List of top Questions asked in BITSAT

The value of \( \lim_{x \to 0} \frac{(1 + x)^{\frac{1}{x}} - e + \frac{1}{2}e^x}{x^2} \) is:

The value of \[ \lim_{x \to 0} \frac{1 - \cos(1 - \cos x)}{x^4} \] is:

If \( A = \{ x : x { is a multiple of 4} \} \) and \( B = \{ x : x { is a multiple of 6} \} \), then \( A \cap B \) consists of multiples of:

If \( \alpha \) be a root of the equation \( 4x^2 + 2x - 1 = 0 \), then the other root of the equation is

If \( \alpha, \beta, \gamma \in [0, \pi] \) and if \( \alpha, \beta, \gamma \) are in AP, then \[ \frac{\sin \alpha - \sin \gamma}{\cos \gamma - \cos \alpha} \] {is equal to:}

Let \( a_1, a_2, a_3, \dots \) be a harmonic progression with \( a_1 = 5 \) and \( a_{20} = 25 \). The least positive integer \( n \) for which \( a_n<0 \) is:

The number of terms in the expansion of \( (1 + 5\sqrt{2}x)^9 + (1 - 5\sqrt{2}x)^9 \) is:

If \[ g(x) = x^2 + x - 2 \] and \[ \frac{1}{2} g \circ f(x) = 2x^2 - 5x + 2, \] then \( f(x) \) is equal to:

The number of ways of arranging the letters of the word HAVANA so that V and N do not appear together is:

If \(\hat{u}\) and \(\hat{v}\) are two non-collinear unit vectors such that \(\left| \frac{\hat{u} + \hat{v}}{2} + \hat{u} \times \hat{v} \right| = 1\), then the value of \(\left| \hat{u} \times \hat{v} \right|\) is equal to:

If in a \( \triangle ABC \), \( 2b^2 = a^2 + c^2 \), then
\[ \frac{\sin 3B}{\sin B} { is equal to:} \]

If \[ \left[ \begin{array}{cc} 1 & -\tan(\theta) \\ \tan(\theta) & 1 \end{array} \right] \left[ \begin{array}{cc} 1 & \tan(\theta) \\ -\tan(\theta) & 1 \end{array} \right]^{-1} = \left[ \begin{array}{cc} a & -b \\ b & a \end{array} \right], \] then:

The value of \[ \int \frac{1}{x^1} \, dx, { is } \left[ \frac{(x - 1)^3}{(x + 2)^5} \right]_1^4 \]

If \( p \neq a \), \( q \neq b \), \( r \neq c \), and the system of equations \[ px + ay + az = 0 \] \[ bx + qy + bz = 0 \] \[ cx + cy + rz = 0 \] has a non-trivial solution, then the value of \[ \frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c} \] is:

The sum of all the solutions of the equation \( \cos \theta \cos \left( \frac{\pi}{3} + \theta \right) \cos \left( \frac{\pi}{3} - \theta \right) = \frac{1}{4} \), for \( \theta \in [0, 6\pi] \) is:

The number of different seven-digit numbers that can be written using only the digits 1, 2, and 3 with the condition that the digit 2 occurs twice in each number is:

If the plane \( 3x + y + 2z + 6 = 0 \) { is parallel to the line} \[ \frac{3x - 1}{2b} = \frac{3 - y}{1} = \frac{z - 1}{a}, \] {then the value of \( 3a + 3b \) is:}

If the straight line \( y = mx + c \) touches the parabola \( y^2 - 4ax + 4a^3 = 0 \), then \( c \) is:

If the sum of the coefficients in the expansion of \( (x + y)^n \) is 1024, then the value of the greatest coefficient in the expansion is:

If \( |w| = 2 \), then the set of points \( z = w - \frac{1}{w} \) is contained in or equal to the set of points \( z \) satisfying:

If \( x \in \left( 0, \frac{\pi}{2} \right) \), then the value of \( \cos^{-1} \left( \frac{7}{2} (1 + \cos 2x) + \sqrt{(\sin^2 x - 48\cos^2 x)\sin x} \right) \) is equal to:

In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. If the middle term of the AP is equal to the middle term of the GP, then the middle term of the entire sequence is:

Let \( \alpha \) be the solution of the equation \[ 16 \sin^2 \theta + 16 \cos^2 \theta = 10, \quad \theta \in \left( 0, \frac{\pi}{4} \right) \] {If the shadow of a vertical pole is \( \frac{1}{\sqrt{3}} \) of its height, then the altitude of the sun is:}

Let \(a, b\) be the solutions of \(x^2 + px + 1 = 0\) and \(c, d\) be the solution of \(x^2 + qx + 1 = 0\). If \((a - c)(b - c)\) and \((a + d)(b + d)\) are the solution of \(x^2 + ax + \beta = 0\), then \(\beta\) is equal to:

The area of the region bounded by the parabola \( (y - 2)^2 = (x - 1) \), the tangent to the parabola at the point \( (2, 3) \), and the X-axis is: