List of practice Questions

P and Q are two positive integers such that $PQ = 64$. Which of the following cannot be the value of $P + Q$?

The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.

If the roots $x_1$ and $x_2$ of the quadratic equation $x^2 - 2x + c = 0$ also satisfy the equation $7x_2 - 4x_1 = 47$, then which of the following is true?

The sum of the areas of two circles, which touch each other externally, is $153\pi$. If the sum of their radii is 15, find the ratio of the larger to the smaller radius.

A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the examination?

In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the vice chairman and a director?

If $\log_{2} \left[ \log_{3} \left( x^{2} - x + 37 \right) \right] = 1$, then what could be the value of $x$?

After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percentage above the cost price does he mark his goods?

If $n$ is an integer, how many values of $n$ will give an integral value of $\frac{16n^{2} + 7n + 6}{n}$?

A dealer buys dry fruits at Rs. 100, Rs. 80 and Rs. 60 per kilogram. He mixes them in the ratio 3 : 4 : 5 by weight, and sells at a profit of 50%. At what price per kilogram does he sell the dry fruit?

Fresh grapes contain 90% water while dry grapes contain 20% water. What is the weight of dry grapes obtained from 20 kg fresh grapes?

The central thrust of the passage is that

A. But, clearly, the government still has the final say.
B. In the past few years, the Reserve Bank of India might have wrested considerable powers from the government when it comes to monetary policy.
C. The RBI’s announcements on certain issues become effective only after the government notifies them.
D. Isn’t it time the government vested the RBI with powers to sanction such changes, leaving their ratification for later?

A. I sat there frowning at the checkered tablecloth, chewing the bitter cud of insight.
B. That wintry afternoon in Manhattan, waiting in the little French restaurant, I was feeling frustrated and depressed.
C. Even the prospect of seeing a dear friend failed to cheer me as it usually did.
D. Because of certain miscalculations on my part, a project of considerable importance in my life had fallen through.

A. Perhaps the best known is the Bay Area Writing Project, founded by James Gray in 1974.
B. The decline in writing skills can be stopped.
C. Today’s back-to-basics movement has already forced some schools to place renewed emphasis on writing skills.
D. Although the inability of some teachers to teach writing successfully remains a big stumbling block, a number of programmes have been developed to attack this problem.

A. After several routine elections there comes a 'critical' election which redefines the basic pattern of political loyalties, redraws political geography and opens up political space.
B. In psephological jargon, they call it realignment.
C. Rather, since 1989, there have been a series of semi-critical elections.
D. On each definition, only the realignment of recent elections qualifies as a critical election.

A. Trivial pursuits marketed by the Congress, is a game imported from Italy.
B. The idea is to create an imaginary saviour in times of crisis so that the party doesn’t fall flat on its collective face.
C. Closest contenders are Mani Shankar Aiyar, who still hears His Master’s Voice and V. George, who is frustrated by the fact that his political future remains Sonia and yet so far.
D. The current champion is Arjun for whom all roads lead to Rome, or in this case, 10 Janpath.

A. Good advertising can make people buy your products even if it sucks.
B. A dollar spent on brainwashing is more cost-effective than a dollar spent on product improvement.
C. That’s important because it takes pressure off you to make good products.
D. Obviously, there’s a minimum quality that every product has to achieve: it should be able to withstand the shipping process without becoming unrecognizable.

A. Almost a century ago, when the father of the modern automobile industry, Henry Ford, sold the first Model T car, he decided that only the best would do for his customers.
B. Today, it is committed to delivering the finest quality with over six million vehicles a year in over 200 countries across the world.
C. And for over 90 years, this philosophy has endured in the Ford Motor Company.
D. Thus, a vehicle is ready for the customer only if it passes the Ford 'Zero Defect Programme'.