List of top Questions asked in CUET (PG)- 2025

If, \(X \sim N(\theta, 1)\) and in order to test \(H_0: \theta=1\) against the alternate \(H_1: \theta=2\) a random sample \((x_1, x_2)\) of size 2 is taken. Then, the best critical region (B.C.R.) is given by (where \(Z_\alpha = 1.64\))

A cyclist covers first five kilometers at an average speed of 10 k.m. per hour, another three kilometers at 8 k.m. per hour and the last two kilometers at 5 k.m. per hour. Then, the average speed of the cyclist during the whole journey, is

A is a, \(n \times n\) matrix of real numbers and \(A^3 - 3A^2 + 4A - 6I = 0\), where I is a, \(n \times n\) unit matrix. If \(A^{-1}\) exists, then

Let P and Q be two square matrices such that PQ = I, where I is an identity matrix. Then zero is an eigen value of

The system of equations given by \( \begin{bmatrix} 1 & 1 & 1 & : & 3 \\ 0 & -2 & -2 & : & 4 \\ 1 & -5 & 0 & : & 5 \end{bmatrix} \) has the solution:

Consider a 2x2 matrix \(A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}\). If \(a+d=1\) and \(ad-bc=1\), then \(A^3\) is equal to

If \(f'(x) = 3x^2 - \frac{2}{x^2}\), \(f(1) = 0\) then, \(f(x)\) is

For Lagrange's mean value theorem, the value of 'c' for the function \(f(x) = px^2+qx+r, p\neq 0\) in the interval \([1, b]\) and \(c \in ]1, b[\), is:

The value of \( \lim_{h \to 0} \left(\frac{1}{h} \int_{4}^{4+h} e^{t^2} dt \right) \) is

The volume of the solid for the region enclosed by the curves \(X = \sqrt{Y}\), \(X = \frac{Y}{4}\) revolve about x-axis, is

The area of the surface generated by revolving the curve \(X = \sqrt{9-Y^2}, -2 \leq Y \leq 2\) about the y-axis, is

Let, random variable \(X \sim \text{Bernoulli}(p)\). Then, \(\beta_1\) is

Three urns contain 3 green and 2 white balls, 5 green and 6 white balls and 2 green and 4 white balls respectively. One ball is drawn at random from each of the urn. Then, the expected number of white balls drawn, is

Let \(X_1, X_2, X_3\) be three variables with means 3, 4 and 5 respectively, variances 10, 20 and 30 respectively and \(cov (X_1, X_2) = cov (X_2, X_3) = 0\) and \(cov (X_1, X_3) = 5\). If, \(Y = 2X_1 +3X_2+4X_3\) then, Var(\(Y\)) is:

The difference between the initial and the final temperature divided by the freezing time is known as

Identify the evaporator

Match the LIST-I with LIST-II

LIST-I		LIST-II
(Type of Fouling)		(Fouling Mechanism)
A	Precipitation	IV	Precipitation of dissolved substances...
B	Freezing	III	Solidification of Liquid components...
C	Particulate	I	Accumulation of fine particles suspended...
D	Corrosion	II	Heat transfer surface reacts with ambient...

Arrange the steps involved in the production of soy sauce
[A.] Roasting of wheat
[B.] Moromi stage
[C.] Lactic/ethanolic fermentation
[D.] Fermentation at 25-30 \(^{\circ}\)C for 2-3 days
Choose the most appropriate answer from the options given below:

Milk fat may be decomposed by various bacteria, yeasts, and molds, the changes that take place in the milk fat are:
A. Oxidation of the unsaturated fatty acids
B. Hydrolysis of the butterfat to fatty acids
C. Alkali production
D. Combined oxidation and hydrolysis to produce rancidity

A 4% commercially available acetic acid is known as_______.

Match the LIST-I with LIST-II
Average composition of Milk

LIST-I		LIST-II
(Constituents)		(Percentage %)
A.	Water	I.	87
B.	Protein	II.	3.3
C.	Lactose	III.	5.0
D.	Total solids	IV.	12.9

Choose the most appropriate answer from the options given below:

Among the following, the egg yolk protein is_______.

Ingredient added in egg proteins to decrease the temperature of coagulation is:

The temperature at which the granules begin to swell rapidly and lose birefringence is called

Match the LIST-I with LIST-II

LIST-I		LIST-II
(Saturated fatty acids found in food lipids)
A.	Heptanoic	I.	CH\(_3\)(CH\(_2\))\(_{12}\)COOH
B.	Hexanoic	II.	CH\(_3\)(CH\(_2\))\(_{4}\)COOH
C.	Pentanoic	III.	CH\(_3\)(CH\(_2\))\(_{3}\)COOH
D.	Tetranic	IV.	CH\(_3\)(CH\(_2\))\(_{5}\)COOH

Choose the most appropriate answer from the options given below: