List of top Mathematics Questions asked in Karnataka PGCET

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:

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:

In how many ways can we form a garland using 6 different flowers?

In how many ways can the letters of the word "CORPORATION" be arranged so that vowels always occupy even places?

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:

If $a^x = b^y = c^z$ and $b^2 = ac$, then the value of $y$ is equal to:

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 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:

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:

If the equation of a circle is $(4a - 3)^2 x^2 + a^2 y^2 + 6x - 2y + 2 = 0$, then its centre 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:

The value of \(\cos \left( \frac12 \cos^-1 \frac18 \right)\) is:

The value of \[ \cos^2 x + \cos^2 \left(x + \frac\pi3\right) + \cos^2 \left(x - \frac\pi3\right) \] is: