List of top Questions asked in MHT CET

The direction ratios of the line of intersection of the planes \( x - y + z - 5 = 0 \) and \( x - 3y - 6 = 0 \), are:

The line passing through the point \( (5, 1, a) \) and \( (3, b, 1) \) crosses the yz-plane at \( (0, \frac{17}{2}, \frac{-13}{2}) \), then the value of \( 2a + 3b \) is:

If \( y = \sin^2 \left( \cot^{-1} \left( \sqrt{\frac{1 - x}{1 + x^2}} \right) \right) \), then \( \frac{dy}{dx} \text{ is:} \)

If \[ f(x) = \begin{cases} x^3 - x^2 + 1, & \text{if } x > 0 \\ e^x \sin x + i x + \lambda \log 4, & \text{if } x \leq 0 \end{cases} \]
is continuous at \( x = 0 \), then the value of 500\(\lambda\) is:

Let \( A \) be a non-singular matrix of order n and \( |A| = k \), then \( (\text{adj} \, A)^{-1} \) is:

Evaluate the integral
\[ \int_{-1}^1 \left( \tan^{-1} \left( \frac{x}{x+1} \right) + \tan^{-1} \left( \frac{x+1}{x} \right) \right) \, dx \]

Given vectors \( \vec{a}, \vec{b}, \vec{c} \) such that \( \vec{a} \) is perpendicular to \( \vec{b} \) and \( \vec{c} \), \( |\vec{a}| = 1 \), \( |\vec{b}| = 2 \), and \( \vec{b} \cdot \vec{c} = 1 \). If there is a nonzero vector \( \vec{d} \) coplanar with \( \vec{a} + \vec{b} \) and \( 2\vec{b} - \vec{c} \), and if \( \vec{d} \cdot \vec{a} = 1 \), then calculate \( |\vec{d}|^2 \).

The area of the region bounded by the curve \( y = |x - 2| \) between \( x = 1 \) and \( x = 3 \).

The value of
\[ \sin \left[ \tan^{-1} \left( \frac{1 - x^2}{2x} \right) + \cos^{-1} \left( \frac{1 - x^2}{1 + x^2} \right) \right] \]

Calculate the relative lowering of vapor pressure of a solution containing 0.56 g nonvolatile solute in 100 g water [molar mass of solute = 60 g mol\(^{-1}\)].

Which among the following has the highest boiling point?

Numbers are selected at random, one at a time from the two-digit numbers 00, 01, 02, ..., 99 with replacement. An event E occurs only if the product of the two digits of a selected number is 24. If four numbers are selected, then the probability that the event E occurs at least 3 times, is

Which of the following species is not tetrahedral?

Calculate the number of \( \text{Ca}^{2+} \) ion in 222 g anhydrous calcium chloride? (At. Mass Ca = 40, Cl = 35.5)

Which of the following compounds is formed as major product in the following reaction?
\[ \text{2-Methylbut-2-ene} \xrightarrow{\text{HBr, Peroxide}} \text{Product} \]

Which from the following elements form superoxide with air?

Identify a copolymer from following.

Which from the following cations forms the least stable complex with the same ligand?

For a reaction, \( A \to B \), rate equation is \( r = k[A]^0 \). If initial concentration of reactant is \( a \) mol dm\(^{-3}\), find the half-life time of the reaction.

What is the number of moles of silver chloride precipitated when excess silver nitrate is treated with one mole of pentaamminecarbonatocobalt (III) chloride?

Identify from the following an example of intensive property.

The mass of 4.48 dm³ of certain gas is 5.6 g at STP. Assuming ideal behavior, identify the probable gas from the following.

Methyl propanoate on hydrolysis with dilute NaOH forms a salt that on further acidification with conc. HCl forms

Identify the defect developed when an ion of an ionic compound is missing from its regular site and occupies an interstitial position between lattice points.

What is the IUPAC name of the following compound?