List of top Questions asked in BITSAT

If the system of linear equations:
\[ 2x + y - z = 7 \] \[ x - 3y + 2z = 1 \] \[ x + 4y + \delta z = k \] has infinitely many solutions, then \( \delta + k \) is:

If \( A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \), \( P = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} \) and \( X = A P A^T \), then \( A^T X^{50} A \) is:

Suppose \( p, q, r \neq 0 \) and the system of equations:
\[ (p + a)x + by + cz = 0 \] \[ ax + (q + b)y + cz = 0 \] \[ ax + by + (r + c)z = 0 \] has a non-trivial solution, then the value of \[ \frac{a}{p} + \frac{b}{q} + \frac{c}{r} \] is:

The variance of 20 observations is 5. If each observation is multiplied by 2, then the new variance of the resulting observation is:

The system of equations:
\[ x - y + 2z = 4 \] \[ 3x + y + 4z = 6 \] \[ x + y + z = 1 \] has:

If A and B are symmetric matrices of the same order such that \( AB + BA = X \) and \( AB - BA = Y \), then \( (XY)^T = \)

The mean of \( n \) items is \( X \). If the first item is increased by 1, second by 2, and so on, the new mean is:

The number of real solutions of
\[ \sqrt{5 - \log_2 |x|} = 3 - \log_2 |x| \] is:

Number of subsets of set of letters of word 'MONOTONE' is:

If \( \cot(\cos^{-1} x) = \sec \left( \tan^{-1} \left( \frac{a}{\sqrt{b^2 - a^2}} \right) \right) \), then:

Let \( [x] \) denote the greatest integer \( \leq x \). If \( f(x) = [x] \) and \( g(x) = |x| \), then the value of:
\[ f \left( g \left( \frac{8}{5} \right) \right) - g \left( f \left( \frac{-8}{5} \right) \right) \] is:

Consider the following two propositions: \[ P_1: \neg (p \rightarrow \neg q) \] \[ P_2: (p \wedge \neg q) \wedge ((\neg p) \vee q) \] If the proposition \( p \rightarrow ((\neg p) \vee q) \) is evaluated as FALSE, then:

In a statistical investigation of 1003 families of Calcutta, it was found that 63 families have neither a radio nor a TV, 794 families have a radio, and 187 have a TV. The number of families having both a radio and a TV is:

If the function \( f(x) \), defined below, is continuous on the interval \([0,8]\), then: \[ f(x) = \begin{cases} x^2 + ax + b, & 0 \leq x < 2 \\ 3x + 2, & 2 \leq x \leq 4 \\ 2ax + 5b, & 4 < x \leq 8 \end{cases} \]

ABC is a triangular park with \( AB = AC = 100 \) m. A TV tower stands at the midpoint of \( BC \). The angles of elevation of the top of the tower at \( A, B, C \) are \( 45^\circ, 60^\circ, 60^\circ \) respectively. The height of the tower is:

The altitude of a cone is 20 cm and its semi-vertical angle is \(30^\circ\). If the semi-vertical angle is increasing at the rate of \(2^\circ\) per second, then the radius of the base is increasing at the rate of:

The function \[ f(x) = \frac{\cos x}{\left\lfloor \frac{2x}{\pi} \right\rfloor + \frac{1}{2}}, \] where \( x \) is not an integral multiple of \( \pi \) and \( \lfloor \cdot \rfloor \) denotes the greatest integer function, is:

The function f: R\(\rightarrow\) R is defined by \[ f(x) = \frac{x}{\sqrt{1 + x^2}} \] is:

Evaluate the integral: \[ \int \frac{x^3 - 1}{x^3 + x} dx \]

Given that \( f(x) = \sin x + \cos x \) and \( g(x) = x^2 - 1 \), find the conditions under which \( g(f(x)) \) is invertible.

The maximum area of a rectangle inscribed in a circle of diameter \( R \) is:

The domain of the real-valued function
\[ f(x) = \sqrt{\frac{2x^2 - 7x + 5}{3x^2 - 5x - 2}} \] is:

If \( x\sqrt{1 + y} + y\sqrt{1 + x} = 0 \), then find \( \frac{dy}{dx} \).

Consider the function \( f(x) = \frac{|x-1|{x^2} \). Then \( f(x) \) is:}