List of top Mathematics Questions asked in COMEDK UGET

If the determinant of the matrix \[ \begin{vmatrix} 1 & 2 \\ 3 & x \end{vmatrix} \] is equal to $-2$, then the value of $x$ is:

If the matrix \[ M= \begin{bmatrix} x+5 & a & -4 \\ -2 & 0 & b \\ c & 6 & y+1 \end{bmatrix} \] is a skew-symmetric matrix, then the value of \[ ab+c^2-xy \] is:

The domain of the function \[ f(x)=\sin^{-1}(\sqrt{x-1}) \] is:

Let \(f:\mathbb{R}\to\mathbb{R}\) be defined by \[ f(x)=x^3-3x+1 \] Then the function \(f\) is:

The function \(f(x)=|x|+|x-1|\) is:

The area enclosed by the curve \(y=-x^2\) and the line \(x+y+2=0\) is:

A student needs to buy notebooks (\(n\)) for a semester. Double the number of notebooks plus \(5\) must strictly exceed \(15\), but the number of notebooks plus \(10\) must be no more than \(22\). What is the range of notebooks they can buy?

Let $A=[a_{ij}]$ be a square matrix of order $3\times3$, where \[ a_{ij}= \begin{cases} i-2j, & i=j \\ 0, & i>j \\ 1, & i<j \end{cases} \] Then the value of $|A^T|$ is:

If \(f(x)=x^3-3x^2+1\), then the interval in which the function is decreasing is:

A coffee roaster has 12 rare coffee beans with intensity scores ranked from 1 (mildest) to 12 (strongest). You choose 7 beans at random and line them up from mildest to strongest: \(C_1<C_2<C_3<C_4<C_5<C_6<C_7\). What is the probability that the third bean \(C_3\) has an intensity score of exactly 4?

The function \[ f(x)=e^{ax}+e^{-ax}, \quad x\in R \] and \(a<0\), is strictly decreasing for all values of \(x\), where:

The whole area surrounded by the curve with the equations $x = a \cos^3 t, y = b \sin^3 t$ is:

A square matrix P satisfies \(P^2 = I - P\). If \(P^n = 5I - 8P\) then n is equal to

The mean of some observations is 54. If each observation is increased by 8 and its sum is divided by 2, then what is the mean of the resulting observations?

Two numbers P and Q are selected from Set {1,2,3,.....,100\,then find the probability of P.Q is divisible by 5.}

If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4 , then the sum of its first twelve terms is

Let \(n(A) = m\) and \(n(B) = n\), if the number of subsets of A is 56 more than of subsets of B, then \(m + n\) is equal to

Out of 8 students in Section Alpha, 10 students in Section Beta and 12 students in Section Gamma, a teacher wants to create a team of three to represent the school in inter-school quiz competition. In how many ways the team can be formed such that all the members of the team are not from the same section ?

The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm minute. The rate of change of lateral surface when the radius = 7 cm and altitude = 24 cm, is

The standard deviation of 100 observations is 10. If 20 is added to each observation, then what will be the new standard deviation?

How many 4-digit numbers that are divisible by 4 can be formed using the digits 1, 2, 3 and 4 (repetition of digits is not allowed)?

If \( A = \begin{bmatrix} 4 & \lambda & -3 0 & 2 & 5 1 & 1 & 3 \end{bmatrix} \), then \( A^{-1} \) exists if:

Solution of the differential equation \( \frac{dy}{dx} + x = 0 \) represents a family of

For any vector \( \vec{p} \), the value of \( 2\left[|\vec{p}\times \hat{i}|^2 + |\vec{p}\times \hat{j}|^2 + |\vec{p}\times \hat{k}|^2\right] \) is

If \( y = x + e^x \) then \( \frac{d^2 x}{dy^2} = \)