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असमानता \(\frac{5x+2}{6}<\frac{x-3}{2}+4\) को हल कीजिए।
Solve the inequality \(\frac{5x+2}{6}<\frac{x-3}{2}+4\).
#linear-inequalities
#fraction-linear
#class-11
#expert
A \(x>\frac{13}{2}\)
B \(x\le \frac{13}{2}\)
C \(x<\frac{13}{2}\)
D \(x\ge \frac{13}{2}\)
Explanation opens after your attempt
Correct Answer
C. \(x<\frac{13}{2}\)
Step 1
Concept
Clearing denominators gives (5x+2<3x+15). Thus (2x<13), so \(x<\frac{13}{2}\).
Step 2
Why this answer is correct
The correct answer is C. \(x<\frac{13}{2}\). Clearing denominators gives (5x+2<3x+15). Thus (2x<13), so \(x<\frac{13}{2}\).
Step 3
Exam Tip
हर हटाने पर (5x+2<3x+15) मिलता है। इससे (2x<13), अतः \(x<\frac{13}{2}\) है।
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यदि \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=\frac{x+1}{2}), तो (f) कैसा है?
If \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=\frac{x+1}{2}), what is (f)?
#relations-functions
#one-one-function
#fraction-linear
#injective
A एकैकी / One-one
B एकैकी नहीं / Not one-one
C स्थिर / Constant
D अपरिभाषित / Undefined
Explanation opens after your attempt
Correct Answer
A. एकैकी / One-one
Step 1
Concept
Assume (f(a)=f(b)).
Step 2
Why this answer is correct
From \(\frac{a+1}{2}=\frac{b+1}{2}\), we get (a+1=b+1), so (a=b).
Step 3
Exam Tip
A linear form with non-zero coefficient remains one-one. चरण 1: मान लें (f(a)=f(b))। चरण 2: \(\frac{a+1}{2}=\frac{b+1}{2}\) से (a+1=b+1), इसलिए (a=b)। चरण 3: शून्य से अलग गुणांक वाले रैखिक रूप में एकैकीता रहती है।
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