List of top Mathematics Questions asked in KCET

If $Cos^{-1} p + Cos ^{-1} q + Cos ^{-1} r = \pi $ then $p^{2} + q^{2} +r^{2} +2pqr=$
The smallest positive integer $n$ for which $(1+i)^{2n} = (1-i)^{2n}$ is
The differential coefficient of $f (Sin \,x)$ w.r.t. $x$ where $f (x) = \log\, x$ is
If $0 \leq x \leq \pi$ and +$81^{sin^2x}+81^{Cos^2x}=30$ then $x=$
The radius of the circle passing through the point $(6, 2)$ and two of whose diameters are $x + y = 6$ and $x + 2y = 4$ is
The coaxal system of circles given by $x^{2} + y^{2} + 2gx + c = 0$ for $c < 0$ represents.
The equation of the director circle of the hyperbola $\frac {x^{2}} {16}-\frac{y^{2}} {4}=1$ is given by .............
The value of $k$ so that $x^{2} + y^{2} + kx + 4y + 2 = 0 $ and $2(x^{2}+y^{2})- 4x - 3y + k = 0$ cut orthogonally is
If $Sin^{-1} \frac {x}{5}+Cosec^{-1} \frac {5}{4}=\frac {\pi}{2}$ then $x=$
The set of all integral multiples of $5$ is a subgroup of
Which of the following is not a proposition.
The distance of the point $'\theta'$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ from a focus is
The distance of a focus of the ellipse $9x^2+16y^2 =144$ from an end of the minor axis is
$\tan^{-1}\frac{1}{3}+\tan^{-1}\frac{1}{7}+\tan^{-1}\frac{1}{18}+.........+\tan^{-1}\left(\frac{1}{n^2+n+1}\right)+....to\infty$ is equal to
If $p \Rightarrow (q \vee r)$ is false, then the truth values of $p, q, r$ are respectively
If one end of a diameter of the ellipse $ 4x^2 + y^2 = 16$ is $(\sqrt{3},2)$, then the other end is
The line $ y = 2x + c$ touches the ellipse $\frac{x^2}{16}+\frac{y^2}{4}=1$ if c is equal to
If the normal at one end of a latus-rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ passes through one extremity of the minor axis, then the eccentricity of the ellipse is given by the equation
The locus of the centre of the circle \(x^2 + y^2 + 4x \,\cos \,\theta - 2y\, sin \theta - 10 = 0\) is
The sum of distances of any point on the ellipse $3x^2+4y^2=24$ from its foci is
The eccentricity of the conic $3x^2 + 4y^2 = 24$ is
The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is 180 cm, then
The maximum volume of the right circular cone with slant height 6 units is
If y=2x3x,then \(\frac{dy}{dx}\) at x=1 is
Which one of the following observations is correct for the features of logarithm function to any base \(b>1\)?