List of top Questions asked in Karnataka PGCET- 2026

In a right angled isosceles triangle $\triangle ABC$, right angle at $C$, if side $a = 2$, then sides $b$ and $c$ are respectively
Two dice are thrown and the sum of the numbers which come up is noted. Among the following events: A: sum is even, B: sum is multiple of 3, C: sum is less than 4, D: sum is greater than 11. Which pair of events are mutually exclusive?
The probability of selecting a man from a crowd containing 20 men and 33 women is
Three cards are drawn successively without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and the third card drawn is an ace?
The Boolean function $AB + AC$ is equivalent to:
The Boolean expressions $(AB)' = A' + B'$ and $(A + B)' = A'B'$ represent
Match List-I with List-II.
Match the postulates in List-I with List-II.
The general solution of $2\cos\theta - \sqrt{3} = 0$ is}
The point of intersection of the lines $3x + 2y = 6$ and $3x - 2y = -2$ is:
The centre of the circle $(x + 5)^2 + (y - 3)^2 = 36$ is:
The reflection of the point $(4, -13)$ about the line $5x + y + 6 = 0$ is:
Consider the triangle with vertices $(0, 0)$, $(5, 0)$ and $(2, 3)$. If scaling of 3 units is applied along both x-axis and y-axis, the new coordinates are:
The equation of the parabola which is symmetric about the y-axis and passes through the point $(2, -3)$ is:
The midpoint of the line joining the points $(2, 4)$ and $(6, -2)$ is:
If $A = \begin{bmatrix} 1 & 2 & 4 \\ -1 & 3 & 0 \\ 1 & 2 & 0 \end{bmatrix}$, then the value of determinant of A is:}
The equation of the line passing through the points $(1, 2)$ and $(-1, 4)$ is:
Let $U$ be universal set. If $A$ and $B$ are subsets of $U$, then match the following and choose the correct answer. {ll} List - I & List - II
(a) $A \cup A'$ & (i) $A$
(b) $(A \cup B)'$ & (ii) $A' \cup B'$
(c) $(A \cap B)'$ & (iii) $A' \cap B'$
(d) $(A')'$ & (iv) $U$ Codes:
Let 'U' be universal set. If A and B are subsets of U, then match the following and choose the correct answer.

If \( A = \begin{bmatrix} 1 & 2 \\ -1 & 3 \end{bmatrix} \), \( B = \begin{bmatrix} -1 & 2 \\ 0 & 4 \end{bmatrix} \), then match the following and choose the correct answer.

\[ \begin{array}{ll} \text{List - I} & \text{List - II} \\ \\ (a)\; A+B & (i)\; \begin{bmatrix} -1 & 10 \\ 1 & 10 \end{bmatrix} \\ (b)\; A-B & (ii)\; \begin{bmatrix} 0 & 4 \\ -1 & 7 \end{bmatrix} \\ (c)\; AB & (iii)\; \begin{bmatrix} 1 & 4 \\ 0 & 10 \end{bmatrix} \\ (d)\; 2A + B' & (iv)\; \begin{bmatrix} 2 & 0 \\ -1 & -1 \end{bmatrix} \end{array} \]

In a shop, the cost of 3 pens and 3 pencils is Rs. 9 and the cost of 4 pens and 6 pencils is Rs. 14. The cost of each pencil in Rs. is:
A person has 2 parents, 4 grandparents, 8 great grandparents and so on. What is the number of his ancestors during the $5^{\text{th}$ generation preceding his own?}
Which of the following is/are true?
• [(i)] $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$
• [(ii)] $(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$
• [(iii)] $(x + a)(x + b) = x^2 + (a + b)x + ab$
Which of the following statements are correct?
• [(a)] Startups are innovation-driven businesses and aim at scalability
• [(b)] Securities and Exchange Board of India regulates stock markets and protects investors
• [(c)] GST is an indirect tax applicable across India and is collected only once at the final stage of the transaction
• [(d)] Blinkit operates in quick commerce, which focuses on fast delivery using dark stores
Which is NOT an advantage of writing Business letter?