List of top Mathematics Questions asked in KCET

If $\cos^{-1} x + \cos^{-1} y + \cos^{-1} z = 3\pi$, then $x(y + z) + y(z + x) + z(x + y)$ equals to:

Let $A = \{2, 3, 4, 5, \ldots, 16, 17, 18\}$. Let $R$ be the relation on the set $A$ of ordered pairs of positive integers defined by $(a, b) R (c, d)$ if and only if $ad = bc$ for all $(a, b), (c, d) \in A \times A$. Then the number of ordered pairs of the equivalence class of $(3, 2)$ is:

Let $(g \circ f)(x) = \sin x$ and $(f \circ g)(x) = \left(\sin \sqrt{x}\right)^2$. Then:

Let $f : \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = x^2 + 1$. Then the pre-images of $17$ and $-3$ respectively are:

Let $f : \mathbb{R} \to \mathbb{R}$ be given by $f(x) = \tan x$. Then $f^{-1}(1)$ is:

Let $a$, $b$, $c$, and $d$ be the observations with mean $m$ and standard deviation $S$. The standard deviation of the observations $a + k, b + k, c + k, d + k$ is:

The negation of the statement “For every real number $x$, $x^2 + 5$ is positive” is:

$\lim_{x \to \frac{\pi}{4}} \frac{\sqrt{2}\cos x - 1}{\cot x - 1}$ is equal to:

The equation of the parabola whose focus is $(6, 0)$ and directrix is $x = -6$ is:

The angle between the line $x + y = 3$ and the line joining the points $(1, 1)$ and $(-3, 4)$ is:

If A.M. and G.M. of roots of a quadratic equation are $5$ and $4$ respectively, then the quadratic equation is:

If $S_n$ stands for the sum to $n$-terms of a G.P. with $a$ as the first term and $r$ as the common ratio, then $\frac{S_1}{S_2}$ is:

In the expansion of $(1 + x)^n$, $\frac{{}^nC_1}{{}^nC_0} + 2 \cdot \frac{{}^nC_2}{{}^nC_1} + 3 \cdot \frac{{}^nC_3}{{}^nC_2} + \dots + n \cdot \frac{{}^nC_n}{{}^nC_{n-1}}$ is equal to:

The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is $180$ cm, then:

The real value of $\alpha$ for which $\frac{1 - i \sin \alpha}{1 + 2i \sin \alpha}$ is purely real is:

If $\triangle ABC$ is right-angled at $C$, then the value of $\tan A + \tan B$ is:

If in two circles, arcs of the same length subtend angles $30^\circ$ and $78^\circ$ at the centre, then the ratio of their radii is:

If $[x]^2 - 5[x] + 6 = 0$, where $[x]$ denotes the greatest integer function, then:

Two finite sets have m and a elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and a respectively are:

The value of \(\begin{vmatrix}     \sin^2 14 \degree & \sin^2 66\degree & \tan 135\degree \\     \sin^2 66\degree & \tan 135\degree &     \sin^2 14 \degree \\     \tan 135\degree & \sin^2 14 \degree & \sin^2 66\degree \end{vmatrix}\)

An enemy fighter jet is flying along the curve given by y = x² + 2. A soldier is placed at (3, 2) wants to shoot down the jet when it is nearest to him. Then the nearest distance is

A particle moves along the curve \(\frac{x^2}{16}+\frac{y^2}{4}=1\). When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is

If \(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\) are in A.P., then p, q, r

n^th term of the series
\(1+\frac{3}{7}+\frac{5}{7^2}+\frac{1}{7^2}+...\) is