281. If x – y = 0 and 2x – y = 2, then the values of x and y are
Answer: 2, 2
282. The value of k for which the system of equations 2x – 3y = 1 and kx + 5y = 7 will have a unique solution
Answer: k ≠ -10/3
283. A quadratic polynomial whose roots are 3 and -5 is
Answer: x² + 2x – 15
284. If △ABC is right-angled at C, then the value of cos(A+B) is
Answer: 0
285. If secA + tanA = x, then tanA =
Answer: (x² – 1)/2x
286. If sin²θ = √3 cosθ, 0 < θ < 90°, then θ =
Answer: 60°
287. If tan²θ + cot²θ = 2 and θ is an acute angle, then tan³θ + cot³θ =
Answer: 3
288. Which of the following is false?
Answer: sinθ = 3
289. If sin(A-B) = 1/2 and cos(A+B) = 1/2, then the values of A and B are respectively
Answer: 45°, 15°
290. If cosθ – sinθ = √2 cosθ, then cosθ + sinθ =
Answer: √2 sinθ
291. If tanθ = 5/4, then (3 sinθ + 4 cosθ) / (3 sinθ – 4 cosθ)² =
Answer: 31²
292. Two men and seven boys can complete a task in 4 days. Four men and four boys can complete the same task in 3 days. In how many days can one boy complete the task alone?
Answer: 60 days
293. In an exam, each correct answer earns 1 point, while each incorrect answer deducts 1/4 point. If a student answered 120 questions and scored 90 points, how many questions did they answer correctly?
Answer: 96
294. If x = a sinθ and y = b tanθ, then a² / x² – b² / y² = ?
Answer: 1
295. The sides of two similar triangles are in the ratio 3:7. What will be the ratio of their areas?
Answer: 9:49
296. The arithmetic mean of a set of 40 values is 65. If each of the 40 values is increased by 5, what is the mean of the new set of values?
Answer: 70
297. The sum of deviations of the values 3, 4, 6, 7, 8, 14 from their mean is
Answer: 0
298. The value of tan 1° tan 2° tan 3° ….. tan 89° is
Answer: 1
299. The quadratic polynomial whose one zero is 5 and the product of the zeros is 0 is
Answer: x² + 5x
300. The value of m for which 4x² – 6x – m is completely divisible by x – 3 is a factor of m.
Answer: 9