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Question: Tick (✓) the correct answer: 6a2 13a+ 6 = ? (a) (2a+ 3)(3a 2) (b) (2a 3)(3a+ 2) (c) (3a 2)(2a 3) (d) (3a+ 1)(2a 3) Solution: (c) (3a 2)(2a 3) $6 a^{2}-13 a+6$ $=6 a^{2}-9 a-4 a+6$ $=3 a(2 a-3)-2(2 a-3)$ $=(3 a-2)(2 a-3)$...
Read More →Which among the following is(are) double displacement reaction(s) ?
Question: Which among the following is(are) double displacement reaction(s) ? (i) Pb + CuCl2 PbCl2+ Cu (ii) Na2SO4+ BaCl2- BaSO4+ 2NaCl (iii) C + O2 CO2 (iv) CH4+ 2O2 CO2+ 2H2O (a)(i) and (iv) (b)(ii) only (c)(i) and (ii) (d)(iii) and (iv) Solution: (b).Only reaction (ii) is double displacement in nature....
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Question: Tick (✓) the correct answer: 2x2+ 5x+ 3 = ? (a) (x+ 3)(2x+ 1) (b) (x+ 1)(2x+ 3) (c) (2x+ 5)(x 3) (d) none of these Solution: (b) (x+ 1)(2x+ 3) $2 x^{2}+5 x+3$ $=2 x^{2}+2 x+3 x+3$ $=2 x(x+1)+3(x+1)$ $=(2 x+3)(x+1)$...
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Question: Tick (✓) the correct answer: 40 + 3xx2= ? (a) (x+ 5)(x 8) (b) (5 x)(8 +x) (c) (5 +x)(8 x) (d) (5 x)(8 x) Solution: (c) (5 +x)(8 x) $40+3 x-x^{2}$ $=40+8 x-5 x-x^{2}$ $=8(5+x)-x(5+x)$ $=(8-x)(x+5)$...
Read More →A dilute ferrous sulphate solution is gradually
Question: A dilute ferrous sulphate solution is gradually added to the beaker containing acidified permanganate solution. The light purple colour of the solution fades and finally disappears. Which of the following is the correct explanation for the observation ? (a)KMnO4is an oxidising agent and it oxidises FeSO4 (b)FeSO4acts as an oxidising agent and it oxidises KMnO4 (c)The colour disappears due to dilution; no reaction is involved (d)KMnO4is an unstable compound and decomposes in presence of...
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Question: Tick (✓) the correct answer: y2+ 2y 3 = ? (a) (y 1)(y+ 3) (b) (y+ 1)(y 3) (c) (y 1)(y 3) (d) (y+ 2)(y 3) Solution: (a) (y 1)(y+ 3) $y^{2}+2 y-3$ $=y^{2}+3 y-y-3$ $=y(y+3)-1(y+3)$ $=(y-1)(y+3)$...
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Question: If $y=\log \sqrt{\frac{1+\tan x}{1-\tan x}}$, prove that $\frac{d y}{d x}=\sec 2 x$ Solution: Given $y=\log \sqrt{\frac{1+\tan x}{1-\tan x}}$ On differentiating $y$ with respect to $x$, we get $\frac{d y}{d x}=\frac{d}{d x}\left(\log \sqrt{\frac{1+\tan x}{1-\tan x}}\right)$ We know $\frac{\mathrm{d}}{\mathrm{dx}}(\log \mathrm{x})=\frac{1}{\mathrm{x}}$ $\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{\left(\frac{1+\tan \mathrm{x}}{1-\tan \mathrm{x}}\right)^{\frac{1}{2}}} \frac{\mat...
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Question: Tick (✓) the correct answer: x2+ 4x 21 = ? (a) (x 7)(x+ 3) (b) (x+ 7)(x 3) (c) (x 7)(x 3) (d) (x+ 7)(x+ 3) Solution: (b) (x+ 7)(x 3) $x^{2}+4 x-21$ $=x^{2}+7 x-3 x-21$ $=x(x+7)-3(x+7)$ $=(x-3)(x+7)$...
Read More →Three beakers labelled as A, B and C each containing 25 mL of water were taken.
Question: Three beakers labelled as A, B and C each containing 25 mL of water were taken. A small amount of NaOH, anhydrous CuS04 and NaCl were added to the beakers A, B and C respectively. It was observed that there was an increase in the temperature of the solutions contained in beakers A and B, whereas in case of beaker C, the temperature of the solution fell. Which one of the following statement(s) is(are) correct ? (i) In beakers A and B, exothermic process has occurred. (ii) In beakers A a...
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Question: Tick (✓) the correct answer: x2+ 6x+ 8 = ? (a) (x+ 3)(x+ 5) (b) (x+ 3)(x+ 4) (c) (x+ 2)(x+ 4) (d) (x+ 1)(x+ 8) Solution: (c) (x+ 2)(x+ 4) $x^{2}+6 x+8$ $=x^{2}+4 x+2 x+8$ $=x(x+4)+2(x+4)$ $=(x+2)(x+4)$...
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Question: Tick (✓) the correct answer: 1 2ab (a2+b2) = ? (a) (1 +ab)(1 +a+b) (b) (1 +a+b)(1 a+b) (c) (1 +a+b)(1 ab) (d) (1 +ab)(1 a+b) Solution: (c) (1 +a+b)(1 ab) $1-2 a b-\left(a^{2}+b^{2}\right)$ $=1-2 a b-a^{2}-b^{2}$ $=1-\left(2 a b+a^{2}+b^{2}\right)$ $=1-(a+b)^{2}$ $=(1-a-b)(1+a+b)$...
Read More →Which of the following are exothermic processes ?
Question: Which of the following are exothermic processes ? (i) Reaction of water with quick lime (ii) Dilution of an acid (iii) Evaporation of water (iv) Sublimation of camphor (crystals) (a)(i) and (ii) (b)(ii) and (iii) (c)(i) and (iv) (d)(iii) and (iv) Solution: (a). (i) Reaction of quick lime with ; water and (ii) dilution of an acid are both exothermic processes. The other two processes (iii) and (iv) are of endothermic nature....
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Question: Tick (✓) the correct answer: x3x= ? (a)x(x2x) (b)x(xx2) (c)x(1 +x)(1 x) (d)x(x+ 1)(x 1) Solution: (d)x(x+ 1)(x 1) $x^{3}-x$ $=x\left(x^{2}-1\right)$ $=x(x-1)(x+1)$...
Read More →Which of the following statements about the given reaction are correct ?
Question: Which of the following statements about the given reaction are correct ? 3Fe(s) + 4H2O(g) - Fe3O4(s) + 4H2(g) (i) Iron metal is getting oxidised (ii) Water is getting reduced (iii) Water is acting as reducing agent (iv) Water is acting as oxidising agent (a)(i), (ii) and (iii) (b)(iii) and (iv) (c)(i), (ii) and (iv) (d)(ii) and (iv). Solution: (c).Statements (i), (ii) and (iv) are all correct....
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Question: Tick (✓) the correct answer: (12m2 27) = ? (a) (2m 3)(3m 9) (b) 3(2m 9)(3m 1) (c) 3(2m 3)(2m+ 3) (d) none of these Solution: (c) 3(2m 3)(2m+ 3) $12 m^{2}-27$ $=3\left(4 m^{2}-9\right)$ $=3(2 m-3)(2 m+3)$...
Read More →The following reaction is an example of a
Question: The following reaction is an example of a 4NH3(g) + SO2(g) - 4NO(g) + 6H2O(g) (i) displacement reaction (ii) combustion reaction (iii) redox reaction (iv) neutralisation reaction (a)(i) and (iv) (b)(ii) and (iii) (c)(i) and (ii) (d)(iii) and (iv) Solution: (c).Oxygen has displaced hydrogen from NH3. It is also a combustion reaction....
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Question: Tick (✓) the correct answer: x2xz+xyyz= ? (a) (xy)(x+ z) (b) (xy)(xz) (c) (x+y)(xz) (d) (xy)(z x) Solution: (c) (x+y)(xz) $x^{2}-x z+x y-y z$ $=x(x-z)+y(x-z)$ $=(x+y)(x-z)$...
Read More →Which of the following is not a physical change ?
Question: Which of the following is not a physical change ? (a)Boiling of water to give water vapours (b)Melting of ice to give water (c)Dissolution of salt in water (d)Combustion of Liquefied Petroleum Gas (LPG) Solution: (d).LPG is a mixture of gases like propane (C3Hg) and butane (C4H10) in liquefied form. These are chemical substances and undergo combustion upon heating with air or oxygen. It is therefore, a chemical change....
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: abab+ 1 = ? (a) (a 1)(b 1) (b) (1 a)(1 b) (c) (a 1)(1 b) (d) (1 a)(b 1) Solution: (a) (a 1)(b 1) $a b-a-b+1$ $=a(b-1)-1(b-1)$ $=(a-1)(b-1)$...
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Question: If $\mathrm{y}=\log \left(\sqrt{\mathrm{x}}+\frac{1}{\sqrt{\mathrm{x}}}\right)$, prove that $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{x}-1}{2 \mathrm{x}(\mathrm{x}+1)}$ Solution: Given $y=\log \left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)$ On differentiating y with respect to $x$, we get $\frac{d y}{d x}=\frac{d}{d x}\left[\log \left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)\right]$ We know $\frac{\mathrm{d}}{\mathrm{dx}}(\log \mathrm{x})=\frac{1}{\mathrm{x}}$ $\Rightarrow \frac{\mathrm{dy}}{...
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Question: Tick (✓) the correct answer: abmn+anbm= ? (a) (ab)(mn) (b) (am)(b+n) (c) (an)(m+b) (d) (ma)(nb) Solution: (b) (am)(b+n) $a b-m n+a n-b m$ $=a b+a n-m n-b m$ $=a(b+n)-m(n+b)$ $=(a-m)(b+n)$...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: pq2+q(p 1) 1 = ? (a) (pq+ 1)(q 1) (b)p(q+ 1)(q 1) (c)q(p 1)(q+ 1) (d) (pq 1) (q+ 1) Solution: (d) (pq 1) (q+ 1) $p q^{2}+q(p-1)-1$ $=p q^{2}+q p-q-1$ $=p q(q+1)-1(q+1)$ $=(p q-1)(q+1)$...
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Question: If $y=\frac{x}{x+2}$, prove that $x \frac{d y}{d x}=(1-y) y$ Solution: Given $y=\frac{x}{x+2}$ On differentiating y with respect to $x$, we get $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{\mathrm{x}}{\mathrm{x}+2}\right)$ Recall that $\left(\frac{\mathrm{u}}{\mathrm{v}}\right)^{\prime}=\frac{\mathrm{vu}^{\prime}-\mathrm{uv}^{\prime}}{\mathrm{v}^{2}}$ (quotient rule) $\Rightarrow \frac{d y}{d x}=\frac{(x+2) \frac{d}{d x}(x)-(x) \frac{d}{d x}(x+2)}{(x+2)^{2...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: a2+bc+ab+ac= ? (a) (a+b)(a+c) (b) (a+b)(b+c) (c) (b+c)(c+a) (d)a(a+b+c) Solution: (a) (a+b)(a+c) $a^{2}+b c+a b+a c$ $=a^{2}+a b+b c+a c$ $=a(a+b)+c(a+b)$ $=(a+c)(a+b)$...
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Question: Tick (✓) the correct answer:(2 50x2) = ? (a) 2(1 5x)2 (b) 2(1 + 5x)2 (c) (2 5x)(2 + 5x) (d) 2(1 5x)(1 + 5x) Solution: (d) 2(1 5x)(1 + 5x) $2-50 x^{2}$ $=2\left(1-25 x^{2}\right)$ $=2(1-5 x)(1+5 x)$...
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