Tick (✓) the correct answer
Question: Tick (✓) the correct answer: If 3(t 3) = 5(2t+ 1), thent= ? (a) 2 (b) 2 (c) 3 (d) 3 Solution: (a) 2 $3(t-3)=5(2 t+1)$ $\Rightarrow 3 t-9=10 t+5$ $\Rightarrow 3 t-10 t=9+5$ $\Rightarrow-7 t=14$ $\Rightarrow-t=\frac{14}{7}=2$ $\Rightarrow t=-2$...
Read More →What are strong and weak acids ?
Question: What are strong and weak acids ? In the following list of acids, separate strong acids from weak acids. Hydrochloric acid, citric acid, acetic acid, nitric acid, formic acid, sulphuric acid. Solution: For the definitions of strong and weak acids and bases, An acid may be defined as a substance which releases one or more H+ions in aqueous solution. These ions exist as hydronium (H2O+) ions. A base may be defined as a substance capable of releasing one or more OHions in aqueous solution....
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Question: Tick (✓) the correct answer If $\frac{n}{n+15}=\frac{4}{9}$, then $n=$ ? (a) 4 (b) 6 (c) 9 (d) 12 Solution: (d) 12 $\frac{n}{n+15}=\frac{4}{9}$ $\Rightarrow 9 n=4(n+15)$ $\Rightarrow 9 n=4 n+60$ $\Rightarrow 9 n-4 n=60$ $\Rightarrow 5 n=60$ $\Rightarrow n=\frac{60}{5}=12$...
Read More →Prove that
Question: Prove that $A \times B=B \times A \Rightarrow A=B$. Solution: Let A and B be any two sets such that $A \times B=\{(a, b): a \in A, b \in B\}$ Now, $B \times A=\{(b, a): a \in A, b \in B\}$ A B = B A (a, b) = (b, a) We can see that this is possible only when the ordered pairs are equal. Therefore, a = b and b = a Hence, Proved...
Read More →Fill in the missing data in the following table
Question: Fill in the missing data in the following table Solution:...
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Question: Tick (✓) the correct answer If $\frac{4 x+8}{5 x+8}=\frac{5}{6}$, then $x=?$ (a) 4 (b) 6 (C) 8 (d) 12 Solution: (C) 8 $\frac{4 x+8}{5 x+8}=\frac{5}{6}$ $\Rightarrow 6(4 x+8)=5(5 x+8)$ $\Rightarrow 24 x+48=25 x+40$ $\Rightarrow 24 x-25 x=-48+40$ $\Rightarrow-x=-8$ $\Rightarrow x=8$...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer If $\frac{x+1}{2 x+3}=\frac{3}{8}$, then $x=?$ (a) $\frac{1}{4}$ (b) $\frac{1}{3}$ (C) $\frac{1}{6}$ (d) $\frac{1}{2}$ Solution: (d) $\frac{1}{2}$ $\frac{x+1}{2 x+3}=\frac{3}{8}$ $\Rightarrow 8(x+1)=3(2 x+3)$ $\Rightarrow 8 x+8=6 x+9$ $\Rightarrow 8 x-6 x=9-8$ $\Rightarrow 2 x=1$ $\Rightarrow x=\frac{1}{2}$...
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Question: Tick (✓) the correct answer If $\frac{n}{2}-\frac{3 n}{4}+\frac{5 n}{6}=21$, then $n=$ ? (a) 30 (b) 42 (c) 36 (d) 28 Solution: (c) 36 $\frac{n}{2}-\frac{3 n}{4}+\frac{5 n}{6}=21$ $\Rightarrow \frac{6 n-9 n+10 n}{12}=21$ $\Rightarrow 7 n=21 \times 12$ $\Rightarrow 7 n=252$ $\Rightarrow n=\frac{252}{7}=36$...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer If $\frac{6 x+1}{3}+1=\frac{x-3}{6}$, then $x=?$ (a) 1 (b) $-1$ (c) 3 (d) $-3$ Solution: (b) $-1$ $\frac{6 x+1}{3}+1=\frac{x-3}{6}$ $\Rightarrow \frac{6 x+1+3}{3}=\frac{x-3}{6}$ $\Rightarrow 6(6 x+4)=3(x-3)$ $\Rightarrow 36 x+24=3 x-9$ $\Rightarrow 36 x-3 x=-24-9$ $\Rightarrow 33 x=-33$ $\Rightarrow x=\frac{-33}{33}=-1$...
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Question: Tick (✓) the correct answer If $2 y+\frac{5}{3}=\frac{26}{3}-y$, then $y=$ ? (a) 1 (b) $\frac{2}{3}$ (c) $\frac{6}{5}$ (d) $\frac{7}{3}$ Solution: (d) $\frac{7}{3}$ $2 y+\frac{5}{3}=\frac{26}{3}-y$ $\Rightarrow \frac{6 y+5}{3}=\frac{26-3 y}{3}$ $\Rightarrow 6 y+5=26-3 y$ $\Rightarrow 6 y+3 y=26-5$ $\Rightarrow 9 y=21$ $\Rightarrow y=\frac{21}{9}=\frac{7}{3}$...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: If 5t 3 = 3t 5, thent= ? (a) 1 (b) 1 (c) 2 (d) 2 Solution: (b) 1 $5 t-3=3 t-5$ $\Rightarrow 5 t-3 t=3-5$ $\Rightarrow 2 t=-2$ $\Rightarrow t=\frac{-2}{2}=-1$...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer If $3 m=5 m-\frac{8}{5}$, then $m=?$ (a) $\frac{2}{5}$ (b) $\frac{3}{5}$ (c) $\frac{4}{5}$ (d) $\frac{1}{5}$ Solution: (c) $\frac{4}{5}$ $3 m=5 m-\frac{8}{5}$ $\Rightarrow 3 m=\frac{25 m-8}{5}$ $\Rightarrow 15 m=25 m-8$ $\Rightarrow 15 m-25 m=-8$ $\Rightarrow-10 m=-8$ $\Rightarrow m=\frac{-8}{-10}=\frac{4}{5}$...
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Question: Tick (✓) the correct answer If $z=\frac{4}{5}(z+10)$, then $z=?$ (a) 40 (b) 20 (c) 10 (d) 60 Solution: (a) 40 $z=\frac{4}{5}(z+10)$ $\Rightarrow 5 z=4(z+10)$ $\Rightarrow 5 z=4 z+40$ $\Rightarrow 5 z-4 z=40$ $\Rightarrow z=40$...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer If $5 x+\frac{7}{1}=\frac{3}{2} x-14$, then $x=?$ (a) 5 (b) 5 (c) 6 (d) 6 Solution: (b) 5 $5 x+\frac{7}{2}=\frac{3}{2} x-14$ $\Rightarrow \frac{10 x+7}{2}=\frac{3 x-28}{2}$ $\Rightarrow 10 x+7=3 x-28$ $\Rightarrow 10 x-3 x=-28-7$ $\Rightarrow 7 x=-35$ $\Rightarrow x=\frac{-35}{7}=-5$...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: If 2x 3 =x+ 2, thenx= ? (a) 1 (b) 3 (c) 5 (d) 7 Solution: (c) 5 $2 x-3=x+2$ $\Rightarrow 2 x-x=3+2$ $\Rightarrow x=5$...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\sin ^{-1}\left\{\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right\},-1x1$ Solution: $y=\sin ^{-1}\left\{\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right\}$ Let $x=\sin \theta$ Now $y=\sin ^{-1}\left\{\frac{\sin \theta+\sqrt{1-\sin ^{2} \theta}}{\sqrt{2}}\right\}$ Using $\sin ^{2} \theta+\cos ^{2} \theta=1$ $y=\sin ^{-1}\left\{\frac{\sin \theta+\cos \theta}{\sqrt{2}}\right\}$ Now $y=\sin ^{-1}\left\{\sin \theta \frac{1}{\sqrt{2}}+\cos \theta \f...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left\{\frac{\mathrm{x}}{\mathrm{a}+\sqrt{\mathrm{a}^{2}-\mathrm{x}^{2}}}\right\},-\mathrm{a}\mathrm{x}\mathrm{a}$ Solution: $y=\tan ^{-1}\left\{\frac{x}{a+\sqrt{a^{2}-x^{2}}}\right\}$ Let $x=a \sin \theta$ Now $y=\tan ^{-1}\left\{\frac{a \sin \theta}{a+\sqrt{a^{2}-a^{2} \sin ^{2} \theta}}\right\}$ Using $\sin ^{2} \theta+\cos ^{2} \theta=1$ $y=\tan ^{-1}\left\{\frac{a \sin \theta}{a+a \sqrt{\cos ^{2} \theta}}\right...
