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

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:
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 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 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:
Reena is twice as old as Sunitha. Three years ago, she was three times as old as Sunitha. How old is Reena now?
If \[ \begin{bmatrix} x + y + z \\ x + y \\ y + z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix} \] then the value of \((x, y, z)\) is:
If the equation of a circle is $(4a - 3)^2 x^2 + a^2 y^2 + 6x - 2y + 2 = 0$, then its centre is:
There are 5 pairs of shoes in a cupboard from which 4 shoes are picked at random. The probability that there is at least one pair is:
The value of \[ \cos^2 x + \cos^2 \left(x + \frac\pi3\right) + \cos^2 \left(x - \frac\pi3\right) \] is:
If A and B are the coefficients of $x^n$ in the expansion of $(1 + x)^2n$ and $(1 + x)^2n - 1$, then:
If the system of linear equations: \[ x + 2ay + az = 0 \] \[ x + 3by + bz = 0 \] \[ x + 4cy + cz = 0 \] has a non-zero solution, then $a, b, c$ are:
In how many ways can the letters of the word "CORPORATION" be arranged so that vowels always occupy even places?
In a group of cows and hens, the number of legs is 14 more than twice the number of heads. The number of cows is:
If $a^x = b^y = c^z$ and $b^2 = ac$, then the value of $y$ is equal to:
Focus of the parabola \(y^2 - 8x - 32 = 0\) is:
A frequency distribution can be presented graphically by a:
If the coefficient of variation and mean of a frequency distribution are 5% and 125 respectively, then the standard deviation is:
The length of the transverse axis of the hyperbola \(3x^2 - 4y^2 = 32\) is:
If eccentricity \(e = \frac13\), then the ratio of the major axis to the minor axis of the ellipse is:
In how many ways can we form a garland using 6 different flowers?
The value of \(\cos \left( \frac12 \cos^-1 \frac18 \right)\) 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 value of \(\cos 1^\circ \cos 2^\circ \cos 3^\circ s \cos 180^\circ\) is:
If \(\tan \theta = \frac12\) and \(\tan \phi = \frac13\) then the value of \(\theta + \phi\) is:
If \(2 \tan^-1 (\cos x) = \tan^-1 (2 \csc x)\) then the value of \(x\) is: