List of top Mathematics Questions asked in COMEDK UGET

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

Two lines \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} \) and \( \frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1} \) intersect at a point. Then the value of \( k \) is

The equation of a line passing through origin with direction angles \( \frac{2\pi}{3}, \frac{\pi}{4}, \frac{\pi}{3} \) is

A straight line makes positive intercepts on the coordinate axes whose sum is 5. If the line passes through the point \( P(-3,4) \) then the equation of the line is

Solve the following differential equation \( \cos^2 x \frac{dy}{dx} + y = \tan x \), given that \( y(0)=1 \). Hence find \( y\left(\frac{\pi}{4}\right) \)

If the foci of the ellipse \( \frac{x^2}{16}+\frac{y^2}{b^2}=1 \) and the foci of the hyperbola \( \frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25} \) coincide, then the value of \( b^2 \) is

If \( \tan \alpha=\frac{1}{7} \) and \( \sin \beta=\frac{1}{\sqrt{10}},\; 0<\alpha,\beta<\frac{\pi}{2} \) then \( 2\beta \) is equal to

If the line \( (3x + 14y + 7) + k(5x + 7y + 6) = 0 \) is perpendicular to x-axis then the value of \( k \) is

A pot contains 5 red and 2 green balls. A ball is drawn at random from this pot. If a drawn ball is green, then a red ball is added to the pot. If a drawn ball is red, then a green ball is added to the pot, while the original ball drawn is not replaced in the pot. Now a second ball is drawn at random from the pot, what is the probability that the second ball drawn is a red ball?

\( \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1+\sqrt{\tan x}}\,dx = \)

If \( P = \{5m : m \in N\} \) and \( Q = \{5^m : m \in N\} \), where \( N \) is set of natural numbers, then

The image of a point \( P(3,5,3) \) in the line \( \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) is \( P'(a,b,c) \). Then \( a+b+c = \)

How many natural numbers are there between 100 and 1000 such that at least one of their digits is 6?

If the area under the curve \( y=\sqrt{a^2-x^2} \) included between the lines \( x=0 \) and \( x=a \) is 4 sq units. Then the value of \( a \) is

If \( \vec{a} \) and \( \vec{b} \) are two vectors such that \( \vec{a}\cdot\vec{b} = |\vec{a}\times\vec{b}| \) then the angle between \( \vec{a} \) and \( \vec{b} \) is

The function \( y=\frac{\log x}{x^3} \) is strictly increasing function for

Given that \( n \) number of arithmetic means are inserted between two pairs of numbers \( a,2b \) and \( 2a,b \); where \( a,b \in R \). If the \( m^{th} \) means in the two cases are the same, then the ratio \( a:b \) is equal to

Two finite sets have \( m \) and \( n \) elements. The total number of proper subsets of the first set is 119 more than the total number of subsets of the second set. Find the value of \( m-n \)

\( \int_{-2}^{2} \frac{|x-3|}{x-3} dx = \)

If the length of the diagonal of a square is increasing at the rate of \( 0.1 \) cm/secWhat is the rate of increase of its area when the side is \( \frac{15}{\sqrt{2}} \) cm?

The relation \( R = \{(1,1),(2,2),(3,3)\ \) on the set \( \{1,2,3\} \) is}

The number of words that can be formed with the letters of the word 'DEFINITE' if two vowels are together and the other two are also together but separated from the first two is

In a game, a man wins \( ₹1000 \) if he gets an even number greater than or equal to 4 on a fair dice and loses \( ₹200 \) for getting any other number on the dice. If he decides to throw the dice until he wins or maximum of three times, then his expected gain/loss in \( ₹ \) is -----------