than once?

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

A cell has been set up as shown in the following diagram and E$^0$ has been measured as 1.00V at 25°C. Calculate $\Delta$G$^0$ for the reaction.

Select the incorrect statement.