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(sin 2A + sin 2B)/ (sin 2A – sin 2B) = tan (A+B)/tan (A-B). Prove.

Solution: We have sin (A + B) = 2 sin (A + B)/2 cos (A – B)/2 sin (A –... View Article

Fill in the blank with the most appropriate word.

“ ____ you married? ” “ No, I ______ .” (a) Aren’t / am (b) Are / am (c) Is... View Article

Name two aquatic animals.

Answer: The animals which live in water are called aquatic animals. Example – dolphin, shark.

The value of sin 12⁰ sin 48⁰ sin 54⁰ is

(a) 2/3 (b) 1/2 (c) 1/8 (d) 1/3 Solution: We know sin A sin B = ½ [ cos (A... View Article

The sum of an integer and its additive inverse is always

Answer: The sum of an integer and its additive inverse is always zero. Consider an example, 8. The additive inverse... View Article

Solve for x: 1/(x-1)(x-2) + 1/(x-2)(x-3) = 2/3. x ≠ 1, 2, 3

Solution: Given 1/(x-1)(x-2) + 1/(x-2)(x-3) = 2/3 [(x-3) + (x-1)]/(x-1)(x-2)(x-3) = 2/3 (2x – 4)/(x-1)(x-2)(x-3) = 2/3 2(x-2)/(x-1)(x-2)(x-3) = 2/3... View Article

Expand (2x + 3y)²

Solution: We use the identity (a+b)2 = a2 + 2ab + b2 (2x + 3y)2 = (2x)2 + 2×2x×3y +... View Article

AIR Spotlight – 20 years of Good Governance: Clean India, Clean Climate

AIR Spotlight is an insightful program featured daily on the All India Radio Newsonair. In this program, many eminent panelists... View Article

The Fourth Buddhist Council Was Held Under The Leadership Of Kanishka At (A) Mathura. (B) Kashmir. (C) Gandhara. (D) Purushapura.

The correct answer is (B) Kashmir. The fourth Buddhist Council was held under the patronage of Kanishka in Kashmir in... View Article

Range Of Sin-1 x – cos-1 x Is?

Sol: Given: \(\begin{array}{l}sin^{-1} x-cos^{-1} x\end{array} \) The range of \(\begin{array}{l}sin^{-1} is x \epsilon [-\frac{\Pi}{2}, \frac{\Pi}{2}]\end{array} \) The range of \(\begin{array}{l}cos^{-1}... View Article

A Kite In The Shape Of Square With A Diagonal 32cm And An Isosceles Triangle Of Base 8cm And Sides 6cm Each Is To Be Made Of Three Different Shades. How Much Paper If Each Shade Has Been Used In It?

Sol: Given: Diagonal = 32cm , Base = 8cm side = 6cm The area of square = \(\begin{array}{l}\frac{1}{2} * (d)^{2}\\\Rightarrow... View Article

Which Of The Following Alphabet Has Many Lines Of Symmetry? (A) A. (B) B. (C) O. (D) Q.

The corrct answer is (C) O. O has infinite (many) lines of symmetry. Explore more such questions and answers at... View Article

Select The Most Appropriate Antonym Of The Given Word: Criticize. (A) Judge. (B) Analyse. (C) Denounce. (D) Appreciate.

The correct answer is (D) Appreciate. Antonym refers to a opposite meaning of another word. The most appropriate antonym of... View Article

Write The Chemical Equation That Represents The Reaction Between Carbon And Oxygen That Produces Carbon?

A balanced chemical equation C + O2 → CO2 For the conversion of carbon to carbon dioxide, carbon is oxidized... View Article

Give A Balanced Chemical Equation For CH4 Reacting With Oxygen Gas To Produce Water And Carbon Dioxide?

A balanced chemical equation CH4 + 2O2 → 2H2O + CO2 This is the balanced reaction equation and is an... View Article

Identify The Type Of Adverb Used In The Sentence: I Have Spoken To Him Already. (A) Adverb Of Place. (B) Adverb Of Time. (C) Adverb Of Manner.(D) Adverb Of Frequency.

The correct answer is (B) Adverb Of Time. In the given sentence: I have spoken to him already. The adverb... View Article

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