Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Find the scalar components and magnitude of the vector joining the points `P(x_1, y_1, z_1) and Q (x_2, y_2, z_2).`

Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin.

Which of the following differential equations has y = c₁ e^x + c₂ e^–x as the general solution?

(A) `(d^2y)/(dx^2) + y = 0`

(B) `(d^2y)/(dx^2) - y = 0`

(C) `(d^2y)/(dx^2) + 1 = 0`

(D) `(d^2y)/(dx^2)  - 1 = 0`

Which of the following differential equation has y = x as one of its particular solution?

A. `(d^2y)/(dx^2) - x^2 (dy)/(dx) + xy = x`

B. `(d^2y)/(dx^2) + x dy/dx + xy = x`

C. `(d^2y)/(dx^2) - x^2 dy/dx + xy = 0`

D. `(d^2y)/(dx^2) + x dy/dx + xy = 0`

Form the differential equation representing the family of curves given by (x – a)² + 2y² = a², where a is an arbitrary constant.

Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.

If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A^–1) = (det A)^k

For the curve y = 5x – 2x³, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3

Show that the family of curves for which `dy/dx = (x^2+y^2)/(2x^2)` is given by  x² - y² = cx

if `A = ((2,3,1),(1,2,2),(-3,1,-1))`, Find `A^(-1)` and hence solve the system of equations 2x + y – 3z = 13, 3x + 2y + z = 4, x + 2y – z = 8

If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/3`

Form the differential equation from the following primitive where constants are arbitrary:
y² = 4ax

Form the differential equation from the following primitive where constants are arbitrary:
y = cx + 2c² + c³

Form the differential equation from the following primitive where constants are arbitrary:
xy = a²