List of top Mathematics Questions asked in Karnataka PGCET

The Boolean expressions \[ (AB)' = A' + B' \] and \[ (A+B)' = A'B' \] represent

A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man?

The variance of 25 observations is 6. If each observation is multiplied by 3, then the new variance of the resulting observations is

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually six.

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 probability of selecting a man from a crowd containing 20 men and 33 women is

Two students A and B appear for an exam. Probability that A passes is 0.05, B passes is 0.10, and both pass is 0.02. Find probability that neither passes.

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 value of $\tan^{-1}(A) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(-\frac{1}{2}\right)$ is}

In a right angled isosceles triangle $\triangle ABC$, right angle at $C$, if side $a = 2$, then sides $b$ and $c$ are respectively

The general solution of $2\cos\theta - \sqrt{3} = 0$ is}

Match List-I with List-II.

The Boolean expressions $(AB)' = A' + B'$ and $(A + B)' = A'B'$ represent

The Boolean function $AB + AC$ is equivalent to:

Match the postulates in List-I with List-II.

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 reflection of the point $(4, -13)$ about the line $5x + y + 6 = 0$ is:

The centre of the circle $(x + 5)^2 + (y - 3)^2 = 36$ is:

The point of intersection of the lines $3x + 2y = 6$ and $3x - 2y = -2$ is:

The midpoint of the line joining the points $(2, 4)$ and $(6, -2)$ is:

The equation of the line passing through the points $(1, 2)$ and $(-1, 4)$ is:

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:

Let 'U' be universal set. If A and B are subsets of U, then match the following and choose the correct answer.

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: