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Sunita is twice as old as Ashima. If six years is subtracted from Ashima’s age and four years added to Sunita’s age, then Sunita will be four times Ashima’s age. How old were they two years ago?

Let the present age of Ashima be ‘x’ years. The present age of Sunita is 2x years Ashima’s new age... View Article

In how many ways can 6 prizes be distributed equally among 3 persons?

Total required number of ways is given by \(\begin{array}{l}= ^6\mathrm{C}_{2} \times ^4 \mathrm{C}_{2} \times ^2 \mathrm{C}_{2}\\=^6 \mathrm{C}_{2} \times ^4 \mathrm{C}_{2}... View Article

In a large housing complex, there are 15 small buildings and 22 large buildings. Each of the large buildings has 10 floors with 2 apartments on each floor. Each of the small buildings has 12 floors with 3 apartments on each floor. How many apartments are there in all?

Number of large buildings = 22 Number of small buildings = 15 Number of floors in 1 large building =... View Article

What annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest?

Let each instalment be Rs.x. First year = [x + (x * 12 * 2) / 100] Second year =... View Article

Solve 3 (x + 2) – 2 (x – 1) = 7 for the value of x.

3 (x + 2) – 2 (x – 1) = 7 ⇒ 3x + 6 – 2x + 2 =... View Article

4x + 1 ≥ 17, where x ∈ N

4x + 1 ≥ 17 ⇒ 4x ≥ 16 ⇒ x ≥ 4 x is a set of natural numbers.... View Article

The highest power of the variable in a linear equation is _____.

The highest power of the variable in a linear equation is 1.

A, B, C, D and E play a game of cards A says to B, “If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has. A and B together have 10 cards more than what D and E together have If B has two cards more than what C has and the total number of cards be 133, how many cards does B have?

B – 3 = E …. (1) B + 3 = D … (2) A + B = D +... View Article

Prove that cos 2x cos (x / 2) – cos 3x cos (9x / 2) = sin 5x sin (5x / 2).

Consider the LHS of the given function. \(\begin{array}{l}\text { LHS: }\\ \cos 2 x \cos \frac{x}{2}-\cos 3 x \cos \frac{9... View Article

Find the value of 99 × 101 using the standard identity.

99 × 101 = (100 – 1) (100 + 1) (a + b) (a – b) = a2 – b2... View Article

If 12 boys earn Rs 840 in 7 days, what will 15 boys earn in 6 days?

Earning of 12 boys in 7 days = Rs 840 Earning of 12 boys in 1 day = Rs 840... View Article

Out of 500 first-year students, 260 passed in the first semester and 21 0 passed in the second semester. If 170 did not pass in either semester, how many passed in both semesters?

A be the set of students who passed the first semester = n (A) = 260 B be the set... View Article

If ¹⁰C_x = ¹⁰C_x+4, then prove that x = 3.

The given combination is \(\begin{array}{l}{ }^{10} \mathbf{C}_{x}={ }^{10} \mathbf{C}_{x+4 \cdots \ldots \ldots(1)}\\ { }^{\mathrm{n}} \mathbf{C}_{\mathbf{r}}={ }^{\mathbf{n}} \mathbf{C}_{\mathbf{n}-\mathbf{r} \cdots \ldots \ldots... View Article

Make a list of seven consecutive numbers, none of which is prime.

90, 91, 92, 93, 94, 95, 96.

The value of cosec 2A – cot 2A – tan A =

The given expression is \(\begin{array}{l}{cosec} 2 \mathbf{A}-\cot 2 \mathbf{A}-\tan A \\ \frac{1}{\sin 2 A}-\frac{\cos 2 A}{\sin 2 A}-\tan A \\... View Article

On simplification x³ = 27 then x is equal to

Consider \(\begin{array}{l}x^{3}=27\\ \Rightarrow \sqrt[3]{x^{3}}=\sqrt[3]{27}\\ \Rightarrow x^{3 \times \frac{1}{3}}=\sqrt[3]{27}\\ \Rightarrow x=\sqrt[3]{27}\\ \Rightarrow x=\sqrt[3]{3 \times 3 \times 3}\\ \Rightarrow x=(3)^{3 \times \frac{1}{3}}\\... View Article

3 – 4i equals

Answer: Given 3 – 4π \(\begin{array}{l}\text { Let } \mathbf{z}=\mathbf{3}-\mathbf{4} \mathbf{i}\\ |\mathbf{z}|=\sqrt{3^{2}+4^{2}}=5\left\{|\mathbf{a}-\mathbf{b i}|=\sqrt{\mathbf{a}^{2}+\mathbf{b}^{2}}\right\}\\ \mathbf{z}=3-4 \mathbf{i}=\mathbf{r e}^{\mathrm{i} \theta}\\ \boldsymbol{\theta}=\mathbf{a r g}... View Article

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