The relation between K1 and K2 for which the system of linear equations K1x + 3y = 8 and 4x + K2y = 16 represents coincident lines, is:
Two pipes X and Y can fill a tank in 14 hours and 21 hours, respectively. Both pipes are opened simultaneously to fill the tank. In how many hours will the empty tank be filled?
\(8 \dfrac{2}{5}\ \text{hours}\)
\(6 \dfrac{2}{5}\ \text{hours}\)
\(7 \dfrac{2}{5}\ \text{hours}\)
\(5 \dfrac{2}{5}\ \text{hours}\)
If x = p secA cosB, y = q secA sinB and z = r tanA, what is the value of the following expression?
\(\dfrac{x^2}{p^2} + \dfrac{y^2}{q^2} - \dfrac{z^2}{r^2}\)
The value of (x+y)2 + (x-y)2 is equal to ?
A circular arc whose radius is 14cm, making an angle of 45° at the centre. Find the perimeter (in cm) of the sector.\(\text{(Use } \pi = \dfrac{22}{7}\text{)}\)
The given table shows the number of clerical and officer cadre employees recruited by four different banks A,B,C and D from 2011-2014.
| Year | A | B | C | D | ||||
| Officer | Clerk | Officer | Clerk | Officer | Clerk | Officer | Clerk | |
| 2011 | 260 | 458 | 255 | 460 | 205 | 428 | 265 | 470 |
| 2012 | 310 | 569 | 286 | 584 | 230 | 539 | 246 | 554 |
| 2013 | 350 | 730 | 321 | 725 | 340 | 740 | 361 | 725 |
| 2014 | 400 | 890 | 452 | 845 | 380 | 850 | 482 | 860 |
Compute the ratio of the number of officer cadre employees of Bank A to the number of officer cadre employees of Bank C.
If m is even, then (8m – 1) is divisible by: