This question tests your knowledge of standard trigonometric ratios for common angles.
Therefore, sin 30° = 0.5
Answer: B) 0.5
By the Angle Bisector Theorem, the angle bisector divides the opposite side in the ratio of the adjacent sides.
Therefore, BD/DC = AB/AC, which gives 4/DC = 6/9.
Solving: DC = (4 × 9)/6 = 36/6 = 6 cm.
This theorem is essential for solving numerous geometry problems in competitive exams.
By the geometric mean altitude theorem, when an altitude is drawn to the hypotenuse of a right triangle, the altitude is the geometric mean of the two segments of the hypotenuse.
Therefore, altitude = √(9 × 16) = √144 = 12 cm.
This is a fundamental property used frequently in competitive exams.
Using Vieta's formulas: p + q = 5 and pq = 6.
We need 1/p + 1/q = (p+q)/pq = 5/6.
This approach avoids finding individual roots and uses the relationship between roots directly.
When three numbers are in arithmetic progression, they can be written as (a-d), a, (a+d) where a is the middle term.
Their sum is (a-d) + a + (a+d) = 3a = 15, giving a = 5.
Therefore, the middle term y = 5.
Rate constant k is independent of reactant concentration; it depends on T, nature of reactants, and catalyst
The slowest step in a mechanism is the rate-determining step (RDS), which is step 2
0 = 0.5 - 0.02t; t = 0.5/0.02 = 25 s
Not all collisions are effective; only those with proper orientation and sufficient energy lead to reaction
After 90 min = 3 half-lives, remaining = (1/2)³ = 1/8