151. If $$\frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}+1}{\sqrt{7}-1}=a+\sqrt{7} b$$ the values of a and b are respectively
152. The value of $$\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+......+\frac{1}{\sqrt{8}+\sqrt{9}}$$ is
153. If $$\frac{\sqrt{a+2b}+\sqrt{a-2b}}{\sqrt{a+2b} - \sqrt{a-2b}}=\frac{\sqrt{3}}{1}$$, find the value of $$\frac{a}{b}$$
154. A point in the 4th quadrant is 6 unit away from x-axis and 7 unit away from y-axis. The point is at
155. PQRST is a cyclic pentagon and PT is a diameter, then $$\angle$$PQR + $$\angle$$RST is equal to
156. If $$x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$$ then $$x^{3} + \frac{1}{x^{3}}$$ is equal to
157. The distance between the centres of the two circles of radii r1, and r2 is d. They will touch each other internally if
158. ΔABC is an isosceles triangle with AB = AC = 10 cm, AD = 8 cm is the median on BC from A. The length of BC is
159. A point Q is 13 crn from the centre of a circle. The length of the tangent drawn from Q to a circle is 12 cm. The distance of Q from the nearest point of the circle is
160. ΔABC is a right angled triangle with AB = 6 cm, AC = 8 cm, ∠BAC = 90′. Then the radius of the incircle is
161. In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is
162. ΔABC is similar to ΔDEF. The ratio of their perimeters is 4 :1. The ratio of their areas is
163. The angle between the minute hand and hour hand of a clock when the time is 7:20 is equal to
164. The value of $$cos^2 30^{\circ} + sin^2 60^{\circ} + tan^2 45^{\circ} + sec^2 60^{\circ} + cos0^{\circ}$$ is
165. If a 48 m tall building has a shadow of 48√3 m., then the angle of elevation of the sun is
166. If $$cos x + cos^{2} x = 1,$$ then $$sin^{8} x + 2 sin^{6} x + sin^{4}$$ x is equal to
167. O is the circumcentre of the triangle ABC and ∠BAC = 85°, ∠BCA = 75°, then the value of ∠OAC is
168. If $$x= p$$ $$cosec θ$$ and $$y= q$$ $$cot θ$$, then the value of $$\frac{x^2}{p^2}-\frac{y^2}{q^2}$$ is
169. From an aeroplane just over a straight road, the angles of depression of two consecutive kilometre stones situated at opposite sides of the aeroplane were found to be 60° and 30° respectively. The height (in km) of the aeroplane from the road at that instant was (Given √3 = 1.732)
170. In ΔABC, ∠C = 90° and AB = c, BC = a, CA = b; then the value of (cosec B - cos A) is
171. $$\sqrt{\sqrt{\sqrt{0.00000256}}}$$
172. If 1 man or 2 women or 3 boys can do a piece of work in 44 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in
173. The digit in the unit place in the square root of 66049 is
174. 8 workers can build a wall 18 m long, 2 m broad and 12 m high in 10 days, working 9 hours a day. Find how many workers will be able to build a wall 32 m long, 3 m broad and 9 m high in 8 days working 6 hours a day ?
175. A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. Find the capacity of the tank.
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