The area enclosed by the parabola \[y^{2}=12 x\] and its latus rectum is

Let \[P=\left[\begin{array}{cc}3 & -5 \\ 7 & -12\end{array}\right]\] and \[Q=\left[\begin{array}{cc}12 & -5 \\ 7 & -3\end{array}\right]\] then incorrect about the matrix \[({PQ})^{-1}\] is

The locus of the centres of the circles which cut the circles \[x^{2}+y^{2}+4 x-6 y+9=0\] and \[x^{2}+y^{2}-5 x+4 y-2=0\] orthogonally is

The equation \[\sin x+x \cos x=0\] has at least one root in

Let L₁ be a straight line passing through the origin and L₂ be the straight line \[x+y=1\]. If the intercepts made by the circle \[{x}^{2}+{y}^{2}-{x}+3 {y}=0\] on L₁ and L₂ are equal, then which of the following equation can represent L₁?

The sum to infinity of the series \[\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\ldots \ldots,\] is equal to

Equation of straight line \[ax + by + c = 0\] where \[3a+4b+ c = 0,\] which is at maximum distance from \[(1, –2),\] is

Statement-1 : If a, b, c are non real complex and \[\alpha, \beta\] are the roots of the equation \[{ax}^{2}+{bx}+{c}=0\] then \[\operatorname{Im}(\alpha \beta) \neq 0\]
because
Statement-2 : A quadratic equation with non real complex coefficient do not have root which are conjugate of each other.

Statement-1 : Period of \[f(x)=\sin 4 \pi\{x\}+\tan \pi[x],\]
where, \[[x]\] & \[\{x\}\] denote the G.I.F. & fractional part respectively is 1.
Statement-1 : A function \[f(x)\] is said to be periodic if there exist a positive number \[T\] independent of \[x\] such that \[f(T+x)={f}(x).\] The smallest such positive value of \[T\] is called the period or fundamental period.