List of top Mathematics Questions asked in KCET

The derivative of $tan ^{-1}[\frac{Sin x}{1+ Cos x}]$ with respect to $tan^{-1}[\frac{Cos x}{1+Sin x}]$ is

The value of $\left| \frac{1+ i \sqrt{3}}{\left( 1 + \frac{1}{i+1}\right)^2} \right|$ is

The sum of the first n terms $ \frac {1^2}{1} +\frac {1^2+2^2}{1+2}+ \frac {1^2 +2^2+3^2}{1+2+3}+$ $\dots$ is

If $\alpha , \beta ,\gamma$ are the roots of $x^3-2x+1=0$, then the value of $(\sum \frac {1} {\alpha +\beta -\gamma}$) is

If the focii of $\frac {x^2}{16}+\frac{y^2}{4}=1 $ and $\frac {x^2}{a^2}-\frac{y^2}{3}=1 $ coincide, then value of $a$ is

Locus of a point which moves such that its distance from the $X-axis$ is twice its distance from the line $x - y = 0$ is

If $\frac {Log\,x}{b-c} = \frac {Log\,y}{c-a}=\frac {Log \,z}{a-b}$ then the value of $ x^{b+c} . y^{c+a}.z^{a+b} $ is

Define a relation $R$ on $A =\{1, 2, 3, 4\}$ as $_xR_y$ if $x$ divides $y$. $R$ is

If rth and (r + 1)th terms in the expansion of $(p + q)^n$ are equal, then $\frac {(n+1)q} {r(p+q)} $ is

The sum of the reciprocals of focal distances of a focal chord $PQ$ of $y^2 = 4ax$ is

If $\vec{a}, \vec{b}$ and $\vec{c}$ are unit vectors such that $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$ then angle between $\vec{a \text { and }} \vec{b}$ is

A value of $ \theta$ satisfying $\sin 5 \theta - \sin 3 \theta + \sin \; \theta=0$ such that $0

If lines represented by $x + 3y - 6 = 0, 2x+y-4=0$ and $kx - 3y + 1 = 0$ are concurrent, then the value of $k$ is

The domain of $ f(x) = sin^{-1} [Log_2 (\frac {x} {2})] $ is

The negation of $p \to (\sim p \vee q) $ is

In any triangle $ABC$, the simplified form of $\frac {Cos 2A}{a^2}-\frac{Cos2B}{b^2}$ is

The value of $\sin 10^{\circ} \cdot \sin 30^{\circ} \cdot \sin 50^{\circ}-\sin 70^{\circ}$ is

In Argand's plane, the point corresponding to $\frac {(1-i\sqrt {3})(1+i)} {(\sqrt {3}+i)}$ lies in

If $a > b > 0, Sec^{-1} \left(\frac{a+b}{a-b} \right)= 2 \; Sin^{-1}x $ then $x = $ _____

For the curve $4x^5 = 5y^4$, the ratio of the cube of the subtangent at a point on the curve to the square of the subnormal at the same point is

Two circles centered at $(2, 3) $ and $(5, 6)$ intersect each other. If the radii are equal, the equation of the common chord is ______

If $\vec{a}, \vec {b}$ and $\vec {c}$ are unit vectors, such that $\vec {a}+\vec {b} +\vec {c}=0$ then $3\vec {a}.\vec {b} +\vec {2b}.\vec {c} +\vec {c}.\vec {a}$

In the binomial expansion of $(1+x)^{15}$ the coefficients of $x^r$ and $x^{r+3}$ are equal Then $r$ is _______

The general solution of $1+\operatorname{Sin}^{2} x=3 \operatorname{Sin} x \cdot \operatorname{Cos} x, \operatorname{Tan} x \neq \frac{1}{2}$ is ......

A space vector makes the angles $150^\circ$ and $60^\circ$ with the positive direction of $X -$ and $Y-$axis. The angle made by the vector with the positive direction of $Z-$axis is .............