IPMAT Indore · Paper 14

One alloy is 60% gold and another is 85% gold, the rest being copper in each. In what ratio should the first alloy be melted with the second to obtain an alloy that is 75% gold?

Ten years ago, Meena was half as old as she will be 8 years from now. What is Meena's present age?

In a circle of radius 21 cm, an arc subtends an angle of $60^\circ$ at the centre. What is the area of the corresponding minor sector? (Take $\pi = \frac{22}{7}$.)

The eight observations 5, 8, 11, $x + 2$, $x + 4$, 20, 21, 25 are arranged in ascending order, and their median is 15. What is their mean?

Pens cost ₹12 each and notebooks ₹30 each. Aman spends exactly ₹300 and buys at least one pen and at least one notebook. How many different combinations of numbers of pens and notebooks could he have bought?

The polynomial $x^3 + ax^2 + bx - 6$ has $(x - 2)$ as a factor and leaves a remainder of $-12$ when divided by $(x + 1)$. What are the values of $a$ and $b$?

In the binomial expansion of $(1 + x)^n$, the 5th term and the 9th term have equal coefficients. What is the coefficient of $x^2$ in this expansion?

For what value of $k$ does the system of equations $x + y + z = 6$, $x + 2y + 3z = 10$ and $x + 2y + kz = 12$ have no solution?

Choose the word most nearly opposite in meaning to the underlined word as used in the sentence.

Her grandparents lived a frugal life, mending old clothes and wasting nothing.

Choose the one word that means: a person who eats no food that comes from animals, including milk, eggs and honey.

Choose the option that best explains the meaning of the underlined idiom.

Missing the morning train turned out to be a blessing in disguise, because the bus I took instead got me to the interview early.

Choose the word that correctly completes the sentence.

Heavy fines are meant to ________ young drivers from using their phones at the wheel.

Identify the part of the sentence that contains a grammatical error.

Rahul is one of / the most honest man / I have ever / had the pleasure of working with.

In the sentence below, choose the meaning of the underlined word as used in context.

The audience laughed throughout, enjoying the narrator's dry humour, which he delivered without ever cracking a smile.

Choose the word that best completes the sentence.

Although critics ________ the novel when it first appeared, it is now regarded as one of the finest books of its century.

The sentences given below, when properly sequenced, form a coherent paragraph. Choose the most logical order.

1. Back home, he looked at the burrs under a microscope and saw that they were covered in tiny hooks that caught on anything with loops, such as fur or cloth.

2. He wondered whether the same pairing of hooks and loops could be made by hand and used to fasten things together.

3. After a walk in the Alps in 1941, the Swiss engineer George de Mestral noticed burrs clinging to his trousers and to his dog's coat.

4. It took him years to copy the idea with man-made fibres, but the fastener he went on to patent, Velcro, is now used on everything from shoes to spacesuits.

Choose the option that best replaces the part in square brackets.

Unless you [will not apply] before Friday, you will lose your place on the waiting list.

Choose the option that best fills both blanks.

The new manager's ________ manner put the nervous interns at ease, and within a week even the shyest of them felt ________ enough to share ideas in meetings.

Read the passage and answer the question that follows.

Many Roman harbour walls and buildings have survived for two thousand years, while modern concrete often begins to crumble within decades. For a long time, the small white lumps found throughout Roman concrete were taken as a sign of careless mixing. Recent studies suggest they may be the secret of its durability. The lumps are pieces of lime left behind when the Romans mixed their concrete using quicklime, which heats up strongly when it meets water. When a crack later forms and rainwater seeps in, the water dissolves some of the lime, and the solution hardens again as calcium carbonate, sealing the crack before it can spread. In effect, the material repairs itself. Engineers are now testing modern concretes that contain similar lime lumps, in the hope of building structures that need less repair.

Which of the following can be inferred from the passage?

Read the passage and answer the question that follows.

In 1968 the ecologist Garrett Hardin argued that any resource shared by many users, such as a pasture, a fishery or a forest, is doomed to be overused. Each herder gains the full benefit of adding one more cow but bears only a small part of the damage to the common pasture, so all keep adding cows until the grass is gone. The only cures, Hardin suggested, were to hand the resource to the state or to divide it into private plots. The political economist Elinor Ostrom spent decades studying what actually happens. From alpine meadows in Switzerland to irrigation channels in Nepal and fishing grounds in Turkey, she found communities that had managed shared resources well for generations, using rules they had made themselves: who may take how much, and when, and what happens to those who cheat. Her work showed that the 'tragedy of the commons' is a risk, not a certainty.

Which of the following best expresses the main idea of the passage?