List of top Mathematics Questions asked in KCET

If $A = \begin{bmatrix} {1}&{-3}\\ {2}&{K} \\ \end{bmatrix}$ and $A^2-14A+10I=A$,then $K$ = is equal to :

On the set $Q$ of all rational numbers the operation $\star$ which is both associative and commutative is given by $a \star b$, is:

A circular sector of perimeter $60$ metre with maximum area is to be constructed. The radius of the circular arc in metre must be

A subset of the additive group of real numbers which is not a sub group is

The value of $\frac{\sin 85^{\circ}-\sin 35^{\circ}}{\cos 65^{\circ}} $ is :

If $O(A) = 2 \times 3, O (B) = 3 \times 2$, and $O(C) = 3 \times 3$, which one of the following is not defined.

If $a, b$ and $c \in N$ which one of the following is not true ?

If $a | (b + c)$ and $a| (b-c)$ where $a,b,c \in \, N $ then

If the area of the parallelogram with \(\vec {a}\) and \(\vec {b}\) as two adjacent sides is \(15\, sq.\space units\),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. unit is

If $a > b > 0$, then the value of $Tan^{-1} \left(\frac{a}{b}\right)+Tan^{-1}\left(\frac {a+b}{a-b}\right) $

The remainder obtained when $(\lfloor 1)^2 + (\lfloor 2)^2 + (\lfloor 3)^2 + ... + (\lfloor 100)^2$ is divided by $10^2$ is ;

If $\sec \theta=m$ and $\tan \theta=n$ , then $\frac{1}{m}\left[(m+n)+\frac{1}{(m+n)}\right] $ is :

If the angles of a triangle are in the ratio $3 : 4 : 5$, then the sides are in the ratio

In the group $G = \{1,5,7,11\}$ under multiplication modulo $12$, the solution of $ 7^{-1} \; \otimes_{12} (x \otimes_{12} 11) = 5$ is $x$ =

The value of $\displaystyle\lim_{x \to 0} \frac {5^x-5^{-x}}{2x}=$ is :

The value of $\begin{vmatrix} x+y&y+z & z+ x \\[0.3em] x & y & z \\[0.3em] x-y & y-z & z-x \end{vmatrix}$ = is equal to :

If $Sin (x + y)+Cos(x + y) = Log (x + y),$ then $\frac {d^2y}{dx^2}$=

If $a, b$ and $c \in N$ which one of the following is not true ?

The digit in the units place in the number $7^{289}$ is

In the group $ (Q^+ ,\star )$ of positive rational numbers w.r.t. the binary operation $\star$ defined by $a^{\star} b=\frac {ab}{3} , \forall a,b \in Q^{+}$ the solution of the equation $5 ^{\star} x=4^{-1}$ in $Q^+$ is

In the group $G. = \{1, 3,7,9 \}$ under multiplication modulo $10$, the inverse of $3$ is

The identity element in the group $M = \left\{ \begin{bmatrix} x & x \\ x & x\\ \end{bmatrix} | x \ \in \ R, x \neq 0 \right\}$ with respect to matrix multiplication is

The converse of the contrapositive of $p \to \sim q$ is

If $A=\begin{bmatrix} {3}&{5}\\ {2}&{0}\\ \end{bmatrix} $ and $B$ = $\begin{bmatrix} {1}&{17}\\ {0}&{-10}\\ \end{bmatrix} $then $|AB|$ is equal to

The solutions of the equation $\begin{vmatrix} {x}&{2} &{-1}\\ {2}&{5}& {x} \\ {-1}&{z}&{x}\\ \end{vmatrix} =0$ are