List of top Questions asked in BITSAT- 2013

The determinant \[ \left| \begin{matrix} 1 & x & x^2 \\ 1 & x^3 & x^4 \\ 1 & x^5 & x^6 \end{matrix} \right| \] vanishes for

If \( \alpha \) and \( \beta \) are the roots of \( x^2 - x + 1 = 0 \), then the equation whose roots are \( \alpha^{100} \) and \( \beta^{100} \) is

\[ \int \frac{1}{(x^2 + 1)^{\frac{3}{4}}} \, dx \] is equal to

Find the variance of the data given below \[ \text{Size of item:} \quad 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5 \\ \text{Frequency:} \quad 3, 7, 22, 60, 85, 32, 8 \]

If \( y = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots + \infty \), then

The equation of all lines having slope 2 which are tangent to the curve \( y = \frac{1}{x - 3} \), is

Let \( R \) be the relation on the set \( \mathbb{R} \) of all real numbers, defined by \( aRb \) if \( |a - b| \leq 1 \). Then, \( R \) is

If the value of mode and mean is 60 and 66 respectively, then the value of median is

If \( f(x) = \begin{cases} \frac{x^2 + 3x - 10}{x^2 + 2x - 15}, & x \neq -5 \\ a, & x = -5 \end{cases} \) is continuous at \( x = -5 \), then the value of \( a \) will be

The function \( f(x) = (x(x - 2))^2 \) is increasing in the set

If \( x \) satisfies \( |3x-2| + |3x-4| \geq |3x-6| \), then

In the truth table for the statement \( (p \land q) \rightarrow (q \lor \neg p) \), the last column has the truth value in the following order is

The set of all real \( x \) satisfying the inequality \[ \frac{3 - |x|}{4 - |x|} \geq 0 \] is

For \( k = 1, 2, 3 \), the box \( B_k \) contains red balls and \( (k+1) \) white balls. Let \( P(B_1) = \frac{1}{2}, P(B_2) = \frac{1}{3}, P(B_3) = \frac{1}{6} \). A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it came from box \( B_2 \) is

The area intercepted by the curves \( y = \cos x \), \( x \in [0, \pi] \) and \( y = \cos 2x \), \( x \in [0, \pi] \), is

The general solution of the differential equation \[ \frac{dy}{dx} + \sin(x + y) = \sin(x - y) \] is

Evaluate \[ \int_0^{\frac{\pi}{2}} \frac{\sin x}{1 + \cos^2 x} \, dx \] is

The solution to the differential equation \[ \frac{dy}{dx} = \frac{yf'(x) - y^2}{f(x)} \] where \( f(x) \) is a given function is

If vectors \( 2i + j + k \), \( 2j - 3k \), and \( 3i + j + 5k \) are coplanar, then the value of \( a \) is

Find the angle between the two planes \( 2x + y - 2z = 5 \) and \( 3x - 6y - 2z = 7 \).

If \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) are three unit vectors such that \[ \mathbf{a} + \mathbf{b} + \mathbf{c} = \mathbf{0}, \quad \mathbf{a} \cdot \mathbf{b} = \mathbf{b} \cdot \mathbf{c} = \mathbf{c} \cdot \mathbf{a} \] then the value of \( \mathbf{a} \cdot \mathbf{a} \) is

A shopkeeper wants to purchase two articles A and B of cost price \( 4 \) and \( 3 \) respectively. He thought that he may earn 30 paise by selling article A and 10 paise by selling article B. He has not to purchase total articles worth more than \( 24 \). If he purchases the number of articles of A and B, \( x \) and \( y \) respectively, then linear constraints are

The coordinates of the point where the line through the points \( A(3, 4, 1) \) and \( B(5, 1, 6) \) crosses the \( XY \)-plane are

The enthalpy of combustion of 2 moles of benzene at 27°C differs from the value determined in bomb calorimeter by

The number of enantiomers of the compound \( \text{CH}_3 \text{CHBr} \text{CHBrCOOH} \) is