List of top Mathematics Questions asked in KCET

If the curves $2x = y^2$ and $2xy = K$ intersect perpendicularly, then the value of $K^2$ is

if $(xe)^y = e^x$, then $\frac{dy}{dx}$ is =

The maximum value of $\frac{log_ex}{x}$, if x > 0 is

If $y = 2x^{n+1} + \frac {3}{x^n}$ ,then $x^2 \frac{d^2y}{dx^2}$ is

The feasible region of an LPP is shown in the figure. If $Z = 11x + 7y$, then the maximum value of $Z$ occurs at

The value of $\int^{\frac{1}{2}}_{-\frac{1}{2}}cos^{-1}xdx$ is

The value of $\,^{16}C_9 + \,^{16}C_{10} -\,^{16}C_6 -\,^{16}C_7$ is

The general solution of the differential equation $x^2dy - 2xydx = x^4\cos\,x\, dx$ is

Events $E_1$ and $E_2$ from a partition of the sample space S. A is any event such that $P(E_1) = P(E_2) = \frac{1}{2}, P(E_2/A) = \frac{1}{2}$ and $P(A/E_2)=\frac{2}{3}$, then $P(E_1/A) $ is

If $A = \{a,b,c\}$, then the number of binary operations on $A$ is

The area of the region bounded by the line $y = 2x + 1$, $x $ - axis and the ordinates $x = -1$ and $x = 1$ is

The probability of solving a problem by three persons $A, B$ and $C$ independently is $\frac{1}{2}$, $\frac{1}{4}$ and $\frac{1}{3}$ respectively. Then the probability of the problem is solved by any two of them is

If the parabola $x^2=4ay$ passes through the point $(2, 1)$, then the length of the latus rectum is

If A = {1,2,3,4,5,6}, then the number of subsets of A which contain at least two elements is

The value of $\sin^2 51^\circ + \sin^2 39^\circ$ is

If A and B are two events such that P(A) = \(\frac{1}{3}\), P(B) = \(\frac{1}{2}\) and P(A ∩ B) = \(\frac{1}{6}\), then P(A'/B) is

The two lines $l x+my=n$ and $l'x+m'y=n'$ are perpendicular if

$\displaystyle \lim_{x\to0}\left(\frac{\tan \,x}{\sqrt{2x +4} - 2}\right)$ is equal to

If the value of a third order determinant is $16$, then the value of the determinant formed by replacing each of its elements by its cofactor is

The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is

The third term of a G.P. is 9. The product of its first five terms is

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set S = {1, 2, 3, 4, 5, 6, 7} and reports that it is even. The probability that it is actually even is

If cos x = |sin x| then, the general solution is

If $A = \{ x | x \in N, x \le 5 \}, B = \{ x | x \in Z, x^2 - 5x + 6 = 0\}$, then the number of onto functions from A to B is

$\sqrt{3}\, cosec \,20^{\circ} - \sec\, 20^{\circ}$ =