List of practice Questions

Let $ X $ be a continuous random variable denoting the temperature measured. The range of temperature is $ [0, 100] $ degrees Celsius and let the probability density function of $ X $ be $ f(X) = 0.01 $ for $ 0 \leq X \leq 100 $. The mean is

If the Boolean expression $ (p \Rightarrow q) \Leftrightarrow (q \land (\sim p)) $ is a tautology, then the Boolean expression $ (p \land (\sim q)) $ is equivalent to

For the function $ f(x) = x^2 e^{-x} $, the maximum occurs when $ x $ is equal to

Two of the eigenvalues of a 3x3 matrix are -1 and 2. The determinant of the matrix is 4. Then the third eigenvalue is

The Newton-Raphson method fails for the function $ f(x) $, if

Register A holds the 8-bit binary 11011001. To change the value of Register A to 01101101, the following logic microoperation has to be performed on the operand respectively.

The number of clock cycles that it takes to process 200 tasks in a six-segment pipeline is

Which of the following is related to DBMS?

The set $ S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\} $ is to be partitioned into three sets $ A, B, C $ of equal size. Thus $ A \cup B \cup C = S $, $ A \cap B = B \cap C = A \cap C = \emptyset $. The number of ways to partition $ S $ is

The union and intersection of the graphs G and H are respectively

Match the following:

Let $ A $ and $ B $ be two independent events, then $ P(A \cap B') = $

The number of binary relations on a set with 3 elements is

The cut vertex set of the graph is

The foot of the perpendicular drawn from a point $ A(1,1,1) $ onto a plane $ \pi $ is $ P(-3,3,5) $. If the equation of the plane parallel to the plane $ \pi $ and passing through the midpoint of $ AP $ is \[ ax - y + cz + d = 0, \] then $ a + c - d $ is:

If the circle S = 0 cuts the circles x² + y² - 2x + 6y = 0, x² + y² - 4x - 2y + 6 = 0, and x² + y² - 12x + 2y + 3 = 0 orthogonally, then the equation of the tangent at (0, 3) on S = 0 is:

12 g of an element reacts with 32 g of oxygen. What is the equivalent weight of the element?

Four identical particles each of mass 'm' are kept at the four corners of a square of side 'a'. If one of the particles is removed, the shift in the position of the centre of mass is:

The elongation of a conical bar of length L under the action of its own weight is ___ that of a prismatic bar of the same length.

What is the language $ L $ generated by the production rules $ SS \rightarrow aSa | bSb | a | b $ of the grammar over the alphabet a, b?

At 240.55 K, for one mole of an ideal gas, a graph of $ P $ (on y-axis) and $ V^{-1} $ (on x-axis) gave a straight line passing through the origin. Its slope (m) is 2000 J mol$^{-1}$. What is the kinetic energy (in J mol$^{-1}$) of the ideal gas?

For a gas in a thermodynamic process, the relation between internal energy (U), the pressure (P), and the volume (V) is given by: \[ U = 3 + 1.5PV \] The ratio of the specific heat capacities of the gas at constant volume and constant pressure is:

The locus of a variable point which forms a triangle of fixed area with two fixed points is:

If $ m $ parallel lines are intersected by $ n $ parallel lines, then how many parallelograms are formed?

The number of multiplications needed to find $ x^{32} $ when $ x $ is given, is