Show that\(\left| \overset { x }{ 2x\underset { a }{ + } 2a } \quad \overset { y }{ 2y\underset { b }{ + } 2b } \quad \overset { z }{ 2z\underset { c }{ + } 2c } \right| =0\)

Find the number of 4 letter words, with or without meaning, which can be formed out of the letters of the word “ NOTE”, where the repetition of the letters is not allowed.

A point in the plane moves so that its distance from the origin is thrice its distance from the y- axis. Find its locus.

Convert the following degree measure into radian measure -320^o

Differentiate the following with respect to x 3x⁴ - 2x³ + x + 8

Find the stationary value and the stationary points f(x) = x² + 2x – 5.

What is the amount of perpetual annuity of Rs. 50 at 5% compound interest per year?

From a pack of 52 cards, two cards are drawn at random. Find the probability that one is a king and the other is a queen.

Calculate the correlation coefficient from the following data:
ΣX = 125, ΣY = 100, ΣX² = 650, ΣY² = 436, ΣXY = 520, N = 25

Draw the network diagram for the following activities

Activity code	A	B	C	D	E	F	G
Predecessor activity	-	-	A	A	B	C	D,E