List of top Mathematics Questions on Algebra asked in BITSAT

If $ x + \frac{1}{x} = 2 \cos \theta $, find the value of \[ x^5 + \frac{1}{x^5} \] in terms of $\theta$.
From the top of a 50 m tall building, the angles of depression to two points on the ground are \( 45^\circ \) and \( 30^\circ \). Find the distance between the two points.
Maximize \( z = 5x + 2y \) subject to \( 2x + y \leq 8 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
If the word "BITS" is coded using \( A=1, B=2, \ldots, Z=26 \), and the code is the sum of the squares of each letter's value, what is the code for the word?
Find the sum of the series \( 1 + 3 + 5 + \ldots + 99 \).
Maximize \( z = 3x + 4y \) subject to \( x + y \leq 4 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
From the top of a 60 m high building, the angles of depression to two points on the ground on the same side of the building are \( 30^\circ \) and \( 60^\circ \). What is the distance between the two points?
If the word "GIFT" is coded using A=1, B=2, ..., Z=26, and each letter’s value is squared, what is the sum of the coded values?
If the number of available constraints is 3 and the number of parameters to be optimised is 4, then
If \( \vec{a} = 2\hat{i} + \hat{j} + 2\hat{k} \), then the value of \( |\hat{i} \times (\vec{a} \times \hat{i})| + |\hat{j} \times (\vec{a} \times \hat{j})| + |\hat{k} \times (\vec{a} \times \hat{k})|^2 \) is equal to:}
If a function \( f: \mathbb{R} \setminus \{1\} \rightarrow \mathbb{R} \setminus \{m\} \) is defined by \( f(x) = \frac{x+3}{x-2} \), then \( \frac{3}{l} + 2m = \)
The domain of the real-valued function
\[ f(x) = \sqrt{\frac{2x^2 - 7x + 5}{3x^2 - 5x - 2}} \] is:
If \( f: \mathbb{R} \to \mathbb{R} \), \( g: \mathbb{R} \to \mathbb{R} \) are defined by \( f(x) = 5x - 3 \), \( g(x) = x^2 + 3 \), then \( g \circ f^{-1}(3) \) is equal to
The function f: R\(\rightarrow\) R is defined by \[ f(x) = \frac{x}{\sqrt{1 + x^2}} \] is:
The number of real solutions of
\[ \sqrt{5 - \log_2 |x|} = 3 - \log_2 |x| \] is:
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:
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:
The system of equations:
\[ x - y + 2z = 4 \] \[ 3x + y + 4z = 6 \] \[ x + y + z = 1 \] has:
If matrix \( A = \begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1 \end{bmatrix} \) and \( A^{-1} = \frac{1}{k} adj(A) \), then \( k \) is
If \( A = \frac{1}{3} \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix} \) is an orthogonal matrix, then

In an examination, 62% of the candidates failed in English, 42% in Mathematics and 20% in both. The number of those who passed in both the subjects is: 
 

If \( p \): 2 is an even number, \( q \): 2 is a prime number, and \( r \): \( 2 + 2 = 2^2 \), then the symbolic statement \( p \rightarrow (q \vee r) \) means:
The Boolean expression: \[ \neg (p \vee q) \vee (\neg p \wedge q) \] is equivalent to:
If the 17th and the 18th terms in the expansion of \((2 + a)^{50}\) are equal, then the coefficient of \(x^{35}\) in the expansion of \((a + x)^{-2}\) is:
The coefficient of the highest power of \(x\) in the expansion of \((x + \sqrt{x^2 - 1})^8 + (x - \sqrt{x^2 - 1})^8\) is: