MCQs — Har Exercise Ki Quick Revision
Ye MCQs poore chapter ka concept check hain. Yahan sabse important concepts summarize kar raha hoon jo MCQs mein poochay gaye:
Exercise 1.1 ke MCQs (Q1–Q12): Quadratic Functions
- Quadratic ka graph hamesha parabola hota hai
- a>0 → upward khulta hai, a<0 → downward
- Vertex ka x-coordinate: x = −b/2a
- Discriminant (b²−4ac) < 0 → parabola x-axis ko chhota bhi nahi
- Completing the square se vertex form milta hai
Exercise 1.2 ke MCQs (Q13–Q24): Exponential/Hyperbolic
- eˣ, x→−∞ par → 0 jata hai; (0,1) se guzarta hai
- e⁻ˣ, eˣ ka y-axis ke around mirror hai
- sinh x = (eˣ−e⁻ˣ)/2 — odd function (origin ke around symmetric)
- cosh x = (eˣ+e⁻ˣ)/2 — even function (y-axis ke around symmetric), minimum value 1 hai x=0 par
Exercise 1.3 ke MCQs (Q25–Q34): Logarithmic Functions
- logₐx sirf x>0 ke liye defined hai
- Vertical asymptote hamesha x=0 par hota hai
- eˣ aur ln x ek dusre ke y=x line ke around mirror hain (inverse functions hain)
- a>1 → increasing, 0<a<1 → decreasing
Exercise 1.4 ke MCQs (Q35–Q45): Transformations
- f(x)+k → upward shift (k units)
- f(x−h) → right shift, f(x+h) → left shift
- −f(x) → x-axis ke around reflection
- f(−x) → y-axis ke around reflection
- c·f(x), c>1 → stretch; 0<c<1 → compression
Exercise 1.5 ke MCQs (Q46–Q55): Even/Odd Functions, Asymptotes
- Even function: f(−x)=f(x), graph y-axis ke around symmetric (jaise cosh x)
- Odd function: f(−x)=−f(x), graph origin ke around symmetric (jaise sinh x)
- Vertical asymptote: jahan function undefined/unbounded ho jaye
- Horizontal asymptote: x→±∞ hone par behaviour describe karta hai
Students ke liye tip: In MCQs ko solve karne ke liye bas definitions aur basic rules yaad hone chahiye — koi lambi calculation nahi hoti, sirf concept clear hona chahiye.
