Mathematics
Find the value of K if the quadratic equations 2x² + Kx + 8 = 0 and 3x² + 4x + 12 = 0 have both roots common.
The larger of two supplementary angles is 28° more than the smaller one. The smaller angle (in degree) is:
Kiran spends 45% of his income. If he saves ₹66,000, then his income (in ₹) is:
A dealer sells two dryers at the rate of ₹63,000 per dryer. On one, he earns a profit of 5% and on the other he loses 30%. What is his loss percentage in the whole transaction?
The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 16% per annum is ₹797. Find the sum (rounded off to the nearest integer).
When x is added to each of 30, 15, 21 and 11, then the numbers so obtained, in this order, are in proportion. Then, if 6x : y :: y : (3x - 9), and y > 0, what is the value of y?
In quadrilateral ABCD, AB = 17 cm, BC = 8 cm, CD = 9 cm, AD = 12 cm, and AC = 15 cm. What is the area (in cm²) of the quadrilateral?
Find the duration (in years) in which ₹1,200 will amount to ₹2,280 at a rate of 4% per annum simple interest.
A vendor bought lemons at 7 for ₹1. How many lemons must he sell for ₹1 to gain 75%?
The larger of two supplementary angles is 50° more than the smaller one. The smaller angle (in degree) is:
If 7.5 : 19.5 :: 16 : x, find the value of x.
The simplified value of 127 - 7 × (17 + 6) + 93 is:
Pipe A can fill a tank in 18 minutes, while pipe B can empty the completely filled tank in 20 minutes. Initially, pipe A is opened and after 6 minutes pipe B is also opened. In how much time (in minutes) will the remaining tank be filled completely?
Simplify (2x - 5y)² + (5x + 2y)² + (2x + 5y)(2x - 5y).
If x + (1/x) = 5, then what is the value of x² + (1/x²)?
A train running at a speed of 72 km/hr crosses a stationary pole in 15 seconds. What is the length of the train (in metres)?
The side of an equilateral triangle is 8 cm. What is the area of this triangle?
A single equivalent discount for successive discounts of 20% and 15% on a marked price is: