CBSE 12 Maths Questio paper-2018

If a * b denotes the larger of ‘a’ and ‘b’, and a o b = (a * b) + 3, then write the value of (5) o (10).

Find the magnitude of each of the two vectors having the same magnitude such that the angle between them is 60° and their scalar product is 2/9.

Find the value of tan–1(3) − cot–1(−3).

If the matrix is skew-symmetric, find the values of 'a' and 'b' in the matrix given.

A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

Differentiate tan–1((xsin)/(xcos+1)) with respect to x.

Find the differential equation representing the family of curves y = a * ebx + 5, where a and b are arbitrary constants.

Prove that: 3 * sin–1(x) = sin–1(3x − 4x^3), where x ∈ [-1/2, 1/2].

The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x³ − 0.02x² + 30x + 5000. Find the marginal cost when 3 units are produced.

Evaluate the integral: ∫(xsin(x) + cos(x))/(x² + 1) dx.

Given the matrix A = [[74, -3], [-2, 3]], compute A⁻¹ and show that 2A⁻¹ = 9I - A.

Evaluate the integral ∫(xsin(x) + cos(x))/(x² + 1) dx.

Find the shortest distance between the lines r = (4i − j) + λ(i + 2j − 3k) and r = (i − j + 2k) + μ(2i + 4j − 5k).

Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

Find the equation of the tangent to the curve 16x² + 9y² = 145 at the point (x1, y1) where x1 = 2 and y1 > 0.

Find the interval in which the function f(x) = 4x⁴ − x³ − 5x² + 24x + 12 is strictly increasing.

If the function f(x) = 4x⁴ − x³ − 5x² + 24x + 12 is strictly decreasing, find the corresponding interval.

Find the tangent and normal to the curve 16x² + 9y² = 145 at the point (x1, y1) where x1 = 2 and y1 > 0.

Given the equation 16x² + 9y² = 145, find the equation of the normal at the point (x1, y1).

Evaluate the integral ∫x² sin(x) dx.

Find the mean and variance of the larger number X selected at random from the first five positive integers.

Find the shortest distance between the lines r = (4i − j) + λ(i + 2j − 3k) and r = (i − j + 2k) + μ(2i + 4j − 5k).

Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

Find the equation of the tangent to the curve 16x² + 9y² = 145 at the point (x1, y1) where x1 = 2 and y1 > 0.

The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x³ − 0.02x² + 30x + 5000. Find the marginal cost when 3 units are produced.

Find the magnitude of the vector a = 4i + 5j - k, where i, j, k are unit vectors along the x, y, and z axes respectively.

Find the area of the triangle with vertices at points A(1, 2), B(4, 6), and C(5, 1).

If the function f(x) = 2x³ + 5x² - 3x + 8 is given, find f'(x).

Solve the quadratic equation x² - 5x + 6 = 0.

Find the integral ∫x² e^x dx.

If the function f(x) = x² + 2x + 1 is given, find the value of f'(x).

Find the area of a circle with a radius of 7 cm.

Find the derivative of the function f(x) = 5x³ - 2x² + 4x - 1.

Solve for x: 2x - 3 = 7.

Find the integral ∫sin(x) dx.

Find the value of the determinant of the matrix A = [[1, 2], [3, 4]].

Find the roots of the quadratic equation x² + 3x + 2 = 0.

Find the derivative of the function f(x) = 6x⁴ - 4x³ + 3x² - 2x.

Find the solution to the equation 3x + 4 = 10.

Evaluate the integral ∫e^x dx.

Find the value of the determinant of the matrix A = [[3, 5], [7, 9]].

Find the area of the triangle with vertices at points A(1, 2), B(4, 5), and C(5, 3).

Find the solution to the quadratic equation x² + 5x + 6 = 0.

Evaluate the integral ∫1/(x² + 1) dx.

Find the value of the derivative of the function f(x) = 7x⁴ − 5x³ + 3x² − x + 6.

Evaluate the integral ∫e^(-x²) dx.

Find the distance between the points (3, 4) and (6, 8).

Find the derivative of the function f(x) = x³ − 3x² + 4x − 7.

Find the area of the triangle with vertices at A(2, 3), B(5, 7), and C(6, 2).

Find the sum of the roots of the quadratic equation x² + 7x + 12 = 0.