List of practice Questions

Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide to work independently. After trying all possible combinations of elements, they conclude that the spell does not work. How many attempts does each wizard make before coming to this conclusion, independently?

In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is \( \frac{1}{4} \) of the number of students who like other branches. The number of students who like both their core and other branches is 500. The number of students who like their core branches is:

For positive non-zero real variables \( x \) and \( y \), if \[ \ln\left(\frac{x + y}{2}\right) = \frac{1}{2}\left[\ln(x) + \ln(y)\right], \] then the value of \( \frac{x}{y} + \frac{y}{x} \) is:

Arrange the following important National Days of India in chronological sequence.
(A) National Science Day
(B) National Teacher's Day
(C) National Youth Day
(D) National Hindi Day
(E) National Children's Day
Choose the correct answer from the options given below:

If x(t) satisfies the differential equation
\(t\frac{dx}{dt}+(t-x)=0\)
subject to the condition x(1) = 0, then the value of x(2) is_____(rounded off to 2 decimal places).

If the value of the double integral
\(\displaystyle\int^{4}_{x=3}\displaystyle\int^{2}_{y=1}\frac{dydx}{(x+y)^2}\)
is \(\log e (\frac{a}{24})\), then a is ____ (answer in integer).

Ramesh invests 1,200 at 5% simple interest. How much additional money must he invest at 8% simple interest so that his total annual income will be equal to 6% of his total investment during this year?

A player can take a maximum of 4 chances to hit a bottle with a flying disc.The probability of hitting the bottle at the first, second,third and fourth shots are 0.1, 0.2, 0.35 and 0.45 respectively.What is the probability that the player hits the bottle with the flying disc?

In the Taylor series expansion of sin z around \(z = 0\), the coefficient of the term \(z^3\) is

The bond length of CO is 113 pm and its dipole moment (𝜇⃗) is 0.1 D. The charge (in units of electronic charge) on carbon in the CO molecule including its sign is (rounded off to three decimal places)
[Given: charge of electron = 1.602×10⁻¹⁹ C; 1 D=3.336 × 10⁻³⁰ Cm]

An object is placed 15 𝑐𝑚 in front of a convex mirror, which has a radius of curvature 30 𝑐𝑚. Which one of the following is true of the image formed?

Which one of the following genetic crosses and their results indicates cytoplasmic inheritance?

A spring-mass system (spring constant 80N/m and damping coefficient 40N-s/m), initially at rest, is lying along the y-axis in the horizontal plane. One end of the spring is fixed and the mass (5kg) is attached at its other end. The mass is pulled along the y-axis by 0.5m from its equilibrium position and then released. Choose the correct statement(s).
(Ignore mass of the spring)

Consider the following C function definition: \begin{verbatim} int f(int x, int y) { for (int i = 0; i<y; i++) { x = x + x + y; } return x; } \end{verbatim} Which of the following statements is/are TRUE about the above function?

Consider the 5-state DFA \( M \) accepting the language \( L(M) \subseteq (0+1)^* \) shown below. For any string \( w \in (0+1)^* \), let \( n_0(w) \) be the number of \( 0 \)'s in \( w \) and \( n_1(w) \) be the number of \( 1 \)'s in \( w \). \begin{center} \includegraphics[width = 6cm]{50.png} \end{center} Which of the following statements is/are FALSE?

Consider the following recurrence relation: \[ T(n) = \begin{cases} \sqrt{n}T(\sqrt{n}) + n & \text{for } n \geq 1,
1 & \text{for } n = 1. \end{cases} \] Which one of the following options is CORRECT?