List of practice Questions

In \(\triangle ABC\), \(AB = 17.5\) cm, \(AC = 9\) cm. Let \(D\) be a point on \(BC\) such that \(AD \perp BC\) and \(AD = 3\) cm. What is the radius of the circumcircle of \(\triangle ABC\)?

Let \(f(x)\) be a function satisfying \(f(x) f(y) = f(xy)\) for all real \(x, y\). If \(f(2) = 4\), then what is the value of \(f\left( \frac12 \right)\)?

The seed of any positive integer \(n\) is defined as: \[ \text{seed}(n) = n, \ \text{if } n<10 \] \[ \text{seed}(n) = \text{seed}(s(n)), \ \text{otherwise} \] where \(s(n)\) is the sum of digits of \(n\). How many positive integers \(n\), such that \(n<500\), will have \(\text{seed}(n) = 9\)?

How many integers, greater than \(999\) but not greater than \(4000\), can be formed with the digits \(0, 1, 2, 3, 4\), if repetition of digits is allowed?

Neelam rides her bicycle from her house at \(A\) to her office at \(B\), taking the shortest path. The number of possible shortest paths that she can choose is:

Neelam rides her bicycle from her house at \(A\) to her club at \(C\), via \(B\) taking the shortest path. The number of possible shortest paths that she can choose is:

The number of common terms in the two sequences \(17, 21, 25, \ldots, 417\) and \(16, 21, 26, \ldots, 466\) is:

A shop stores \(x\) kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of \(x\)?

If the roots of the equation \(x^3 - ax^2 + bx - c = 0\) are three consecutive integers, then what is the smallest possible value of \(b\)?

What are the last two digits of \(7^{2008}\)?

What is the other root of \(f(x) = 0\)?

What is the value of \(a + b + c\) given the above conditions?

The integers \(1, 2, \ldots, 40\) are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say \(a\) and \(b\), currently on the blackboard are erased and a new number \(a + b - 1\) is written. What will be the number left on the board at the end?

The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is :

$2N HCl$ solution will have same molar concentration as a

Which of the following is not a plant product?

Starting with a sample of pure ${ }^{66} Cu , 7 / 8$ of it decays into $Zn$ in $15 \,min$. The corresponding half-life is

The distance between the parallel lines $ y=x+a,\,\,y=x+b $ is

The vector equation of the line passing through the points $ (3,2,1) $ and $ (-2,1,3) $ is

A dihybrid test cross yielding a result of 1 : 1 : 1 : 1 ratio is indicative of

If the circles $x ^2 + y ^2 =9$ and $x^2 + y^ 2 + 2\alpha x + 2y +1 = 0$ touch each other internally, then $\alpha$ =

Which one of the following chlorohydrocarbons readily undergoes solvolysis?

Methoxy methane and ethanol are

In a party everyone gave a gift to everyone else. If the total number of gifts exchanged in the party was 600, how many persons were there in the party?

$50 \, mL $ of $H_2O$ is added to $50 \, mL$ of $1 \times 10^{-3}\, M$ barium hydroxide solution. What is the pH of the resulting solution?