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Q:

If $3^{x - y} = 27$ , $3^{x + y} = 243$ then find the x value

A) 2	B) 8
C) 4	D) 1

Answer & Explanation Answer: C) 4

Explanation:

Given that $3^{x - y} = 27$ , $3^{x + y} = 243$

$\Rightarrow 3^{x - y} = 3^{3}, 3^{x + y} = 3^{5}$

=> x-y=3, x+y=5

=> x = 4

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Filed Under: Simplification
Exam Prep: CAT
Job Role: Bank Clerk

Q:

${(31)}^{31} \times {(31)}^{- 27} = ?$

A) 961 x 861	B) 961 x 961
C) 961 x 2	D) 29791

Answer & Explanation Answer: B) 961 x 961

Explanation:

We know that $a^{m} \times a^{n} = a^{m + n}$

$∴ {(31)}^{31 - 27}$ = $31^{4}$ = 961 x 961.

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Filed Under: Numbers
Exam Prep: CAT
Job Role: Bank PO

Q:

Boron cannot form which one of the following anions?

(1) $B O_{2}^{-}$

(2) $B F_{6}^{3 -}$

(3) $B H_{4}^{-}$

(4) $B (O H)_{4}^{-}$

A) Option 1	B) Option 2
C) Option 3	D) Option 4

Answer & Explanation Answer: B) Option 2

Explanation:

Due to absence of low lying vacant d orbital in B, $s p^{3} d^{2}$ hybridization is not possible hence $B F_{6}^{3 -}$ will not formed.

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Filed Under: Chemistry
Exam Prep: AIEEE

Q:

The degree of dissociation ( $α$ ) of a weak electrolyte, $A_{x} B_{y}$ is related to van't Hoff factor (i) by the expression:

$1 . α = \frac{x + y + 1}{i - 1}$

$2 . α = \frac{x + y - 1}{i - 1}$

$3 . α = \frac{i - 1}{x + y + 1}$

$4 . α = \frac{i - 1}{x + y - 1}$

A) 1 is correct	B) 2 is correct
C) 3 is correct	D) 4 is correct

Answer & Explanation Answer: D) 4 is correct

Explanation:

Van't Hoff factor (i) = $\frac{O b s e r v e d C o l l i g a t i v e P r o p e r t y}{N o r m a l C o l l i g a t i v e P r o p e r t y}$

$\begin{matrix} A_{x} B_{y} \\ 1 - α \end{matrix} \to \begin{matrix} x A^{+ y} \\ x α \end{matrix} + \begin{matrix} y B^{- x} \\ y α \end{matrix}$

Total Moles = $1 - α + x α + y α$ = $1 - α (x + y - 1)$

$i = \frac{1 + α (x + y - 1)}{1}$

$\Rightarrow α = \frac{i - 1}{x + y - 1}$

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Filed Under: Chemistry
Exam Prep: AIEEE

Q:

The magnetic moment (spin only) of $[N i C l_{4}]^{2 -}$ is

A) 1.41 BM	B) 1.82 BM
C) 5.46 BM	D) 2.82 BM

Answer & Explanation Answer: D) 2.82 BM

Explanation:

Hybridisation of Ni is $e^{-}$

Unpaired $3 d^{8}$ in is 2

So $Ω = \sqrt{n (n + 2)} B M = \sqrt{2 x 4} = \sqrt{8} = 2.82 B M$

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Filed Under: Chemistry
Exam Prep: AIEEE

Q:

Virginia is a place in U.S.A. famous for growing _____ .

A) Weed	B) Cannabis
C) Tobacco	D) None of the above

Answer & Explanation Answer: C) Tobacco

Explanation:

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Filed Under: Famous Places

Q:

Plants growing in sunlight are called

A) sciophytes	B) xerophytes
C) heliophytes	D) hydrophytes

Answer & Explanation Answer: C) heliophytes

Explanation:

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Filed Under: Biology

Q:

Replace each letter for a unique digit so that the equation is correct

$\left ( J+O+I+N+T \right )^3=JOINT$

Answer

(1+9+6+8+3) x (1+9+6+8+3) x (1+9+6+8+3) = 19683

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Subject: Math Puzzles Exam Prep: Bank Exams , AIEEE
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