If $p \Rightarrow (q \vee r)$ is false,then the truth values of $p, q, r$ are respectively:

$A$ conducting ring is placed around the core of an electromagnet as shown in the figure. When key $K$ is pressed,the ring

Let $p = (x + 4y)\,a + (2x + y + 1)\,b$ and $q = (y - 2x + 2)\,a + (2x - 3y - 1)\,b,$ where $a$ and $b$ are non-collinear vectors. If $3p = 2q,$ then the values of $x$ and $y$ are:

Let $PQ$ and $RS$ be tangents at the extremities of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle,then $2r$ equals

If $f(2)=4$ and $f^{\prime}(2)=1$,then $\lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}$ is equal to

The equation of the normal to the curve $y^4=ax^3$ at $(a, a)$ is