Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:

𝐴' Is another viewer standing on the same line of observation across the road. If the width of the road is 5 meters, then the difference between ∠CAB and ∠CA'B is ______.

The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:

Domain and Range of tan^-1 x = ________.

Find the particular solution of the following differential equation, given that y = 0 when x = `pi/4`.

`(dy)/(dx) + ycotx = 2/(1 + sinx)`

Find the value of `sin^-1 [sin((13π)/7)]`

Prove that the function f is surjective, where f: N → N such that `f(n) = {{:((n + 1)/2",", if "n is odd"),(n/2",", if  "n is even"):}` Is the function injective? Justify your answer.

If `ysqrt(1 - x^2) + xsqrt(1 - y^2)` = 1, then prove that `(dy)/(dx) = - sqrt((1 - y^2)/(1 - x^2))`

Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.

Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.

Find the general solution of the differential equation:

`log((dy)/(dx)) = ax + by`.

Find the general solution of the differential equation:

`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`

If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.

If f(x) = `{{:(ax + b; 0 < x ≤ 1),(2x^2 - x; 1 < x < 2):}` is a differentiable function in (0, 2), then find the values of a and b.

A function f : [– 4, 4] `rightarrow` [0, 4] is given by f(x) = `sqrt(16 - x^2)`. Show that f is an onto function but not a one-one function. Further, find all possible values of 'a' for which f(a) = `sqrt(7)`.

Read the following passage:

Based on the above information, answer the following questions:

1. Can the above function be used to estimate number of vehicles in the year 2000? Justify. (2)
2. Prove that the function V(t) is an increasing function. (2)

If `d/dx f(x) = 2x + 3/x` and f(1) = 1, then f(x) is ______.

The function f(x) = [x], where [x] denotes the greatest integer less than or equal to x; is continuous at ______.

The interval in which the function f(x) = 2x³ + 9x² + 12x – 1 is decreasing is ______.

Write the domain and range (principle value branch) of the following functions:

f(x) = tan^–1 x.

If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.

The function f(x) = x | x |, x ∈ R is differentiable ______.