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

The variance of the following grouped data is:

For what value of \( \alpha \), the matrix A is a singular matrix if \(A=\begin{bmatrix} 1 & 3 & \alpha+2 \\[0.3em] 2 & 4 & 8 \\[0.3em] 3 & 5 & 10 \end{bmatrix}\) ?

In how many ways we can select a group of 2 males and 2 females from the family of 5 males and 3 females?
The number of permutations of word DEPENDENT is:

The eccentricity of \((\frac {x}{25})^2 + (\frac {y}{16})^2 = 1\) is:

Note: Assuming the intended equation is \( \frac{x^2}{25} + \frac{y^2}{16} = 1 \) based on the options. The literal interpretation \( \frac{x^2}{625} + \frac{y^2}{256} = 1 \) yields\(e =\frac {\sqrt{369}}{25}\), which is not among the options.

Find the equation of circle with center at \( (2, 5) \) and radius 5 units.
In what ratio the segment joining \( (-1, -12) \) and \( (3, 4) \) divided by x-axis?

If \( A \), \( B \), and \( C \) are any three arbitrary events such that \(P(A) = P(B) = P(C) = \frac{1}{4}\), \( P(A \cap B) = P(B \cap C) = 0 \), and \( P(C \cap A) = \frac{1}{8} \), find the probability that at least one of the events \( A \), \( B \), or \( C \) occur.}

If \( a \), \( b \), \( c \) are nonzero vectors such that \( a = 8b \) and \( c = -7b \), then the angle between \( a \) and \( c \) is:
If \( x^2 + ax + b = 0 \) and \( x^2 + bx + a = 0 \) have exactly one common root, then the value of \( (a + b) \) is:
If \( \sin y = x \sin(a + y) \), then \( \frac{dy}{dx} \) is:
If \( \int \sec^2(7 - 4x) \, dx = \tan(7 - 4x) + C \), then the value of \( a \) is:
The number of four-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5 with at least one digit repeated is:
A point on the curve \( y = x^3 - 3x \), where the tangent is parallel to the chord joining \( (1, -2) \) and \( (2, 2) \), is:
If \( A \) is the set of even natural numbers less than 8 and \( B \) is the set of prime numbers less than 7, then the number of relations from \( A \) to \( B \) is:
The value of \( x \), if \( \left| 5^2 - 4 \right| = 12x - 4 \), is:
The area of the figure bounded by the curve \( y = \log_e x \), the x-axis and the straight line \( x = e \) is
The pair of equations \( x + 3y = 6 \) and \( 2x - 3y = 12 \) :
Which of the following statements is false?
If A is a \( 3 \times 3 \) matrix, \( |A| \neq 0 \) and \( |3A| = k |A| \), then the values of k is:
The coefficient of variation of the two frequency distributions is 60% and 40% respectively. Both series have the same mean = 15. What is their standard deviation?
If \( \vec{A}, \vec{B} \) are unit vectors. If \( \vec{C} = \vec{A} + 2\vec{B} \) and \( \vec{D} = 5\vec{A} - 4\vec{B} \) are perpendicular, then angle between \( \vec{A} \) and \( \vec{B} \) is:
If a, b, c are nonzero vectors such that a=8b, and c= -7b, then the angle between a and c is:
The solution of the equation \( |z| = z + 1 + 2i \) is:
If a= (1, 1, 1), b= (x, y, z), c= (0, 1, -1) are three vectors such that \( a \cdot b = 3, a \times b = c \), then b is