Let pqr be a three digit number. Then, pqr + qrp + rpq will not be always divisible by: 9 37 3 p + q + r

The base QR of an equilateral triangle PQR lies on the x-axis. The coordinates of the point Q are (4, 0) and the origin is the midpoint of the base. Find the coordinates of points P and R.

Let $O$ be the origin, and $\overrightarrow{OX}, \overrightarrow{OY}, \overrightarrow{OZ}$ be three unit vectors in the directions of the sides $\overrightarrow{QR}, \overrightarrow{RP}, \overrightarrow{PQ}$, respectively, of a triangle $PQR$.

If the triangle $PQR$ varies, then the minimum value of $$ \cos(P+Q) + \cos(Q+R) + \cos(R+P) $$

(A) $-\frac{5}{3}$ (B) $-\frac{3}{2}$ (C) $\frac{3}{2}$ (D) $\frac{5}{3}$

Let $A(9,-6)$, $B(1,2)$, and $C(4,4)$ be three points on the parabola $y^{2}=4x$. The equation of the circumcircle formed by the point of intersections of the tangents at $A$, $B$, and $C$ is $x^{2}+y^{2}+kx-ky+h=0$.

Then, the value of $k+h$ is:

A) 0 B) 1 C) -1 D) 2

If $y = \frac{1}{1 + x^{G-p} + x^{r-p}} + \frac{1}{1 + x^{r-a} + x^{p-q}} + \frac{1}{1 + x^{p-r} + x^{q-r}}$ then $\frac{dy}{dx} =$

A. 1

B. $(p+q+r) x^{p+q+r}$

C. $\frac{p+q+r}{x^{p+q+r}}$

A wire PQR is bent as shown in the figure and is placed in a region of uniform magnetic field $B$. The length of PQ = QR = l. A current I ampere flows through the wire as shown. The magnitude of the force on PQ and QR will be

A. $BIL, 0$ B. $2BIL, 0$

C. $0, B |$ D. 0, 0