List of top Questions asked in MHT CET

If the displacement of a particle at time \(t\) is given by \[ s = 3t^2 - 12t + 14, \] then the displacement of the particle when its velocity becomes zero is

The joint equation of a pair of lines passing through \((2,3)\) and parallel to the lines \[ x^2 - y^2 = 0 \] is

The area bounded by the circle \(x^2 + y^2 = 16\) and the lines \(x = 0\) and \(x = 2\) is

Evaluate the integral \[ \int_{0}^{\pi} \frac{x \cos x \sin x}{\cos^3 x + \cos x}\,dx \]

Given \(A = \{1,2,3,4,5\}\), \(B = \{1,4,5\}\). If \(R\) is a relation from \(A\) to \(B\) such that \((x,y) \in R\) with \(x>y\), then the range of \(R\) is

The equation of a plane passing through the intersection of the planes \(x + 2y - 3z + 2 = 0\) and \(6x + y + z + 1 = 0\) and parallel to the line \(x - 1 = y + 2 = 7 - z\) is

The value of \(x\) such that the matrix \[ \begin{bmatrix} x & 2 & 3 \\ 4 & 5 & 6 \\ 2 & 3 & 5 \end{bmatrix} \] is not invertible is

If \[ A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix} \] then

Identify the number of oxygen atoms present in saccharic acid.

What is the approximate ratio of roasted ore, coke, and lime stone respectively in the charge to be added into the blast furnace for extraction of iron?

Relation between \( \Delta H \) and \( \Delta U \) for the reaction \[ \text{2SO}_3 (g) \rightarrow \text{2SO}_2 (g) + \text{O}_2 (g) \] is

At what new pressure will 100 mL of a gas at pressure 720 mm occupy volume of 84 mL, keeping temperature constant?

Evaluate the integral: \[ \int \left[ \log(1+\cos x) - x \tan\left(\frac{x}{2}\right) \right] dx \]

If the population grows at the rate of 5% per year, the time taken for the population to become double is (Given \( \log 2 = 0.6912 \))

The reaction \( \text{N}_2\text{O}_5 \rightarrow 2\text{NO}_2 + \text{O}_2 \) is first order in \( \text{N}_2\text{O}_5 \), having rate constant \( 6 \times 10^{-4} \, \text{L}^{-1} \, \text{s}^{-1} \). What is the value of rate of reaction when concentration of \( \text{N}_2\text{O}_5 \) is 1.25 mol L\(^{-1}\)?

Which of the following properties is of thermoplastic polymer?

The molecular mass of an organic monobasic acid is 129 and the value of \( n \) is 2, what is empirical formula mass of compound?

What is the value of \( K_f \) if 30 g urea (molar mass 60) dissolved in 0.5 dm³ of water decreases freezing point by 0.15°C?

An aqueous solution of sodium nitrite on boiling with \( \alpha \)-chlorosodium propionate gives

What is the molality of a solution containing 300 mg of urea (molar mass 60) dissolved in 30 g of water?

Which of the following elements exhibits oxidation states other than +3?

The IUPAC name of isobutyl bromide is

What is the molecular formula of allyl chloride?

Which of the following molecules does not obey octet rule?

Which among the following oxides is amphoteric in nature?