List of practice Questions

Narmada Bachao Andolan : Medha Patkar :: Bhudan Andolan : ?
A clock is correct on Monday at 3{:00 AM but gains 2 minutes per hour. What time will it show when the actual time is 7{:}30 PM on Tuesday?}
Find \(\sqrt{4^{6x^{2}} 25^{y/2} 9 z^{4}}\).
Two oranges, three bananas and four apples cost ₹ 15. Three oranges, two bananas and one apple cost ₹ 10. How much will I pay for 3 oranges, 3 bananas and 3 apples?
Two equal glasses filled with mixtures of alcohol and water in the proportions of \(2:1\) and \(1:1\) respectively were emptied into a third glass. What is the proportion of alcohol and water in the third glass?
₹ 776 is divided among 300 students (boys and girls). Each boy gets ₹ 2.40 and each girl gets ₹ 2.80. Find the number of girls.
Ritu wants to make a trapezium such that \(AB\) is parallel to \(CD\). \(\angle ABC=90^\circ\) and \(\angle BAD=45^\circ\). Lengths: \(CD=5\ \mathrm{cm}\) and \(BC=4\ \mathrm{cm}\). Find the area of the trapezium.
If 100 fewer students had applied and 50 fewer were selected, the ratio selected:unselected would be \(7:4\). In reality, the ratio selected:unselected was \(3:2\). How many students had applied?
₹ 45000 is deposited at compound interest for 4 years. The rates are 6% (1st year), then increase by 1% each year (so 7%, 8%, 9%). Find the approximate amount at the end of 4 years.
A shopkeeper marks 30% above cost and allows a 15% discount. He also uses a faulty balance: sells “1 kg” but delivers only 800 g. Find his actual profit percentage.
Ram and Shyam are 10 km apart. They both see a hot-air balloon making angles of elevation \(60^\circ\) and \(30^\circ\) respectively. What is the height at which the balloon could be flying?
Average monthly expenditure for January--June is ₹ 3200. He spends ₹ 3000 (July), ₹ 3600 (Aug), ₹ 3900 (Sept), ₹ 4200 (Oct). If November’s expenditure is $50%$ of December’s and the average for the entire year is ₹ 3200, find November’s expenditure.
Despite his repeated failures, the entrepreneur remained __________ in his pursuit of success.
Choose the pair that best expresses the same relationship as: FLORIST : FLOWERS
Choose the pair that best expresses the same relationship as: SENTINEL : WATCH
The manager’s decision to fire the employee was seen as a __________ act of revenge rather than a professional choice.
The compound that will undergo SN1 reaction with the fastest rate is
Who, of the following, defined Human Geography as “Conception resulting from a more synthetic knowledge of the physical laws governing our earth and of the relations between the living beings which inhabit it”?
(1) Ratzel
(2) Blache
(3) Taylor
(4) Semple
If the determinant of a 3rd order matrix \( A \) is \( K \), then the sum of the determinants of the matrices \( (AA^T) \) and \( (A - A^T) \) is:
Two dice are thrown simultaneously. If $X$ denotes the number of fours, then the expectation of $X$ will be:
For all positive integers \( n \), if \( 3(5^{2n+1}) + 2^{3n+1 \) is divisible by \( k \), then the number of prime numbers less than or equal to \( k \) is:}
A ball falling freely from a height of \( 4.9 \) m/s hits a horizontal surface. If \( e = \frac{3}{4} \), then the ball will hit the surface the second time after:
If \( f(x) = \sqrt{x - 1 \) and \( g(f(x)) = x + 2\sqrt{x} + 1 \), then \( g(x) \) is:}
If \(A + B + C = 2S\), then \[ \sin(S - A)\,\cos(S - B)\;-\;\sin(S - C)\,\cos S \;=\;? \]
If a function \( f: \mathbb{R} \to \mathbb{R} \) is defined by \( f(x) = x^3 - x \), then \( f \) is: