List of top Mathematics Questions asked in COMEDK UGET

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

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

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?

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

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 ?

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

A bag contains \(5\) red balls and \(3\) blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?

The number of relations, defined on the set {a, b, c, d which are both reflexive and symmetric, is equal to:}

A coach needs to select a \(4\)-player starting lineup from a pool of \(10\) players consisting of:
• \(5\) guards
• \(3\) forwards
• \(2\) centres Find the number of different selections if the lineup must include:
• At least \(1\) guard
• At most \(1\) forward
• Exactly \(1\) centre

Evaluate: \[ \int \tan^{-1}\left( \sqrt{\frac{1-\sin x}{1+\sin x}} \right)\,dx \]

If the projection of \[ \vec a = 5\hat i+\hat j+\lambda\hat k \] on \[ \vec b = 2\hat i+6\hat j+3\hat k \] is \(4\) units, then \(\lambda=\)

Find the area bounded by the curve \(y=|2-x|\), the \(x\)-axis, and the lines \(x=0\) and \(x=5\).

If \[ A= \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, \qquad B= \begin{bmatrix} 2 & 0 \\ 1 & 5 \end{bmatrix} \] then \(AB\) is equal to:

If \[ \vec{a}=2\hat{i}-\hat{j}+3\hat{k} \] and \[ \vec{b}=\hat{i}+4\hat{j}-2\hat{k}, \] then \(\vec{a}\cdot\vec{b}\) is equal to:

The polynomial \[ p(x)=x^4-5x^2+4 \] has:

If the arithmetic mean between two positive numbers is \(10\) and the geometric mean is \(8\), then the numbers are:

Evaluate: \[ \lim_{x\to \frac{\pi}{2}} \left( \frac{1-\sin x}{\cos x} \right) \]

The variance of a set of 20 observations is \(16\). If \(7\) is added to each observation, and then \(5\) is subtracted from each resulting observation, what will be the new standard deviation?

The second derivative of \( \sin 3x \cos 5x \) is:

If \[ y=\tan^{-1}\left( \frac{\sqrt{1+x^3}+\sqrt{1-x^3}} {\sqrt{1+x^3}-\sqrt{1-x^3}} \right) \] then \(\dfrac{dy}{dx}\) is equal to:

A line \(L\) passes through the point of intersection of the lines \(3x+y-10=0\) and \(x-y-2=0\). If the perpendicular distance of the line \(L\) from the point \((5,1)\) is exactly \(\dfrac{2}{\sqrt{5}}\) units, which of the following represents the equation of line \(L\)?

The conjugate of the multiplicative inverse of the complex number \[ z=\frac{1+7i}{3+i} \] is:

If \[ (\vec a+\vec b)\perp \vec b \quad \text{and} \quad (\vec a+2\vec b)\perp \vec a, \] then

Let the line \( l_1 \) be a line passing through the point \( (0,-6) \) and making an angle of \(150^\circ\) with the positive \(x\)-axis. The equation of a line \( l_2 \) parallel to \( l_1 \) and crossing the \(y\)-axis at a distance \(2\) units below the origin is:

Evaluate the integral \[ \int_{0}^{\frac{\pi}{2}} \frac{3\sin x+4\cos x}{\sin x+\cos x}\,dx \]