261. If cot θ = 7/8, then the value of (1+sin θ)(1-sin θ)/(1+cos θ)(1-cos θ) is
Answer: 49/64
262. If the points A(2, 3), B(4, k), C(6, -3) are collinear, then the value of k is
Answer: 1
263. If the points A(6, 1), B(8, 2), C(9, 4), D(p, 3) are the vertices of a parallelogram in sequence, then the value of p is
Answer: 7
264. In what ratio will the line joining the points (5, 6) and (-1, -4) be divided by the y-axis?
Answer: 3:2
265. ABC and BDE are two equilateral triangles such that D is the midpoint of BC. The ratio of the areas of triangles ABC and BDE is
Answer: 2:1
266. In an arithmetic sequence, if the first and last terms are 17 and 350 respectively, and the common difference is 9, then the number of terms is
Answer: 40
267. The sum of the first 15 multiples of 8 is
Answer: 240
268. A sum of ₹700 was used to give seven cash prizes to students of a school for their academic achievements. If each prize is ₹20 less than the previous one, what is the amount of the first prize?
Answer: ₹150
269. How many three-digit numbers are divisible by 7?
Answer: 128
270. In the series 3, 8, 13, …, 253, the 20th term from the last term is
Answer: 158
271. In a flower bed, there are 23 rose flowers in the first row, 21 in the second row, 19 in the third row, and so on. If there are 5 rose flowers in the last row, the number of rows in the flower bed is
Answer: 10
272. Three years ago and 5 years from now, the sum of the reciprocals of Ms. Sona’s age (in years) is 1/3. What is Sona’s current age?
Answer: 7
273. A motorboat has a speed of 18 km/h in still water and travels with the current at 24 km/h to reach the same spot it returns to. The speed of the current is
Answer: 6 km/h
274. If the quadratic equation \( kx(x-2) + 6 = 0 \) has two equal roots, then the value of \( k \) is
Answer: 6
275. Two consecutive positive odd numbers are such that the sum of their squares is 290. What are those numbers?
Answer: 11, 13
276. The value of \( k \) for which the system of equations \( 3x – y + 5 = 0 \) and \( 6x – 2y + k = 0 \) has no solution
Answer: k ≠ 10
277. The value of \( k \) for which the lines \( 3x + 4y = 5 \), \( 5x + 4y = 4 \), and \( kx + 4y = 6 \) meet at the same point
Answer: 1
278. Which of the following cannot be the difference between a two-digit number and the number formed by reversing its digits?
Answer: 48
279. The pair of lines \( y = 0 \) and \( y = -7 \) has
Answer: No solution
280. If \( x^3 + ax^2 – bx + 6 \) has a factor \( x + 3 \) and \( a + b = 7 \), then the values of \( a \) and \( b \) are, respectively
Answer: 0, 7