Class 12 Maths One-Liner Questions for Quick Revision | Board Exam Special

Hello students! Agar aapki Class 12 Board Exams bilkul paas hain aur aapko poore Maths syllabus ka revision jaldi se karna hai, toh One-Liner Questions aapke liye sabse best option hain. One-liners ki madad se aap formulas, important theorems, aur core concepts ko kuch hi ghanto mein revise kar sakte hain. Aaiye dekhte hain kuch most important Class 12 Maths one-liner questions jo exams mein bar-bar puche jaate hain.

1. Relations and Functions One-Liners

• Q: Agar ek relation R kisi set A par reflexive, symmetric aur transitive teeno ho, toh us relation ko kya kehte hain?
  Ans: Equivalence Relation.
• Q: Ek function f: A → B one-one (injective) kab hota hai?
  Ans: Jab f(x₁) = f(x₂) imply karta hai x₁ = x₂ sabhi x₁, x₂ ∈ A ke liye.
• Q: Inverse trigonometric function sin⁻¹x ki Principal Value Branch kya hoti hai?
  Ans: [−π/2, π/2].

2. Calculus One-Liners

• Q: Integral of eˣ [f(x) + f′(x)] dx ka direct formula kya hota hai?
  Ans: eˣ f(x) + C.
• Q: Derivative of log(sec x + tan x) with respect to x kya hota hai?
  Ans: sec x.
• Q: Agar koi function f(x) continuous hai kisi interval mein, toh kya woh hamesha differentiable hoga?
  Ans: Nahi, continuity differentiability ki guarantee nahi deti (e.g., f(x) = |x| at x = 0).

3. Vectors aur 3D Geometry One-Liners

• Q: Do perpendicular vectors a⃗ aur b⃗ ka dot product kitna hota hai?
  Ans: Zero (a⃗ · b⃗ = 0).
• Q: Agar do lines ke direction ratios a₁, b₁, c₁ aur a₂, b₂, c₂ hain, toh parallel hone ki condition kya hai?
  Ans: a₁/a₂ = b₁/b₂ = c₁/c₂.

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