List of top Questions asked in Karnataka Post Graduate Common Entrance Test

The probability that A passes a test is \( \frac{2}{3} \) and the probability that B passes the same test is \( \frac{3}{5} \). The probability that only one passes is
If \( P(A) = \frac{1}{4} \), \( P(B) = \frac{1}{3} \) and \( P(A \cup B) = \frac{1}{2} \), then \( P(A \cap B) = \)
If \( x \) and \( y \) are Boolean variables, then which of the following statement is/are incorrect?
a. \( x \lor 0 = x, \, x \land 1 = x \)
b. \( x \lor x' = 1, \, x \land x' = 0 \)
c. \( x \land (x \lor y) = x \)
d. \( x \land (x \land y) = x \lor y \)
The Boolean equation of NOR gate is
The dual of \( x \lor (y \land 0) \) is
In Boolean algebra, if \( a \land x = b \land x \) and \( a \land x' = b \land x' \), then which of the following statements is correct ?
In Boolean algebra \( [B, \land, \lor, ', 0, 1] \), the value of \( x' \land (x \lor y) \) is
The value of \( \sqrt{2 + \sqrt{2 + 2 \cos 4\theta}} \) is
The value of \( \tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) \) is equal to
In the expansion of \( \left( x - \frac{3}{x^2} \right)^9 \), the constant term is:
If \( A = \begin{bmatrix} \cos \theta & \sin \theta & 0 \\ \sin \theta & -\cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \), then the value of \( AA' \) is:
If the latus rectum of an ellipse is equal to half of the minor axis, then its eccentricity is:
The equation of the tangent at \( (2, -3) \) on the hyperbola \( x^2 - \frac{y^2}{3} = 1 \) is:
The angle between \( x^2 = y \) and \( y^2 = x \) at \( (1, 1) \) is:
The distance between the foci of the hyperbola \( \frac{x^2}{16} - \frac{y^2}{9} = 1 \) is:
What is the annual income derived by investing ₹6800 in 10\% stock at 136?
How many 5’s are there in the following sequence which are immediately followed by 3 but not immediately preceded by 7?
8953253855687335775363535738
If the height of a pole is \( 2\sqrt{3} \) metres and the length of its shadow is 2 metres, what is the angle of elevation of the sun?
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is:
If \( \log_3 2, \log_3 (2^x - 5), \log_3 \left(2^x - \frac{7}{2}\right) \) are in A.P., then \(x\) is:
If the sum of the roots of a quadratic equation \( ax^2 + bx + c = 0 \) is equal to the sum of the square of their reciprocals, then \( \frac{a}{c}, \frac{b}{a}, \frac{c}{b} \) are in:
The value of \( \sum_{a,b,c} \frac{1}{1 + \log_a bc} \) is:
Four milkmen rented a pasture. A grazed 24 cows for 3 months, B, 10 cows for 5 months, C, 35 cows for 4 months and D, 21 cows for 3 months. If A’s share of rent is ₹720, then the total rent of the field is:
If the cost price of an article is ₹632, selling price of an article is ₹765 and total profit earned is ₹1596, then the number of articles sold are:
A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is: