UP BOARD CLASS 12 MATHS: PHASE 1 (Q1 - Q3)
[Total Weightage: 18 Marks | High Scoring Foundation Zone]
QUESTION 1: MCQ / OBJECTIVE TYPE 05 MARKS
Setter's Secret: Bhai, yahan Board tumhare dimag se khelta haią„¤ Calculations lambi nahi hongi, lekin logical traps hongeą„¤ Syllabus ke MCQ points par focus karoą„¤
- Matrices: Agar Matrix A ka order $m \times n$ hai aur B ka $n \times p$, toh AB ka order $m \times p$ hogaą„¤ Ye 2024-25 ke sets mein baar-baar aaya hai ą„¤
- Relations: $R = \{(a,b): a=b-1, b \ge 3\}$ jaise conditions check karnaą„¤
- DE Order/Degree: Fractions aur Roots (ą¤ą„ą¤øą„ $\sqrt[3]{...}$ ) hata kar hi Degree batana, warna zero marks milengeą„¤
Confusing MCQ Pattern:
Differential Equation:
$$ \frac{d^{2}y}{dx^{2}}=\sqrt[4]{x+\left(\frac{dy}{dx}\right)^{2}} $$
Order = 2, but Degree = 4 (Taking 4th power on both sides)
QUESTION 2: VERY SHORT ANSWER 05 MARKS
Expert Analysis: Yahan 'Direct Definition' aur 'Principal Values' ka raaj haią„¤ Q2 mein 3D Geometry ka ek 1-mark ka question hamesha hota haią„¤
| Top Predicted Topic |
Question Style |
Board Pattern |
| Inverse Trigo |
Principal Value (ą¤®ą„ą¤ą„ą¤Æ ą¤®ą¤¾ą¤Ø) |
$\csc^{-1}(-\sqrt{2})$ ą¤Æą¤¾ $\cot^{-1}(-\frac{1}{\sqrt{3}})$ |
| 3D Geometry |
Direction Cosines |
$y$-axis ya $z$-axis ki dik-kojyaen (0, 1, 0) |
| Probability |
Conditional Prob. |
$P(A|B)$ calculate karna jab values di hon |
Common Mistake: $\cos^{-1}(-x)$ ka value nikalte waqt $\pi - \cos^{-1}(x)$ karna mat bhoolna, students aksar minus sign misplace kar dete hainą„¤
QUESTION 3: SHORT ANSWER TYPE (2 MARKS) 08 MARKS
Setter's Radar: Is section mein 'Proof-based' sawal aane start ho jate hainą„¤ 2-markers mein **Relations & Functions** ka Equivalence (ą¤¤ą„ą¤²ą„ą¤Æą¤¤ą¤¾) proof Board ka favorite haią„¤
- Calculus Proof: $y = A \cos \theta + B \sin \theta \implies \frac{d^{2}y}{d\theta^{2}} = -y$ą„¤
- Equivalence Relation: Condition like $a+d=b+c$ on $N \times N$ą„¤
- Vector Magnitude: $|\vec{a}-\vec{b}|$ nikalna agar $|\vec{a}|, |\vec{b}|$ aur $\vec{a} \cdot \vec{b}$ diye honą„¤
Must-Master Integration ($\int$):
$$ \int e^{x}\left(\tan^{-1}x + \frac{1}{1+x^2}\right) dx = e^{x}\tan^{-1}x + C $$
Pattern: $\int e^{x}[f(x) + f'(x)] dx$ hamesha practice karke jao!
TEACHER'S FINAL TIP FOR Q1-Q3
Agar tumhe 90+ score karna hai, toh ye initial 18 marks sirf 40 minutes mein complete karne hongeą„¤ Formulas ki ek choti notebook bana lo aur daily principal value ranges check karoą„¤