List of top Mathematics Questions on Geometric Progression asked in MHT CET

Two players A and B are alternately throwing a coin and a die together. A player who first throws a head and a 6 wins the game. If A starts the game, then the probability that B wins the game is:
The solution of the differential equation \( \sqrt{1 - y^2} \, dx + x \, dy - \sin^{-1} y \, dy = 0 \) is:

The range of  the function  \( f(x) = \sin^{-1}(x - \sqrt{x}) \) is equal to?

The function \( f(x) = \tan^{-1} (\sin x + \cos x) \) is an increasing function in:

If \( A = \begin{bmatrix} 1 & 0 \\ 1/2 & 1 \end{bmatrix} \), then \( A^{50} \) is:

The tangent at the point \( (x_1, y_1) \) on the curve \( y = x^3 + 3x^2 + 5 \) passes through the origin. Then \( (x_1, y_1) \) does NOT lie on the curve:
Let the following system of equations: $$ kx + y + z = 1, \quad x + ky + z = k, \quad x + y + kz = k^2 $$ have no solution. Find $|k|$:
If \( x = \frac{1 - t^2}{1 + t^2} \) and \( y = \frac{2t}{1 + t^2} \), then \( \frac{dy}{dx} \) is equal to:

Let \( f(x) = \frac{2 - \sqrt{x + 4}}{\sin 2x}, \, x \neq 0 \). In order that \( f(x) \) is continuous at \( x = 0 \), \( f(0) \) is to be defined as:

The absolute maximum value of the function \( f(x) = 2x^3 - 3x^2 - 36x + 9 \) defined on \( [-3, 3] \) is
The equation of a circle with center \( (5, 4) \) and touching the \( Y \)-axis is:
Evaluate \( i^2 + i^3 + \dots + i^{4000} \):
Evaluate the following limit: \[ \lim_{\theta \to -\frac{\pi}{4}} \frac{\cos\theta + \sin\theta}{\theta + \frac{\pi}{4}}. \]

Calculate the area of the intersection between the disk \(x^2 + y^2 \leq 1\) and the region defined by \(y^2 \leq 1 - x\).

Let \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k}, \, \vec{b} = \hat{i} - \hat{j} + \hat{k}, \, \text{and} \, \vec{c} = \hat{i} + \hat{j} - \hat{k} \). A vector in the plane of \( \vec{a} \) and \( \vec{b} \) whose projection on \( \vec{c} \) is \( \frac{1}{\sqrt{3}} \), is: