List of top Questions asked in CUET (PG)

Arrange the following steps in sequence to find the variance of individual observations.
• [A.] Compute the mean \(\bar{X}\) of the given observations \(x_1, x_2, \ldots, x_n\).
• [B.] Square the deviations obtained and obtain the sum \(\sum_{i=1}^{n} (x_i - \bar{X})^2\).
• [C.] Divide the sum \(\sum_{i=1}^{n} (x_i - \bar{X})^2\) by \(n\).
• [D.] Take the deviations of the observations from mean i.e., \(x_i - \bar{X}, i=1,2,\ldots,n\).
Choose the correct answer from the options given below:

Arrange the following determinants in decreasing order. \[ A = \begin{vmatrix} 1 & 3 & 5 \\ 2 & 6 & 10 \\ 31 & 11 & 38 \end{vmatrix} \quad B = \begin{vmatrix} 67 & 19 & 21 \\ 39 & 13 & 14 \\ 81 & 24 & 26 \end{vmatrix} \] \[ C = \begin{vmatrix} 1 & -3 & 2 \\ 4 & -1 & 2 \\ 3 & 5 & 2 \end{vmatrix} \quad D = \begin{vmatrix} 1 & 4 & 9 \\ 4 & 9 & 16 \\ 9 & 16 & 25 \end{vmatrix} \]

Which of the following statements are correct? \[ \lim_{x \to 0} \frac{\sin x}{x} = 1,\quad \lim_{x \to 0} \frac{\tan x}{x} = 1 \]
• [A.] Limit exists and equals \(\frac{1}{\sqrt{2}}\)
• [B.] Limit does not exist
• [C.] Limit exists and equals \(\frac{1}{2\sqrt{2}}\)
• [D.] Limit exists and equals \(\frac{1}{2}\left(1 + \frac{1}{3}\right)\)
Choose the correct answer from the options given below:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Let \(f\) be a function defined by \[ f(x) = \begin{cases} \dfrac{\tan x}{x}, & x \neq 0 1, & x = 0 \end{cases} \] Assertion (A): \(x = 0\) is point of minima of \(f\).
Reason (R): \(f'(0) = 0\). In the light of the above statements, choose the most appropriate answer from the options given below:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The sequence \(\frac{1}{3}, -\frac{1}{2}, \frac{3}{4}, -\frac{9}{8}, \ldots\) is an A.P.
Reason (R): The constant sequence is the only sequence which is both an A.P. as well as G.P. In the light of the above statements, choose the most appropriate answer from the options given below:

Arrange the following parabolas in increasing order of the length of their latus rectum.
• [A.] \(y^2 = 8x\)
• [B.] \(4x^2 + y = 0\)
• [C.] \(y^2 - 4y - 3x + 1 = 0\)
• [D.] \(y^2 - 4y + 4x = 0\)
Choose the correct answer from the options given below:

If the curves \(y^2 = 4ax\) and \(y = kx\) cut at right angles, then the value of \(k\) is:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Let \(A\) and \(B\) be two symmetric matrices of order 3. Assertion (A): \((AB)\) and \((BA)\) are symmetric matrices.
Reason (R): \(AB\) is a symmetric matrix, if matrix multiplication of \(A\) with \(B\) is commutative. In the light of the above statements, choose the most appropriate answer from the options given below:

If the foci of a hyperbola coincide with the foci of the ellipse \(\frac{x^2}{25} + \frac{y^2}{9} = 1\), then the equation of the hyperbola having its eccentricity 2 is:

Let the equation of the pair of lines \(px - y = 0\) and \(qx - y = 0\) be written as \((y - px)(y - qx) = 0\). Then, the equation of the pair of angle bisectors of the lines \(x^2 - 4y^2 - 5xy = 0\) is:

The area of the region \(|x| + 2|y| \leq 4\) is given by:

Let the mean and variance of 12 observations be \(a\) and \(4\) respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is \(\sigma^2\), where \(m\) and \(n\) are coprime, then \(m+n\) is equal to:

Evaluate the value of: \[ \int_{0}^{\pi} \frac{\sin^2 x}{1 + \sin x \cos x}\, dx \]

In a university, out of 100 students, 15 offered Mathematics only, 12 offered Statistics only, 8 offered Physics only, 40 offered Physics and Mathematics, 10 offered Mathematics and Statistics, 25 offered Physics. What is the number of students who did not offer any of the three subjects?

In a certain code, CONDEMN is written as CNODMEN. TEACHER will be written as CT__E__. Fill in the blanks by identifying the correct sequence. Options for blanks:
• [A.] H
• [B.] A
• [C.] D
• [D.] E

If a matrix is both symmetric and skew symmetric, then

Choose the sets of numbers from the four alternative sets, that is similar to the given set: \[ \text{Given set: } (3,\ 16,\ 36) \] A. (2, 35, 50) B. (2, 30, 16) C. (4, 24, 48) D. (5, 36, 60)
Choose the correct answer from the options given below:

Arrange the following games in decreasing order, on the basis of the players in their playing terms.
• [A.] Basketball
• [B.] Table Tennis
• [C.] Lawn Tennis
• [D.] Cricket

Which of the following relationship are correct?
• [A.] Chocolate : Sugar :: Building : Cement
• [B.] Sound : Feeble :: Colour : Faded
• [C.] Diabetes : Indisposable :: Painful : Tormenting
• [D.] Calligraphy : Writing :: Chapter : Stanza
• [E.] Restaurant : Menu :: Library : Catalogue
Choose the correct answer from the options given below:

Identify the letters which have their mirror images identical to the letter itself: A. A B. K C. H D. C
Choose the correct answer from the options given below:

Which of the following is the correct sequence of books from top to bottom based on the given statements? Consider the following statements:
• [A.] There are seven books, one each on Psychology, Hindi, English, Sociology, Economics, Education and Accountancy lying on a table one above the other.
• [B.] Sociology is on top of all books.
• [C.] Accountancy is immediately below education which is immediately below Sociology.
• [D.] Economics is immediately above Psychology but not in the middle.
• [E.] Hindi is immediately below Psychology.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Copper is used to make electrical wires.
Reason (R): Copper has a very low electrical resistance. In the light of the above statements, choose the most appropriate answer from the options given below: