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 radius of a metallic sphere is 9 cm. It was melted to make a wire of diameter 4 mm. Find the length of the wire. Answer: 243 m Volume of sphere =4/3π(9)³=972π cm³. Wire radius = 2 mm = 0.2 cm. Volume of wire =π(0.2)²L=0.04π L . 0.04π L=972π⇒ L=24300\ cm... 1
- The area of a sector of a circle of 6 cm radius is 15π sq.cm. Find the measure of the arc and length of the arc corresponding to the sector. Answer: Measure of arc = 150°, length of arc = 5π cm θ/360×π×36=15π⇒θ=15×360/36=150^° Area =l× r/2⇒15π=l×6/2⇒ l=5π cm. 1
- Seg AB is a chord of a circle with centre P. If PA = 8 cm and distance of chord AB from the centre P is 4 cm, find the area of the shaded portion (minor segment AB). (π = 3.14, √3 = 1.73) Answer: ≈ 39.31 cm² Let PM ⊥ AB, PM = 4, PA = 8. In right ΔPMA, cos∠ APM=4/8=1/2 , so ∠ APM=60^° and ∠ APB=120^° . AM=√(64-16)=4sqrt3 , so A... 1
- Square ABCD is inscribed in the sector A-PCQ. The radius of sector C-BXD is 20 cm. Complete the activity to find the area of the shaded region. (π = 3.14) Answer: Total shaded area = 86 + 228 = 314 cm² Side of square = radius of sector C-BXD = 20 cm. Area of square =20²=400 cm². Shaded region i... 1
- Balance the following equation stepwise: H2S2O7(l) + H2O(l) → H2SO4(l) Balanced equation: H₂S₂O₇(l) + H₂O(l) → 2H₂SO₄(l) Step 1: Count atoms in the skeletal equation. ElementReactant sideProduct side H2 + 2 = 42... 1
- Balance the following equation stepwise: SO2(g) + H2S(aq) → S(s) + H2O(l) Balanced equation: SO₂(g) + 2H₂S(aq) → 3S(s) + 2H₂O(l) Step 1: Count atoms in the skeletal equation. Left: S = 2, O = 2, H = 2. Right: S = 1... 1
- Balance the following equation stepwise: Ag(s) + HCl(aq) → AgCl + H2 Balanced equation: 2Ag(s) + 2HCl(aq) → 2AgCldownarrow + H₂uparrow Step 1: Count atoms. Left: Ag = 1, H = 1, Cl = 1. Right: Ag = 1, Cl = 1, H... 1
- Balance the following equation stepwise: NaOH(aq) + H2SO4(aq) → Na2SO4(aq) + H2O(l) Balanced equation: 2NaOH(aq) + H₂SO₄(aq) → Na₂SO₄(aq) + 2H₂O(l) Step 1: Count atoms. Left: Na = 1, O = 1 + 4 = 5, H = 1 + 2 = 3, S = 1. Righ... 1
- Identify the endothermic and exothermic reaction: HCl + NaOH → NaCl + H2O + heat Exothermic reaction. Heat is written on the product side, which means heat is given out when hydrochloric acid neutralises sodium hydroxide:... 1
- Identify the endothermic and exothermic reaction: 2KClO3(s) → 2KCl(s) + 3O2 (on heating) Endothermic reaction (as expected in the textbook). The symbol Δ above the arrow shows that heat has to be supplied to potassium chlorate to... 1
- Identify the endothermic and exothermic reaction: CaO + H2O → Ca(OH)2 + heat Exothermic reaction. CaO + H₂O → Ca(OH)₂ + heat When quicklime (calcium oxide) is added to water, slaked lime (calcium hydroxide) is formed... 1
- Identify the endothermic and exothermic reaction: CaCO3(s) → CaO(s) + CO2 (on heating) Endothermic reaction. Calcium carbonate (limestone) decomposes into calcium oxide and carbon dioxide only when it is strongly heated ( Δ abo... 1
- Match the column in the following table (reactants, products, type of chemical reaction). Correct matching: ReactantsProductsType BaCl₂(aq) + ZnSO₄(aq) BaSO₄downarrow + ZnCl₂(aq) Double displacement 2AgCl(s) 2Ag(s) + Cl₂(g) Decomp... 1
- Complete the following chart comparing asexual reproduction and sexual reproduction. Completed chart: Asexual reproductionSexual reproduction 1. Reproduction that occurs with the help of somatic cells is asexual reproduction.... 1
- Fill in the blanks: In humans, sperm production occurs in the organ ----------------. Answer: Testes In humans, sperm production occurs in the testes. The testes lie in the scrotum, outside the abdominal cavity. They contain n... 1
- Prove that: sec⁶x – tan⁶x = 1 + 3sec²x × tan²x Answer: LHS simplifies to RHS, as shown below. Let a=sec²x , b=tan²x . Then a-b=1 . Using a³-b³=(a-b)³+3ab(a-b) : sec⁶x-tan⁶x=1³+3ab(1) =1+3... 1
- Prove that: tanθ/(secθ + 1) = (secθ – 1)/tanθ Answer: LHS simplifies to RHS, as shown below. Multiply numerator and denominator of the LHS by (secθ-1) : LHS=tanθ(secθ-1)/sec²θ-1 =tanθ(se... 1
- Prove that: (tan³θ – 1)/(tanθ – 1) = sec²θ + tanθ Answer: LHS simplifies to RHS, as shown below. Using a³-1=(a-1)(a²+a+1) with a=tanθ : LHS=(tanθ-1)(tan²θ+tanθ+1)/tanθ-1 =(1+tan²θ)+tanθ=sec²... 1