List of top Mathematics Questions asked in KCET

Consider the following statements :
Statement 1 : If y = log10x + logex then \(\frac{dy}{dx}=\frac{\log_{10}e}{x}+\frac{1}{x}\)
Statement 2 : \(\frac{d}{dx}(\log_{10}x)=\frac{\log x}{\log 10}\ \text{and}\ \frac{d}{dx}(\log_ex)=\frac{\log x}{\log e}\)
If the area of the parallelogram with \(\vec{a}\) and \(\vec{b}\) as two adjacent sides is 15 sq.units then the area of the parallelogram having \(3\vec{a}+2\vec{b}\) and \(\vec{a}+3\vec{b}\) as two adjacent sides in sq.units is
A car manufacturing factory has two plants X and Y. Plant X manufactures 70% of cars and plant Y manufactures 30% of cars. 80% of cars at plant X and 90% of cars at plant Y are rated as standard quality. A car is chosen at random and is found to be standard quality. The probability that it has come from plant X is
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is
If A,B and C are three independent events such that P(A) = P(B) = P(C) = P then P(at least two of A, B, C occur) =
Given that A and B are two events such that P(B) = \(\frac{3}{5}\) P(A/B) = \(\frac{1}{2}\) and P(A ∪ B) = \(\frac{4}{5}\) then P(A) =
The shaded region is the solution set of the inequalities
Shaded Region
The area of the quadrilateral ABCD, when A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to
If a plane meets the coordinate axes at A, B and C in such a way that the centroid of triangle ABC is at the point (1, 2, 3) then the equation of the plane is
The angle between the lines whose direction cosines are \((\frac{\sqrt3}{4},\frac{1}{4},\frac{\sqrt3}{2})\) and \((\frac{3}{4},\frac{1}{4},\frac{-\sqrt3}{2})\) is
The equation of the line joining the points (-3, 4, 11) and (1, -2, 7) is
The diagonals of a parallelogram are the vectors \(3\hat{i}+6\hat{j}-2\hat{k}\) and \(-\hat{i}-2\hat{j}-8\hat{k}\) then the length of the shorter side of parallelogram is
A vector \(\vec{a}\) makes equal acute angles on the coordinate axis.Then the projection of vector \(\vec{b}=5\hat{i}+7\hat{j}-\hat{k}\) on \(\vec{a}\) is
The number of solutions of \(\frac{dy}{dx}=\frac{y+1}{x-1}\) when y(1) = 2 is
Solution of Differential Equating xdy – ydx = 0 represents
If the area of the Ellipse is \(\frac{x^2}{25}+\frac{y^2}{\lambda^2}=1\) is 20π square units, then λ is
The area of the region bounded by \(y=\sqrt{16-x^2}\) and x-axis is
The value of \(\int\limits_0^{4042}\frac{\sqrt{x}\ dx}{\sqrt{x}+\sqrt{4042-x}}\) is equal to
If \(I_n=^{\frac{\pi}{4}}_0\int\tan^n x\ dx\) where n is positive integer then I10 + I8 is equal to
The value of \(\int e^x[\frac{1+\sin x}{1+\cos x}]dx\) is equal to
The value of \(\int\frac{xe^x dx}{(1+x)^2}\) is equal to
The value of \(\int\frac{x^2dx}{\sqrt{x^6+a^6}}\) is equal to
\(\int\frac{x^3\sin(\tan^{-1}(x^4))}{1+x^8}dx\) is equal to
The maximum slope of the curve y = -x3 + 3x2 + 2x -27 is
The function f(x) = x2 - 2x is strictly decreasing in the interval