List of top Questions asked in CUET (PG)

If \[ \frac{1}{a(b + c)} + \frac{1}{b(c + a)} + \frac{1}{c(a + b)} = k, \text{ then the value of } k \text{ is:} \]

Bag $A$ contains 3 Red and 4 Black balls while Bag $B$ contains 5 Red and 6 Black balls. One ball is drawn at random from one of the bags and is found to be Red. Then, the probability that it was drawn from Bag $B$ is:

If $\; f(x)=\begin{cases} x\sin\!\left(\tfrac{1}{x}\right), & x\neq 0 \\[6pt] 0, & x=0 \end{cases}, \; \text{then } f(x) \text{ is}$

Match List-I with List-II.\[\begin{array}{|c|c|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A) \; \text{If } A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}, \; \Delta \text{ is} & (I) \; 0 \\ \hline (B) \; \text{If } A = \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}, \; \Delta \text{ is} & (II) \; 1 \\ \hline (C) \; \text{If } A = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}, \; |A^{-1}| \text{ is} & (III) \; -2 \\ \hline (D) \; \text{If } A = \begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix}, \; a \text{ is} & (IV) \; 2 \\ \hline \end{array}\]

If $ \frac{1}{9!} + \frac{1}{10!} = \frac{x}{11!} $, then the value of $ x $ is:

If $ (x - 1) $ is a factor of $ 2x^2 - 5x + k = 0 $, then the value of $ k $ is:

External fragmentation occurs .................. .

Which disk scheduling algorithm looks for the track closest to the current head position?

Match List-I with List-II:
\[\begin{array}{|c|c|}\hline \textbf{List-I} & \textbf{List-II} \\ \hline (A)\ \text{Seek Time} & (IV)\ \text{Time taken for the disk arm to move the heads to the cylinder containing the desired sector} \\ \hline (B)\ \text{Access Time} & (III)\ \text{Seek Time + Rotational Latency} \\ \hline (C)\ \text{Rotational Latency} & (II)\ \text{Time taken for the disk to rotate the desired sector to the disk head} \\ \hline (D)\ \text{Disk Bandwidth} & (I)\ \text{Total number of bytes transferred, divided by the total time between the first request for service and the completion of the last transfer} \\ \hline \end{array}\] Choose the correct answer from the options given below:

Match List-I with List-II:
\[\begin{array}{|c|c|}\hline \textbf{List-I} & \textbf{List-II} \\ \hline (A)\ \text{Binary Search} & (I)\ T(n) = T(n/2) + c \\ \hline (B)\ \text{Merge Sort} & (II)\ T(n) = 2T(n/2) + \Theta(n) \\ \hline (C)\ \text{Quick Sort (worst case)} & (III)\ T(n) = T(n-1) + \Theta(n) \\ \hline (D)\ \text{Linear Search} & (IV)\ T(n) = T(n-1) + c \\ \hline \end{array}\] Choose the correct answer from the options given below:

Perform the arithmetic addition of the two decimal numbers given in List-I using the signed-complement system. Match the corresponding output of List-I with binary number representation given in List-II.
\[\begin{array}{|c|c|}\hline \text{List-I} & \text{List-II} \\ \hline \text{(A) +6, +13} & \text{(I) 00000111} \\ \hline \text{(B) -6, +13} & \text{(II) 00010011} \\ \hline \text{(C) +6, -13} & \text{(III) 11101011} \\ \hline \text{(D) +6, -13} & \text{(IV) 11111101} \\ \hline \end{array}\]

Arrange the following steps in the correct order to understand the functioning of a 3 to 8 line decoder.
(A) The encoder enable input is set to 1.
(B) The decoder activates one of its 8 output lines based on the input code.
(C) The input binary code is applied to the decoder.
(D) The decoder converts the 3-bit binary input into 8 possible outputs.

Consider the following statements.
(A) Combinational logic circuits do not have memory, while sequential logic circuits have memory elements.
(B) Sequential logic circuits depend only on the current inputs, while combinational logic circuits depend on both current and past inputs.
(C) Flip-flops and latches are examples of combinational logic circuits.
(D) Multiplexer is an example of combinational logic circuit.

Match List-I with List-II.\[\begin{array}{|c|c|}\hline \textbf{J K Flip Flop Inputs} & \textbf{Next State} \\ \hline (A)\ 0\ 0 & (I)\ \text{No Change} \\ \hline (B)\ 0\ 1 & (II)\ \text{Reset} \\ \hline (C)\ 1\ 0 & (III)\ \text{Set} \\ \hline (D)\ 1\ 1 & (IV)\ \text{Toggle} \\ \hline \end{array}\]

Which of the following statement is true about IEEE754 representation of +0 and -0?

To provide a memory capacity of 32K X 16 how many address lines and data lines are required?

If $ x^2 = -16y $ is an equation of a parabola, then:

(A) Directrix is $ y = 4 $
(B) Directrix is $ x = 4 $
(C) Co-ordinates of focus are $ (0, -4) $
(D) Co-ordinates of focus are $ (-4, 0) $
(E) Length of latus rectum is 16

Find the number of triangles in the given figure.

In a binary search tree, the worst case time complexity of inserting and deleting a key is:

Minimum number of 2:1 Multiplexers required to design a 16:1 Multiplexer is?

Details of a paging system for memory management are as follows:
Logical address space: 32 KB
Page Size: 4 KB
Physical Memory size: 64 KB
The number of pages in the logical address space and number of page frames in physical memory, respectively, are:

Out of 5 consonants and 4 vowels, how many words of 3 consonants and 3 vowels can be made?

What should be the output of the following boolean expression after simplifying it to a minimum number of variables? \[ a'b' + ab + a'b \]

If $ a, b, c $ are in Geometric Progression and $ a^x = b^y = c^z $, then $ x, y, z $ are in:

The center and radius for the circle $ x^2 + y^2 + 6x - 4y + 4 = 0 $ respectively are: