Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

The degree of the differential equation `("d"^2y)/("d"x^2) + "e"^((dy)/(dx))` = 0 is ______.

The degree of the differential equation `sqrt(1 + (("d"y)/("d"x))^2)` = x is ______.

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b ∀ a, b ∈ T. Then R is ____________.

Let us define a relation R in R as aRb if a ≥ b. Then R is ____________.

Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is ____________.

Let A = {1, 2, 3, …. n} and B = {a, b}. Then the number of surjections from A into B is ____________.

Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is ____________.

Let S = {1, 2, 3, 4, 5} and let A = S x S. Define the relation R on A as follows:
(a, b) R (c, d) iff ad = cb. Then, R is ____________.

Let R be the relation “is congruent to” on the set of all triangles in a plane is ____________.

Total number of equivalence relations defined in the set S = {a, b, c} is ____________.

The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R^-1 is given by ____________.

Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is ____________.

Solve for x : {xcos(cot^-1 x) + sin(cot^-1 x)}² = `51/50`

If `vec"a"` and `vec"b"` are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.

A vector `vec"r"` has magnitude 14 and direction ratios 2, 3, – 6. Find the direction cosines and components of `vec"r"`, given that `vec"r"` makes an acute angle with x-axis.

Find the sine of the angle between the vectors `vec"a" = 3hat"i" + hat"j" + 2hat"k"` and `vec"b" = 2hat"i" - 2hat"j" + 4hat"k"`.

The value of sin `["cos"^-1 (7/25)]` is ____________.

If A, B, C, D are the points with position vectors `hat"i" + hat"j" - hat"k", 2hat"i" - hat"j" + 3hat"k", 2hat"i" - 3hat"k", 3hat"i" - 2hat"j" + hat"k"`, respectively, find the projection of `vec"AB"` along `vec"CD"`.

The value of tan `("cos"^-1  4/5 + "tan"^-1  2/3) =`

The equation sin^-1 x – cos^-1 x = cos^-1 `(sqrt3/2)` has ____________.