(v) Simplify: `a times a times a times c times c times c times d`

Evaluate a times a times c times c times c times c times d

Write the following in the exponential form: (a) b times b times b times...10 times. (b) y times y times...15 times (c) 9times a times a times a times b times b times b times b times b (d)8times x times x times y times y times y

Evaluate a^(7)times b^(7)times c^(-4)times c^(5)times d^(9)

At 17^(@)C , the osmotic pressure of sugar solution is 580 torr. The solution is diluted and the temperature is raised to 57^(@)C , when the osmotic pressure is found to be 165 torr. The extent of dilution is a.2 times ,b.3 times ,c.4 times ,d.5 times

In the past 2000 million years, continents have circled the earth (a) 40 times (b) 10 times (c) 4 times (d) 2 times

If vectors barb, bar c ,bard are not coplanar then prove that (bara times barb) times (barc times overlind)+(bara times barc) times (bard times barb)+(bara times bard) times (barb times barc) is parallel to bara .

The radius of a wire is decreased to one-third. If volume remains the same, the length will become 3 times (b) 6 times (c) 9 times (d) 27 times

The prefix mega-indicates (a) Million times (b) Hundred times (c) Thousands times (d) 1 lakh times

A non-immunized pregnant lady is given tetanus vaccination (a) Four times (b) Three times (c) Two times (d) Once

IF bar(a),bar(b),bar(c ) are vectors from the origin to three points A,B,C show that bara times barb +barb times barc+barc times bara is perpendicular to the plane ABC.