List of top Mathematics Questions asked in KCET

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

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

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

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 .............

The derivative of $e^{ax} \cos\,bx$ with respect to $x$ is $re^{ax}$ $\cos\, (bx-Tan^{-1} \frac {b}{a})$ When $a >0, b > 0$,the value of $r$ is ............

The $n^{th}$ term of the series $1+3 + 7 + 13 + 21 + $ is $9901$. The value of $n$ is ................

A wire of length $20\,cm$ is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is ____

If $m$ is the slope of one of the lines represented by $ax^2 + 2hxy + by^2 = 0,$ then $(h + bm)^2$ = ______

The line joining $A (2, -7)$ and $B(6, 5)$ is divided into $4$ equal parts by the points $ P,Q$ and $R$ such that $AQ = RP = QB$. The midpoint of $ PR$ is _______

The number $(49^2 -4) (49^2 -49)$ is divisible by ..................

The constant term of the polynomial $\begin{vmatrix} {x+3}&{x} &{x+2}\\ {x}&{x+1}& {x-1} \\ {x+2}&{2x}&{3x+1}\\ \end{vmatrix} $ is ________

The order and degree of the differential equation y =$ \frac {dp}{dx}x +\sqrt {a^2p^2+b^2}$ where $ p=\frac {dy}{dx}$(here $a$ and $b$ are arbitrary constants) respectively are

Equation of the circle centered at $(4, 3)$ touching the circle $x^2+y^2-1$ externally, is _____

A simple graph contains $24$ edges. Degree of each vertex is $3$. The number of vertices is .................

If $A$ is a $3 \times 3$ nonsingular matrix and if $|A | = 3$, then $|(2A)^{-1}|$= _______

$ \displaystyle\lim _{n \rightarrow \infty} n \sin \frac{2 \pi}{3 n} \cdot \cos \frac{2 \pi}{3 n}$ is

If $y =tan ^{-1} \sqrt {x^2-1}$ then the ratio $\frac {d^2y}{dx^2}: \frac {dy}{dx}$=_________

Which of the following is NOT true?

The sides of a triangle are $6+\sqrt {12} , \sqrt {48} $ and $\sqrt {24}$. The tangent of the smallest angle of the triangle is