List of top Questions asked in COMEDK UGET- 2025

If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( a \neq 0 \) and \( \vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c}) \), \( |\vec{a}| = |\vec{c}| = 1 \), \( |\vec{b}| = 4 \) and \( |\vec{b} \times \vec{c}| = \sqrt{15} \), if \( \vec{b} - 2\vec{c} = \lambda \vec{a} \) then \( \lambda^2 \) equals:

The general solution of the differential equation \( (x-y)dy=(x+y)dx \) is

A line \(L_1\) passes through the points \( (h,k), (1,2) \) and \( (-3,4) \). The points \( (4,3) \) and \( (h,k) \) lie on the line \(L_2\). Given \(L_1 \perp L_2\), then \( (k-h) \) equals to

P is a point on the line joining the points \( (3,5,-1) \) and \( (6,3,-2) \). If \( y \)-coordinate of point P is 2, then \( x \)-coordinate will be

\( -\frac{2\pi}{5} \) is the principal value of

The variance of 25 observations is 8. If each observation is multiplied by 3, then the new variance of the resulting observations is

The least value of \( a \) such that the function \( x^2 + ax + 1 \) is increasing on \([1,2]\) is

Three fair dice are thrown. What is the probability of getting a total of 15 given that they exhibit three different numbers that are in arithmetic progression?

The digits of a three-digit number taken in an order are in geometric progression. If one is added to the middle digit, they form an arithmetic progression. If 594 is subtracted from the number, then a new number with the same digits in reverse order is formed. The original number is divisible by

\( 0.2 + 0.22 + 0.022 + \cdots \) up to \( n \) terms is equal to

The order of the differential equation \( \frac{d}{dz}\left[\left(\frac{dy}{dz}\right)^3\right]=0 \) is

The solution set of the system of inequalities \( 5-4x \leq -7 \) or \( 5-4x \geq 7,\ x \in R \) is

Find the value of \( \displaystyle \lim_{h \to 0} \frac{(a+h)^2 \sin(a+h) - a^2 \sin a}{h} \)

The solution of \( (x+\log y)dy+ydx=0 \) when \( y(0)=1 \) is