List of top Questions asked in CUET (PG)

Given below are two statements.
Assertion (A):
Security has services like confidentiality, integrity, authentication, access control, et
C.
Reason (R):
Encryption, digital signature, MD5 and secure hash algorithm may be used for authentication and confidentiality, et
C.

Arrange the following in increasing order on the basis of dispersion of data with given mean, number of data points and sum of squares:
A. \(n=5,\ \sum x^2=100,\ \bar{x}=3\);
B. \(n=5,\ \sum x^2=100,\ \bar{x}=4\);
C. \(n=10,\ \sum x^2=100,\ \bar{x}=2\);
D. \(n=10,\ \sum x^2=100,\ \bar{x}=3\).

Arrange the probabilities for the following normal distribution problem from lowest to highest:
A. \(\mu=604,\ \sigma=50,\ P(X<635)\);
B. \(\mu=48,\ \sigma=10,\ P(X<20)\);
C. \(\mu=37,\ \sigma=5,\ P(X>35)\);
D. \(\mu=156,\ \sigma=10,\ P(X>170)\).

Construct the confidence interval specified to estimate \(\mu\). Arrange the intervals from lowest to highest based on length of the interval:
A. \(95\%\) confidence for \(\bar{x}=20,\ \sigma=3,\ n=49\);
B. \(95\%\) confidence for \(\bar{x}=20,\ \sigma=3,\ n=81\);
C. \(95\%\) confidence for \(\bar{x}=115,\ \sigma=25,\ n=49\);
D. \(95\%\) confidence for \(\bar{x}=115,\ \sigma=25,\ n=81\).

The standard deviation for the given data is:

For two distributions, the standard deviations are \(21\) and \(14\) respectively and their coefficients of variations are \(60\) and \(70\) respectively. Which of the following is correct for their arithmetic means?

For the given dataset:
\[ \begin{array}{c|ccc} x & 2 & 3 & 4\\ \hline f(x) & \frac14 & \frac12 & \frac14 \end{array} \] Which of the following is the expected value of \(x\)?

In statistics, ANOVA stands for:

When a coin having head and tail is thrown, which of the following is probability of not getting head?

Given below are two statements.
Assertion (A):
For a random variable \(X\), if \(x=0,1,2,\ldots\) and \[ P(X=x)=k\frac{\lambda^x}{x!}, \] then for it to be a probability mass function, \(k=e^{-\lambda}\).
Reason (R):
In a probability distribution, the sum of all probabilities must be \(1\).

Which of the following is the median of the heights in cm of the following 9 students? \[ 155,\ 160,\ 145,\ 149,\ 150,\ 147,\ 152,\ 144,\ 148 \]

In a small factory one supervisor and four labourers work. The labourers draw salary of \(\rupee 5000\) per month each while supervisor gets \(\rupee 15000\) per month. Which of the following are mean and mode of the salaries?

Match List-I with List-II. Suppose \(A,B,C\) are three non-empty sets. List-I:
A. De-Morgan's Law,
B. Associative Law,
C. Distributive Law,
D. Difference of sets Law.

Which of the following statements are true? A. For any two vectors \(\vec{a}\) and \(\vec{b}\), \(|\vec{a}+\vec{b}|\leq |\vec{a}|+|\vec{b}|\).
B. Scalar product of two non-zero vectors might be zero.
C. For any two vectors \(\vec{a}\) and \(\vec{b}\), \(|\vec{a}\cdot \vec{b}|\leq |\vec{a}||\vec{b}|\).
D. Cross product of two vectors is not a vector.
E. Dot product of two vectors is a scalar.

The function \(f(x)=|x-2|+|x|+|x+2|\) is not differentiable at which points?

Given below are two statements:

Assertion (A):
The angle between the pair of lines \[ \frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4} \quad \text{and} \quad \frac{x+1}{1}=\frac{y-4}{1}=\frac{z-5}{2} \] is \(\cos^{-1}\left(\frac{8\sqrt{3}}{15}\right)\).
Reason (R):
The angle between the two lines is \[ \cos\theta=\frac{a_1a_2+b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}. \]

Arrange the following in ascending order based on their values:
A. \(\displaystyle \int_0^{\frac{\pi}{2}}\frac{1}{1+\sin x}\,dx\),
B. \(\displaystyle \int_1^2 x^2\,dx\),
C. \(\displaystyle \int_0^{\frac{\pi}{2}}\sin x\,dx\),
D. \(\displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\sin^3x\,dx\).

Which of the following statements are true? A. \(2^{4n}-1\) is divisible by \(15\).
B. \(5,12\) and \(13\) is Pythagorean triplet.
C. \(n^7-n\) is divisible by \(42\).
D. \(1^2+2^2+3^2+\cdots+n^2=\left[\dfrac{n(n+1){2}\right]^2\).}

Given below are two statements:

Assertion (A):
The function \(f(x)=x|x|\) is continuous at \(x=0\) and derivative of \(f\) also exists at \(x=0\).
Reason (R):
It is necessary and sufficient that every continuous function is derivable at any point.

If one of the roots of equation \(ax^4+bx^3+cx^2+dx+e=0\) is \(\sqrt{2}+\sqrt{-3}\), then arrange the following in non-decreasing order \((a\neq 0)\). A. \(a\),
B. \(b\),
C. \(c\),
D. \(d\),
E. \(e\).

Which of the following is/are solution of the LPP? \[ \text{Min }Z=12x+9y \] Subject to \[ x+2y\leq 40,\quad 3x+y\geq 30,\quad 4x+3y\geq 60,\quad x,y\geq 0 \] A. \((15,0)\),
B. \((40,0)\),
C. \((4,18)\),
D. \((6,12)\),
E. \((10.5,6)\).

Which of the following is the median of the heights in cm of the following 9 students? \[ 155,\ 160,\ 145,\ 149,\ 150,\ 147,\ 152,\ 144,\ 148 \]

Which of the following is the variance of the data? \[ 6,\ 8,\ 10,\ 12,\ 14,\ 16,\ 18,\ 20,\ 22,\ 24 \]

When a dice of six faces \(\{1,2,3,4,5,6\}\) is thrown, which of the following is the probability of getting an even number?

Match List-I with List-II on the basis of relationship. List-I:
A. Complement operation,
B. Power set operation,
C. Cartesian product,
D. Union and intersection. List-II:
I. Collection of subsets, II. Tuples ordered, III. Universal set, IV. Difference symmetri
C.