List of practice Questions

Let \(C_1\) and \(C_2\) be concentric circles such that the diameter of \(C_1\) is 2 cm longer than that of \(C_2\). If a chord of \(C_1\) has length 6 cm and is a tangent to \(C_2\), then the diameter, in cm, of \(C_1\) is
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In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent ₹ 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent ₹ 450 on rice in April, then how much did he spend on wheat in May?
In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is
A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is [This Question was asked as TITA]
A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially? [This Question was asked as TITA]
Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been
An alloy is prepared by mixing three metals A, B and C in the proportion 3: 4: 7 by volume. Weights of the same volume of the metals A, B and C are in the ratio 5: 2: 6. In 130 kg of the alloy, the weight, in kg, of the metal C is
Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is
A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to 2 : 3? [This Question was asked as TITA]
The area, in sq. units, enclosed by the lines \(x=2\), \(y=|x-2|+4\), the \(X\)-axis and the \(Y\)-axis is equal to
The vertices of a triangle are (0,0),(4,0) and (3,9). The area of the circle passing through these three points is
In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and \(∠BAD=45°\). If DC=5cm , BC=4 cm, the area of the trapezium in sq cm is ? [This Question was asked as TITA]
The number of real-valued solutions of the equation \(2^x+2^{-x}=2-(x-2)^2\) is
How many distinct positive integer-valued solutions exist to the equation \((x^2-7x+11)^{(x^2-13x+42)}=1\)?
If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is
Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is
In how many ways can a pair of integers \((x , a)\) be chosen such that \(x^2-2|x|+|a-2|=0\) ?
The number of integers that satisfy the equality \((x^2-5x+7)^{x+1} = 1\) is
If \(x = (4096)^{7+4√3}\), then which of the following equals \(64\) ?
If f \((5+x) = f (5-x)\) for every real x, and \(f(x)=0\) has four distinct real roots, then the sum of these roots is
The number of distinct real roots of the equation \(\bigg(\frac{x+1}{x}\bigg)^2-3\bigg(\frac{x+1}{x}\bigg)+2=0\) equals
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Under Section 82 of the Indian Penal Code, nothing is an offence which is done by a child under the age of:
The provisions of Indian Penal Code apply also to any offence committed by:
Deliberate and malicious acts, intended to outrage religious feelings of any class by insulting its religion or religious beliefs, – is an offence under:
Peek Vs. Gurney is a famous case related to: