Mathematical Sk...

Determine the equation for the ellipse if the center is at (0, 0), the major axis on the y-axis and ellipse passes through the points (4, 3) and (2, 5)

A tank has a leak which would empty a completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minute in the tank, the leak takes 15 hours to empty the tank. How many litres of water does the tank hold?

A family gets 1 kg more sugar for Rs. 80 due to reduction of price of sugar by Rs. 4 per kg then what is the percentage reduction in price of sugar.

If the vertex of the parabola x = y² - 6y + c lies on the y-axis, then the value of c is?

A woman can row 5 km/hr in still water and the speed of the stream is 2 km/hr, then find in how much time it will cover 154 km downstream.

If \(\cos A=\frac{3}{4},\) then what is the value of \(\sin \left(\frac{A}{2}\right) \sin \left(\frac{3 A}{2}\right) ?\)

In 1998, the price of an article increased by 25% with respect to that in 1997. In 1999 the price of the article is reduced by 10% with respect to that in 1998 and sold at 7200 rupees then what is the price of the article in 1996 if the price of the article in 1996 and 1997 are in a ratio 3 : 2?

Two trains, each 100 m long, moving in opposite directions, cross each other in 12 sec. If one is moving twice as fast as the other, then the speed of the faster train is _______.

In a class there are total 550 students. Ratio of boys and girls is 6 : 5. How many girls should join the class so that ratio becomes 5 : 6.

A sum of Rs. 25,000 in the bank. Simple interest on one part for 5 years @ 6% p.a. is equal to second part for 4 years @ 5% p.a. Calculate second part of the sum lent.