CBSE 12 Maths Question Paper-2021 Term-2

Find ∫ log(x) / (1 + log(x))^2 dx

Write the sum of the order and the degree of the following differential equation: d/dx(dy/dx) = 5

If 𝑎̂ and 𝑏̂ are unit vectors, prove that |𝑎̂ + 𝑏̂| = 2cos(θ/2), where θ is the angle between them

Find the direction cosines of the following line: 3 − 𝑥/−1 = 2𝑦 − 1/2 = 𝑧/4

A bag contains 1 red and 3 white balls. Find the probability distribution of the number of red balls if 2 balls are drawn at random without replacement.

Two cards are drawn at random from a pack of 52 cards. What is the probability of getting the first card red and the second card Jack?

Find ∫ (x + 1) / (x² + 1) dx

Find the general solution of the following differential equation: x(dy/dx) = y - xsin(y/x)

If vector A ≠ 0, prove that |A × B| = |A| |B| sin(θ), where θ is the angle between A and B

Find the shortest distance between the following lines: r = (i + j - k) + s(2i + j + k), r = (i + j + 2k) + t(4i + 2j + 2k)

Evaluate: ∫ |x³ - 3x² + 2x| dx from -1 to 2

Using integration, find the area of the region in the first quadrant enclosed by the line x + y = 2, the parabola y² = x and the x-axis.

Find the foot of the perpendicular from the point (1, 2, 0) upon the plane x - 3y + 2z = 9.

Case Study: What is the probability that a new policyholder will have an accident within a year of purchasing a policy, given that 20% of the population is accident prone?

Case Study: What is the probability that a policyholder who had an accident is accident-prone?

Find the value of the integral: ∫ (x + 1) / (x² + 1) dx

Find the equation of the plane containing the point (i + 2j − k) and parallel to the lines r = (i + 2j + 2k) + s(2i − 3j + 2k) and r = (3i + j − 2k) + t(i − 3j + k)

Find the foot of the perpendicular from the point (1, 2, 0) upon the plane x − 3y + 2z = 9.

Using integration, find the area of the region enclosed by the parabola y² = x and the line x = 2.

If a system of equations has a unique solution, what does that imply about the determinant of the coefficient matrix?

The sum of the angles in a triangle is always equal to which angle?

Find the value of the integral ∫ e^(−x²) dx from −∞ to +∞.

The solution to the equation x² − 5x + 6 = 0 is:

Which of the following is true for the system of equations 3x + 2y = 5 and 4x + 3y = 6?

What is the probability of drawing a red ball from a bag containing 5 red and 3 blue balls?

If a triangle has sides 3, 4, and 5, what type of triangle is it?

What is the value of sin²(θ) + cos²(θ)?

The area of a circle is given by A = πr². What happens to the area if the radius is doubled?

What is the sum of the interior angles of a hexagon?

What is the solution to the equation 2x + 3 = 7?