List of top Mathematics Questions asked in BITSAT

Roots of the equation \( x^2 + bx - c = 0 \) (\( b, c>0 \)) are:
Evaluate the integral: \[ I = \int \frac{x + 3}{(x + 4)^2} e^x \,dx \]
Simplify \( i^{57} + \frac{1}{i^{25}} \) and find its value:
The interval in which the function \( f(x) = 4x^2 + x \) is decreasing is:
If \( \int \frac{e^x (1 + \sin x)}{1 + \cos x} \, dx = e^x f(x) + C \), then \( f(x) \) is equal to:
A circle touches both the y-axis and the line \( x + y = 0 \). Then the locus of its center is:
Number of words from the letters of the word BHARAT in which B and H will never come together is:
A set A has 3 elements and another set B has 6 elements. Then:

The range of the function \( f(x) = \sqrt{3x^2 - 4x + 5} \) is: 
 

If one root of the equation \( x^2 + px + 12 = 0 \) is \( 4 \), while the equation \( x^2 + px + q = 0 \) has equal roots, then the value of \( q \) is:
The roots of the given equation \( (p - q)x^2 + (q - r)x + (r - p) = 0 \) are:
The number of solutions of the differential equation \[ \frac{dy}{dx} = \frac{y+1}{x-1} \] when \( y(1) = 2 \) is:
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
If the eccentricity and length of the latus rectum of a hyperbola are \( \frac{\sqrt{13}}{3} \) and \( \frac{10}{3} \) units respectively, then what is the length of the transverse axis?
Negation of the Boolean expression \( p \Leftrightarrow (q \Rightarrow p) \) is:
The probability of getting a sum greater than 7 when a pair of dice are thrown is:

x=logp and y=1/p differential equation

The equation of a common tangent to the parabolas \( y = x^2 \) and \( y = -(x - 2)^2 \) is:
The function \( f(x) = \tan^{-1}(\sin x + \cos x) \) is an increasing function in:
Bag P contains 6 red and 4 blue balls, and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?
Find the mean deviation about the mean for the data: \( 4, 7, 8, 9, 10, 12, 13, 17 \)
The derivative of \( e^{x^3} \) with respect to \( \log x \) is:
Find: \( \lim_{x \to 0} \frac{| \sin x |}{x} \)
If \[ A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix} \] and \[ kA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}, \] then the values of \( k \), \( a \), and \( b \) respectively are:

Solution of \( 2^x + 2^{|x|} \geq 2\sqrt{2} \) is: