Explanation

If one angle of an isosceles triangle is 68°, then:

- If 68° is the vertex angle, the other two equal angles = (180 - 68) / 2 = 56°  

- If 68° is one of the equal base angles, then the vertex angle = 180 - 2×68 = 44°

So, possible values for the second angle are 44° or 56° 

Explanation

The theorem you mentioned is known as Pythagoras' Theorem, which states:

$$c^2 = a^2 + b^2$$

where:

• $c$ is the hypotenuse (the longest side of a right-angled triangle).
• $a$ and $b$ are the other two sides.

It was discovered by the ancient Greek mathematician Pythagoras and is fundamental in geometry.

Explanation

log₁₀(1000) means “10 raised to what power gives 1000?”  

Since 10³ = 1000,  

log₁₀(1000) = 3.

Explanation

The value of the log can be either with base 10 or with base e.

The log10 10 value is 1

while the value of loge 10 or ln(10) is 2.302585.

ND18-9-2023

Explanation

To evaluate the expression:

Log₁₀ √10

First, rewrite the square root as an exponent:

√10 = 10^(1/2)

Now, apply the logarithm:

Log₁₀ 10^(1/2)

Using the property of logarithms that states logₐ a^x = x:

Log₁₀ 10^(1/2) = 1/2

Explanation

The standard derivative of sin(x) with respect to x is cos(x).  

d/dx [sin(x)] = cos(x)

Explanation

The RMS (Root Mean Square) value of an AC signal is a measure of its effective value,

Representing the DC equivalent that would produce the same amount of heat in a resistive load.

For a given AC signal, its RMS value is a constant and does not vary with the instantaneous phase angle.

Explanation

- 14 dozen eggs = Rs.100  

- 48 eggs = 4 dozen → 4 × 12 = Rs.48  

- Total = Rs.100 + Rs.48 = Rs.148

Last updated 14-feb-2026

Explanation

Dog, Cow, and Tiger are mammals — they are warm-blooded, have fur/hair, and give birth to live young (most of the time).

Snake is a reptile — it is cold-blooded, has scales, and lays eggs.

So, Dog, Cow, and Tiger are more alike, and Snake is the odd one out.

Explanation

51, 64, 121, 144, 256

Check if they are perfect squares:

- 51 → Not a perfect square  

- 64 → 8²  

- 121 → 11²  

- 144 → 12²  

- 256 → 16²  

All are perfect squares except 51.