If a and b are positive real numbers. Match List-I with List-II, List-I, List-II, Identities, Relation, (A) (√a+√b)(√a-√b), (I) =a-b, (B) (a+√b)(a-√b), (II) =a^2-b, (C) (√a+√b)^2, (III) =a-b^2, (D) (√a)^2-(√b)^4, (IV) =a+2√ab+b, Choose the correct answer from the options given below: Option 1: (A) - (I), (B) - (II), (C) - (III), (D) - (IV) Option 2: (A) - (II), (B) - (I), (C) - (III), (D) - (IV) Option 3: (A) - (I), (B) - (II), (C) - (IV), (D) - (III) Option 4: (A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Answer: (A) - (I), (B) - (II), (C) - (IV), (D) - (III). Solution: Apply (x+y)(x-y) = x^2 - y^2 and (x+y)^2 = x^2 + 2xy + y^2. (A) a - b, so (I). (B) a^2 - b, so (II). (C) a + 2√ab + b, so (IV). (D) (√a)^2 = a and (√b)^4 = b^2, giving a - b^2, so (III).

Quantitative Reasoning

Number System

Medium

If a and b are positive real numbers. Match List-I with List-II

List-I List-II
Identities Relation
(A) $(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})$ (I) $=a-b$
(B) $(a+\sqrt{b})(a-\sqrt{b})$ (II) $=a^2-b$
(C) $(\sqrt{a}+\sqrt{b})^2$ (III) $=a-b^2$
(D) $(\sqrt{a})^2-(\sqrt{b})^4$ (IV) $=a+2\sqrt{ab}+b$

Choose the correct answer from the options given below:

List-I	List-II
Identities	Relation
(A) $(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})$	(I) $=a-b$
(B) $(a+\sqrt{b})(a-\sqrt{b})$	(II) $=a^2-b$
(C) $(\sqrt{a}+\sqrt{b})^2$	(III) $=a-b^2$
(D) $(\sqrt{a})^2-(\sqrt{b})^4$	(IV) $=a+2\sqrt{ab}+b$

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (II), (B) - (I), (C) - (III), (D) - (IV)

(A) - (I), (B) - (II), (C) - (IV), (D) - (III)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

✅ Correct Option: 3

Apply $(x+y)(x-y) = x^2 - y^2$ and $(x+y)^2 = x^2 + 2xy + y^2$ .

(A) $a - b$ , so (I).

(B) $a^2 - b$ , so (II).

(D) $(\sqrt{a})^2 = a$ and $(\sqrt{b})^4 = b^2$ , giving $a - b^2$ , so (III).

2023: 5 June Shift 2

Simplify : $2 \times [4 - \{2 - (2-3) - (2+3)\} - 1] - 5 \times [-3 - (3-2)]$

2022: 20 Aug Shift 1

If P consumes 1500 ml of milk every day. How many liters of milk will be consumed in 4 weeks ?

2025: 24 May Shift 2

Given below are two statements:

Statement (I): 2469385422 is divisible by 18.

Statement (II): 3475824638 is divisible by 11.

In light of the above statements, choose the most appropriate answer from the options given below.

2022: 23 Aug Shift 1

The sum of greatest five digits and lowest/smallest four digits number is:

2026: 22 May Shift 2

Find the missing number:

2023: 11 June Shift 2

The smallest five digit number which is exactly divisible by 12, 15 and 18 is:

Solution

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