List of top Questions asked in COMEDK UGET

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

The expression \[ \frac{\tan\left(x-\frac{\pi}{2}\right)\cos\left(\frac{3\pi}{2}+x\right)-\sin^2\left(\frac{7\pi}{2}-x\right)} {\cos\left(x-\frac{\pi}{2}\right)\tan\left(\frac{3\pi}{2}+x\right)} \] simplifies to:

The function \[ x+y=\tan^{-1}y \] is the solution of which of the following differential equations?

The absolute maximum and minimum values of the function \[ f(x)=\sin x+\sqrt3\cos x,\quad x\in[0,\pi] \] are:

Let point \( Q \) be the image of point \( P(2,-1) \) in the line \[ 3x+5=4y. \] Find the area of the circle that has the segment \( PQ \) as the diameter.

Every term of a geometric progression is positive, and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is:

Cards are numbered from \(12\) to \(51\). Two cards are drawn one after the other without replacement. Find the probability that one card is a multiple of \(6\) and the other card is a multiple of \(8\).