Explanation

Given y = x²/(1 + x²),

∫y dx = ∫[x²/(1 + x²)] dx = ∫[1 - 1/(1 + x²)] dx = x - arctan(x) + C.

Given ∫y dx = C + f, f = x - arctan(x).

x - 1 + 1/(x + 1)

Explanation

Given that 1 - i is a root of the equation x² + ax + b = 0, and the coefficients are real, the complex conjugate 1 + i must also be a root.

The sum of the roots = (1 - i) + (1 + i) = 2 = -a

So, a = -2

The product of the roots = (1 - i)(1 + i) = 1² - i² = 1 + 1 = 2 = b

So, b = 2

Now, a - b = -2 - 2 = -4

Explanation

C.P. of 1 toy = 375/12 = Rs. 31.25

S.P of 1 toy = Rs. 33

Profit = 1.75/31.25 * 100 = 28/5 = 5.6%

Explanation

Onslaught means a fierce or violent attack, which fits well with "by the enemy".

Onslaught means حملہ

Explanation

Skew lines are non-coplanar, do not intersect, and are not parallel.

They exist in 3D geometry, not lying in the same plane.

Explanation

Explanation

The given inequalities define a region in the Cartesian plane:

a - δ ≤ x ≤ a + δ (horizontal bounds)

b - δ ≤ y ≤ b + δ (vertical bounds)

This region forms a square with:

Center at (a, b)

Side length of 2δ

The answer is A square.

Explanation

1. Leibniz’s theorem gives a formula to find the nth derivative of the product of two functions.

2. It uses the binomial expansion:

Explanation

Coerced means forced or pressured to do something against one’s will.

Sentence: "He was coerced to give this confessional statement." makes logical and grammatical sense.

Explanation

Exonerated means cleared from blame or charges.

Sentence: "He was exonerated from all charges leveled against him." is grammatically and contextually correct.