List of top Mathematics Questions asked in Karnataka PGCET

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:
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?
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:
The value of \( \frac{1}{\sin 10^\circ} - \frac{\sqrt{3}}{\cos 10^\circ} \) is equal to
The equation of the tangent at \( (2, -3) \) on the hyperbola \( x^2 - \frac{y^2}{3} = 1 \) 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?
The value of \( \tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) \) is equal to
The distance between the foci of the hyperbola \( \frac{x^2}{16} - \frac{y^2}{9} = 1 \) is:
In the expansion of \( \left( x - \frac{3}{x^2} \right)^9 \), the constant term is:
If \( \cot^{-1}(n)>\frac{\pi}{6} \), \( n \in N \), then the maximum value of n is
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?
Quartile coefficient of skewness is
A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds and him in 8 seconds. The length of the train is:
What is the annual income derived by investing ₹6800 in 10\% stock at 136?
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?
If \( \cos B = \frac{\sin A}{2 \sin C} \), then the triangle is
The value of \( \sqrt{2 + \sqrt{2 + 2 \cos 4\theta}} \) is
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is:
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 \( \log_3 2, \log_3 (2^x - 5), \log_3 \left(2^x - \frac{7}{2}\right) \) are in A.P., then \(x\) is:
The circumference of the circle \(x^2 + y^2 - 18x - 16y + 120 = 0\) is:
If the angle between two lines is \(\frac\pi4\) and slope of one of the lines is \(\frac12\), then the slope of the other line is:
The inverse of a symmetric matrix is a:
If the equation of a circle is $(4a - 3)^2 x^2 + a^2 y^2 + 6x - 2y + 2 = 0$, then its centre is: