List of top Mathematics Questions asked in Karnataka PGCET

Solve the following differential equation:
\[ \frac{d^2y}{dx^2} + 4\frac{dy}{dx} + 4y = 0 \]
The value of \( \tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) \) is equal to
The probability that a person aged 60 years will live up to 70 is 0.65. What is the probability that out of 10 persons aged 60, at least 7 of them will live up to 70?
Quartile coefficient of skewness is
If \( P(A) = \frac{1}{4} \), \( P(B) = \frac{1}{3} \) and \( P(A \cup B) = \frac{1}{2} \), then \( P(A \cap B) = \)
The distance between the foci of the hyperbola \( \frac{x^2}{16} - \frac{y^2}{9} = 1 \) is:
The value of \( \sum_{a,b,c} \frac{1}{1 + \log_a bc} \) 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:
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:
Reena is twice as old as Sunitha. Three years ago, she was three times as old as Sunitha. How old is Reena now?
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
The equation of the tangent at \( (2, -3) \) on the hyperbola \( x^2 - \frac{y^2}{3} = 1 \) is:
Suppose that there is a chance for a newly constructed house to collapse whether the design is faulty or not. The chance that the design is faulty is 10\%. The chance that the house will collapse if the design is faulty is 95\% and otherwise it is 45\%. It is seen that the house collapsed. What is the probability that the design is faulty?
The value of \( \frac{1}{\sin 10^\circ} - \frac{\sqrt{3}}{\cos 10^\circ} \) is equal to
The angle between \( x^2 = y \) and \( y^2 = x \) at \( (1, 1) \) is:
A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. What is the speed of the river current in km/hr?
If \( \cos B = \frac{\sin A}{2 \sin C} \), then the triangle 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 \( A = \begin{bmatrix} \cos \theta & \sin \theta & 0 \\ \sin \theta & -\cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \), then the value of \( AA' \) is:
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is:
In the expansion of \( \left( x - \frac{3}{x^2} \right)^9 \), the constant term is:
If 20 men can build a wall 56 metres long in 6 days, what length of a similar wall can be built by 35 men in 3 days?
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:
The value of \( \sqrt{2 + \sqrt{2 + 2 \cos 4\theta}} \) is