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

Mark the correct alternative in the following question:

For real numbers x and y, define xRy if `x-y+sqrt2` is an irrational number. Then the relation R is ___________ .

Find the domain of `sec^(-1)(3x-1)`.

Find the domain of `sec^(-1) x-tan^(-1)x`

A firm manufactures two products, each of which must be processed through two departments, 1 and 2. The hourly requirements per unit for each product in each department, the weekly capacities in each department, selling price per unit, labour cost per unit, and raw material cost per unit are summarized as follows:
 

The problem is to determine the number of units to produce each product so as to maximize total contribution to profit. Formulate this as a LPP.

Determine the order and degree (if defined) of the following differential equation:-

\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]

Determine the order and degree (if defined) of the following differential equation:-

y"' + 2y" + y' = 0

Determine the order and degree (if defined) of the following differential equation:-

(y"')² + (y")³ + (y')⁴ + y⁵ = 0

Determine the order and degree (if defined) of the following differential equation:-

y"' + 2y" + y' = 0

Determine the order and degree (if defined) of the following differential equation:-

y" + (y')² + 2y = 0

Determine the order and degree (if defined) of the following differential equation:-

y" + 2y' + sin y = 0

Determine the order and degree (if defined) of the following differential equation:-

y"' + y² + e^y' = 0

In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

y = x² + 2x + C            y' − 2x − 2 = 0

In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

y = cos x + C            y' + sin x = 0

In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

`y=sqrt(1+x^2)`                     `y'=(xy)/(1+x^2)`

In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

y = x sin x              `xy'=y+xsqrt(x^2-y^2)`

Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) . 

Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.

Show that the relation R on the set Z of integers, given by R = {(a,b):2divides (a - b)} is an equivalence relation. 

If `f(x) = (4x + 3)/(6x - 4), x ≠ 2/3`, show that fof (x) = x for all `x ≠ 2/3`. Also, find the inverse of f.

Write the order and degree of the differential equation `((d^4"y")/(d"x"^4))^2 =  [ "x" + ((d"y")/(d"x"))^2]^3`.