141. The mean of the first 12 natural numbers is:
Answer: 6.5
142. y is 7 years older than x, and 15 years ago, x’s age was 3/4 of y’s age. What is x’s current age?
Answer: 21 years
143. In a right-angled triangle, the hypotenuse is 20 cm. The difference in the lengths of the other two sides is 4 cm. What are the lengths of the two sides?
Answer: 11 cm, 15 cm
144. If 3 – √3 is a root of the quadratic equation, then the equation is:
Answer: x² – 6x + 6 = 0
145. The coordinates of the point that divides the line joining points A(-1, 7) and B(4, -3) in the ratio 2:3 are:
Answer: (-1, 3)
146. The value of sin48° cos42° + cos48° sin42° is:
Answer: 1
147. The sum of the areas of two squares is 468 m². If the difference in their perimeters is 24 cm, then the lengths of the sides of the two squares are:
Answer: 18 m, 12 m
148. In a flower arrangement, the first row has 23 rose plants, the second row has 21, the third row has 19, and so on. If the last row has 5 rose plants, how many rose plants are there in total in the arrangement?
Answer: 150
149. Which term in the arithmetic series -3, -8, -13, … is -78?
Answer: 16th
150. If the graph intersects the x-axis at two points, then the number of zeros of the quadratic polynomial is:
Answer: 2
151. If x = a tanθ and y = b secθ, then y²/b² – x²/a² =
Answer: 1
152. The decimal expansion of 1411/120 will terminate after how many decimal places?
Answer: 3
153. If A(1, 3), B(-1, 4), C(2, 5) and D(x, 4) are the vertices of a parallelogram ABCD, what is the value of x?
Answer: 3
154. The simplest form of sec²θ – 1/(cosec²θ – 1) is
Answer: 1
155. In the given figure, O is the center of a circle, PQ is a chord, and PT is a tangent at point P. If ∠POQ = 70°, what is the value of ∠TPQ?
Answer: 35°
156. How many terms should be taken from the A.P. 18, 16, 14, … so that their sum is zero?
Answer: 18
157. A bucket with a height of 15 cm has circular ends with radii 14 cm and r cm (r < 14 cm). If the volume of the bucket is 5390 cm³, what is the value of r? (Use π = 22/7)
Answer: 6 cm
158. If the mean of the following frequency distribution is 65.6, find the missing frequencies (f₁, f₂).
Answer: (f₁, f₂) = (11, 4)
159. If the distance between the points (x, -1) and (3, 2) is 5, what is the value of x?
Answer: 7, -1
160. The graph of the linear equations 3x + y = 7 and 6x + 2y = 8 represents two lines that are
Answer: Parallel