Arts (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

Assertion (A): The domain of the function sec^–12x is `(-∞, - 1/2] ∪ pi/2, ∞)`

Reason (R): sec^–1(–2) = `- pi/4`

Make a rough sketch of the region {(x, y): 0 ≤ y ≤ x², 0 ≤ y ≤ x, 0 ≤ x ≤ 2} and find the area of the region using integration.

Find the area bounded by the curve y = |x – 1| and y = 1, using integration.

Find the area of the region bounded by curve 4x² = y and the line y = 8x + 12, using integration.

Using integration, find the area of the region bounded by the curves x² + y² = 4, x = `sqrt(3)`y and x-axis lying in the first quadrant.

Find the area of the region enclosed by the curves y² = x, x = `1/4`, y = 0 and x = 1, using integration.

Using integration, find the area of the region bounded by line y = `sqrt(3)x`, the curve y = `sqrt(4 - x^2)` and Y-axis in first quadrant.

Find the area of the smaller region bounded by the curves `x^2/25 + y^2/16` = 1 and `x/5 + y/4` = 1, using integration.

`sin[π/3 + sin^-1 (1/2)]` is equal to ______.

Find the value(s) of 'λ' if the function

f(x) = `{{:((sin^2 λx)/x^2",", if x ≠ 0  "is continuous at"  x = 0.),(1",", if x = 0):}`

Sketch the region bounded by the lines 2x + y = 8, y = 2, y = 4 and the Y-axis. Hence, obtain its area using integration.

Find the area of the following region using integration ((x, y) : y² ≤ 2x and y ≥ x – 4).

Find the area of the minor segment of the circle x² + y² = 4 cut off by the line x = 1, using integration.

Find the value of k for which the function f given as

f(x) =`{{:((1 - cosx)/(2x^2)",", if x ≠ 0),(       k",", if x = 0 ):}` 

is continuous at x = 0.

Using integration, find the area of the region bounded by y = mx (m > 0), x = 1, x = 2 and the X-axis.

If f(x) = `{{:((kx)/|x|"," if x < 0),(  3","   if x ≥ 0):}` is continuous at x = 0, then the value of k is ______.

Make a rough sketch of the region {(x, y) : 0 ≤ y ≤ x² + 1, 0 ≤ y ≤ x + 1, 0 ≤ x ≤ 2} and find the area of the region, using the method of integration.

Write the antiderivative of `(3sqrtx+1/sqrtx).`

Let A = {1, 2, 3,......, 9} and R be the relation in A × A defined by (a, b) R (c, d) if a + d = b + c for (a, b), (c, d) in A × A. Prove that R is an equivalence relation. Also, obtain the equivalence class [(2, 5)].

Evaluate : `∫(sin^6x+cos^6x)/(sin^2x.cos^2x)dx`