Explanation

The Pyrometer is used for measuring very high temperatures.

Pyrometers can measure temperatures without direct contact.

This making them ideal for extreme conditions.

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

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

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

The derivative of 2^(-x) is -2^(-x) * ln(2), which can be written as -2⁻ˣ·log2 (considering log as ln or log base e implicitly in the derivative formula).

Explanation

The formula ∂f/∂x = lim(h → 0) [f(x + h, y) - f(x, y)]/h represents the partial derivative of f with respect to x, and it's evaluated at the point (x, y).

The answer is x at (x, y).

Explanation

Step 1: Evaluate the integral

∫(x² - x - 1) dx = (x³ / 3) - (x² / 2) - x

Step 2: Apply the limits of integration

[(1³ / 3) - (1² / 2) - 1] - [((-1)³ / 3) - ((-1)² / 2) - (-1)]

= [(1/3) - (1/2) - 1] - [(-1/3) - (1/2) + 1]

Step 3: Simplify the expression

= (1/3) - (1/2) - 1 + (1/3) + (1/2) - 1

= (2/3) - 2

= (2/3) - (6/3)

= -4/3

Explanation

Every subgroup of a cyclic group is also cyclic.

This is a key result in group theory under abstract algebra.

Explanation

Total ways to draw 3 balls = C(15, 3) = 455

Ways to draw 3 red balls = C(5, 3) = 10

Probability = 10/455 = 2/91