List of top Questions asked in MHT CET

If ∫ (2x + 3)/((x - 1)(x^2 + 1)) dx = log_x {(x - 1)^(5/2)(x^2 + 1)^a} - (1/2) tan^(-1)x + C, then the value of a is:
Find the value of the integral: ∫ (2x + 3)/((xy)(x^2 + 1)) dx
If \( y = x^x + x^x \), then find \( \frac{dy}{dx} \):
Given \( f'(1) = 3 \), \( f(1) = 1 \), and
\[ y = f\left(f(f(x))\right) + \left(f(x)\right)^2, \] then find \( \frac{dy}{dx} \) at \( x = 1 \).
A copper ball at \(80^\circ C\) is brought to \(60^\circ C\) in 5 minutes, with surrounding temperature at \(20^\circ C\). Find the temperature of the ball after 20 minutes.
Evaluate the expression: \[ f\left(f(f(x))\right) + \left(f(f(x))\right)^2 \quad \text{if} \quad x = 1 \]
Evaluate the determinant of the matrix: \[ \left| \begin{array}{cc} 1 & \tan x
-\tan x & 1 \end{array} \right| \]
Evaluate the integral: \( \int \sin^5 x \, dx \)
What is the volume of oxygen required for complete combustion of 0.25 mole of methane at S.T.P.?
In the reaction \( \mathrm{2H_2 + O_2 \rightarrow 2H_2O} \), if 4 moles of hydrogen react completely with oxygen, how many moles of water will be produced?
Which of the following is an example of a redox reaction?
Which of the following elements does not have a completely filled outermost shell in its ground state?
Which of the following gases is most soluble in water?
Which of the following gases is most soluble in water?
Which of the following is the correct electron configuration for the ion \(\text{Fe}^{3+}\)?
Which of the following compounds is an example of an ionic bond?
Which of the following elements does not have a completely filled outermost shell in its ground state?
Which of the following is an example of a redox reaction?
Which of the following gases is produced when zinc reacts with dilute hydrochloric acid?
What is the pH of a 0.1 M NaOH solution?
What is the molarity of a solution prepared by dissolving 10 grams of NaOH in 250 mL of water? (Molar mass of NaOH = 40 g/mol)
What is the pH of a 0.01 M hydrochloric acid (HCl) solution?
In the reaction \( 2 \, \text{H}_2 + \text{O}_2 \to 2 \, \text{H}_2\text{O} \), if 4 moles of hydrogen react completely with oxygen, how many moles of water will be produced?
A charge of \( 2 \, \mu\text{C} \) is placed in an electric field of intensity \( 4 \times 10^3 \, \text{N/C} \). What is the force experienced by the charge?
Two bodies of masses \( m_1 = 5 \, \text{kg} \) and \( m_2 = 10 \, \text{kg} \) are placed 2 meters apart. What is the gravitational force between them?