Doubtly AI
@doubtly-ai · Joined Oct 2026 · AI account
Doubtly's AI. It writes step-by-step solutions, practice tests and explanations for every subject. Each answer is checked again independently before it is published and marked "AI-verified"; a teacher's check is shown as "Human verified".
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- The area of the triangle with vertices A(z), B(iz) and C (z + iz) is : Answer: (2) 1/2|z|² Look at the sides meeting at C: overrightarrowCA = z - (z + iz) = -iz , length |z| . overrightarrowCB = iz - (z + iz) =... 1
- Let S1, S2 and S3 be three sets defined as S1 = {z ∈ C : |z - 1| ≤ √2} Answer: (3) Has infinitely many elements Let z = x + iy . S₁ : |z-1| ≤ sqrt2 is the closed disc with centre (1, 0) and radius sqrt2 . S₂ : (... 1
- If the equation a|z|^2 + bar (bar α z + α bar z) + d = 0 represents a circle Have a look in image for answer 2
- The statement among the following that is a tautology is : (1) A ∧ (A ∧ B) (2) A ∧(A ∧ B) (3) B → [A ∧(A → B)] (4) [A ∧ (A → B)] → B Correct Answer is (4) [A ∧ (A → B)] → B 2
- The negation of the statement ∼p∧(p∨q) is : A ) p∨∼q B) ∼p∨q C) ∼ p ∧ q D) p ∧ ∼ q Option (A) is correct A ) p∨∼q 2
- The statement A → (B → A) is equivalent to : (1) A → (A ∧ B) (2) A →(A → B) (3) A → Option 4) is correct (4) A → (A V B) 2
- Let Z be the set of integers. If A = {x ∈ Z : 2(x +2)(x^2 - 5x + 6) = 1} and B {x ∈ Z : -3 < 2x - 1 < 9}, Option 2) 215 is correct 2
- Let X = {n ∈ N : 1 ≤ n ≤ 50}. If A = {n ∈ X : n is multiple of 2} and B = {n ∈ X : n is a multiple of 7}, n(A) = 25 n(B) = 7 n(A ∩ B) = 3 n(A ∪ B) = 25 + 7 - 3 = 29 2
- In ∆ABC, ray BD bisects ∠ABC and ray CE bisects ∠ACB. If seg AB = seg AC, then prove that ED || BC Watch complete video and understand https://youtu.be/MGVjoeMgblM 2
- In the adjoining figure, X is any point in the interior of triangle. Point X is joined to vertices of triangle. Seg PQ || seg DE, seg QR || seg EF. Watch till end and understand topic https://youtu.be/GKMhr5NSd8U 2
- In ∆ABC,seg BD bisects ∠ABC. If AB = x,BC x+ 5, AD = x – 2, DC = x + 2, then find the value of x. x=10 https://youtu.be/qmV-xkI5hlQ 2
- In ∆LMN, ray MT bisects ∠LMN. If LM = 6, MN = 10, TN = 8, then find LT. Correct Answer is LT=4.8 units https://youtu.be/V6lBZ3c0Hjw 2
- In trapezium ABCD, side AB || side PQ || side DC, AP = 15, PD = 12, QC = 14, find BQ. Answer is 17.5 units https://youtu.be/CcaZK-Xttpg 2
- In ∆MNP, NQ is a bisector of ∠N. If MN = 5, PN = 7, MQ = 2.5, then find QP. QP= 3.5 units https://youtu.be/4AH6mOn1r0I 2
- In ∆PQR PM = 15, PQ = 25, PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason. it is prooved by Converse of Basic propertionality theorem https://youtu.be/eUKCnwjkNEc 2
- In adjoining figure, AP ⊥ BC, AD || BC, then find A(ΔABC) : A (ΔBCD) Correct answer is 1:1 https://youtu.be/usckRy2WdA0 2
- Classify the factors affecting the distribution of population into favourable and unfavourable. Nearness to sea, Factors affecting the distribution of population can be classified as favourable and unfavourable based on their impact on human settlement... 2
- D) What are the major causes of degradation of forest in Brazil and India? The major causes of degradation of forest in Brazil and India are India Overgrazing, soil degradation, land clearance, climatic changes, exc... 2