Question : On a certain date, Pakistan had a success rate of 60% against India in all the ODIs played between the two countries. They lost the next 30 ODIs in a row to India and their success rate came down to 30%. The total number of ODIs played between the two countries:
Option 1: 50
Option 2: 45
Option 3: 60
Option 4: 30
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Correct Answer: 60
Solution : Given: On a certain date, Pakistan had a success rate of 60% against India in all the ODIs played between the two countries. They lost the next 30 ODIs in a row to India, and their success rate came down to 30%. Let the total number of ODIs be 10$x$. Pakistan had a success rate of 60% ⇒ They won (10$x$ × $\frac{60}{100}$) = 6$x$ matches. Losing the next 30 ODIs, their success rate came down to 30%. So, the total number of matches = (10$x$ + 30) Now, 6$x$ = (10$x$ + 30) × $\frac{30}{100}$ ⇒ 6$x$ × $\frac{100}{30}$ = 10$x$ + 30 ⇒ 20$x$ = 10$x$ + 30 ⇒ 10$x$ = 30 ⇒ $x$ = 3 Therefore, the total number of ODIs played between the two countries = (10 × 3) + 30 = 60 Hence, the correct answer is 60.
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Question : Which of the following is India's military offensive against Pakistan in the Kargil War?
Option 1: Operation Kargil
Option 2: Operation LOC
Option 3: Operation Vijay
Option 4: Operation Success
Question : A car travels from A to B at the rate of 40 km/h and returns from B to A at the rate of 60 km/h. Its average speed during the whole journey is:
Option 1: 48 km/h
Option 2: 50 km/h
Option 3: 45 km/h
Option 4: 60 km/h
Question : If $\sec( 4x-50°)=\operatorname{cosec}( 50°-x)$, then the value of $x$ is:
Option 1: 45°
Option 2: 90°
Option 3: 30°
Option 4: 60°
Question : The angles of elevation of the top of a temple, from the foot and the top of a building 30 m high, are 60° and 30°, respectively. Then the height of the temple is:
Option 1: 50 metres
Option 2: 43 metres
Option 3: 40 metres
Option 4: 45 metres
Question : Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30° and 45°, respectively. If the height of the tower is 50 metres, the distance between the two men is: (take $\sqrt{3}=1.732$)
Option 1: $136.6$ metres
Option 2: $50\sqrt{3}$ metres
Option 3: $100\sqrt{3}$ metres
Option 4: $135.5$ metres
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