List of top Questions asked in CUET (UG)

Benzene reacts with a mixture of carbon monoxide (\( \text{CO} \)) and hydrogen chloride (\( \text{HCl} \)) gas in the presence of an anhydrous aluminium chloride (\( \text{AlCl}_3 \)) catalyst to yield Benzaldehyde. This organic transformation is officially known as the:
Which of the following oxidation state configurations represents the most common, energetically stable, and dominant oxidation state exhibited by nearly all the Lanthanoid elements across the f-block series?
A charged particle enters perpendicular to a uniform magnetic field. The path followed by the particle is:
The efficiency of an ideal transformer is:
In an AC circuit, the average value of alternating current over one complete cycle is:
The self inductance of a coil depends upon:
The forbidden energy gap in conductors is approximately:
Which of the following liquid mixtures forms an ideal solution that strictly obeys Raoult's Law across the entire concentration range at a constant temperature?
Aldehydes and ketones react with semicarbazide (\( \text{NH}_2\text{NHCONH}_2 \)) in a weakly acidic medium to form crystalline semicarbazone derivatives. Which of the three nitrogen atoms in a semicarbazide molecule acts as the primary nucleophilic center during this reaction?
In a series \(LCR\) circuit, resonance occurs when:
A semiconductor diode is forward biased. The depletion layer width will:
The drift velocity of electrons in a conductor increases when:
A long solenoid has \(1000\) turns per meter and carries a current of \(2\,A\). The magnetic field inside the solenoid is: \[ (\mu_0 = 4\pi \times 10^{-7}\,TmA^{-1}) \]
The magnetic field at the center of a circular coil carrying current is directly proportional to:
Find the maximum value of the linear objective optimization function \[ Z = 4x + y \] evaluated over a feasible region bounded by the corner vertices: \[ (0,0), \ (3,0), \ (2,3), \ \text{and} \ (0,4). \]
An unbiased coin is tossed twice. Let event \( A \) represent getting a head on the first toss, and event \( B \) represent getting a head on the second toss. Determine the mathematical relationship between events \( A \) and \( B \).
If \( A \) is a square matrix of order 3 such that its determinant is \( |A| = 3 \), calculate the value of the scalar matrix determinant represented by \( |2A| \).
Find the equation of the normal to the curve \( y = x^2 - x \) at the coordinate point position \( (1, 0) \).
Evaluate the value of the following definite integral using standard calculus integrations: \( \int_{0}^{1} x e^x \, dx \)
Find the shortest distance between the two parallel straight lines whose vector position equations are given by: \[ \vec{r} = (\hat{i} + 2\hat{j} - 4\hat{k}) + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k}) \] \[ \vec{r} = (3\hat{i} + 3\hat{j} - 5\hat{k}) + \mu(2\hat{i} + 3\hat{j} + 6\hat{k}) \]
If \( A \) is a non-singular square matrix of order \( 3 \times 3 \) such that its determinant is \( |A| = 5 \), find the absolute value of the determinant of its adjoint matrix, represented as \( |\text{adj}(A)| \).
The shadow of a tower standing on a level plane is \(30\) m longer when sun’s elevation changes from \(60^\circ\) to \(30^\circ\). Find the height of the tower.
Find the open interval across which the cubic polynomial function \( f(x) = 2x^3 - 3x^2 - 36x + 7 \) is classified as strictly decreasing.
The mean of \(10\) observations was calculated as \(40\). It was detected on rechecking that the value of one observation \(45\) was wrongly copied as \(15\). Find the correct mean.
Indu gives Bindu a loan of Rs \(1250\) for \(2\) years at \(4%\) annual compound interest rate. How much rupee would he have lost if he had given that amount on loan for \(2\) years at \(4%\) simple interest?