Read More →In one of the industrial processes used for the manufacture
Question: In one of the industrial processes used for the manufacture of sodium hydroxide, a gas X is formed as by-product. The gas X reacts with lime water to give a compound Y which is used as a bleaching agent in chemical industry. Identify X and Y giving the chemical equation of the reactions involved. Solution: Sodium hydroxide is manufactured by the electrolysis of a strong solution of sodium chloride (called brine). As a result, chlorine (X) is evolved at anode while hydrogen at cathode. ...
Read More →Salt ‘A’ commonly used in bakery products on heating
Question: Salt A commonly used in bakery products on heating gets converted into another salt B which itself is used for the removal of hardness of water and a gas C is evolved. The gas C when passed through lime water, turns it milky. Identify A, B and C. Solution: The salt A is sodium hydrogen carbonate (baking soda) and is commonly used in bakeries as a constitutent of baking power. Upon heating, it changes to sodium carbonate B and evolves carbon dioxide gas C. Sodium carbonate removes hardn...
Read More →How would you distinguish between
Question: How would you distinguish between baking soda and washing soda upon heating ? Solution: Baking soda is sodium hydrogen carbonate (NaHCO3). Upon heating, it will evolve CO2gas which upon passing through lime water, will make it milky. Washing soda is sodium carbonate decahydrate (Na2CO3.10H2O). Upon heating, it will not evolve any gas....
Read More →A student prepares solutions of (i) an acid and (ii) a base
Question: A student prepares solutions of (i) an acid and (ii) a basein two separate beakers. She forgets to label the solutions and litmus paper is not available in the laboratory. Since both the solutions are colourless, how will she distinguish between the two ? Solution: Phenolphthalein and methyl orange are also acid-base indicators. They can be used in place of litmus. Procedure : Transfer a portion of the colourless solutions to two glass tubes. Add one or two drops of henolphthalein indi...
Read More →What happens when egg shell is placed
Question: What happens when egg shell is placed in concentrated nitric acid taken in a beaker ? Solution: Egg shell contains calcium carbonate as its main constituent. When dipped in concentrated nitric acid, calcium carbonate reacts to evolve carbon dioxide. As a result, egg shell slowly dissolves....
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left\{\frac{\mathrm{x}}{1+\sqrt{1-\mathrm{x}^{2}}}\right\},-1\mathrm{x}1$ Solution: $y=\tan ^{-1}\left\{\frac{x}{1+\sqrt{1-x^{2}}}\right\}$ Let $x=\sin \theta$ Now $y=\tan ^{-1}\left\{\frac{\sin \theta}{1+\sqrt{1-\sin ^{2} \theta}}\right\}$ Using $\sin ^{2} \theta+\cos ^{2} \theta=1$ $y=\tan ^{-1}\left\{\frac{\sin \theta}{1+\sqrt{\cos ^{2} \theta}}\right\}$ $y=\tan ^{-1}\left\{\frac{\sin \theta}{1+\cos \theta}\righ...
Read More →Name the acid present in ant sting and give
Question: Name the acid present in ant sting and give its chemical formula. Also give the common method to get relief from the discomfort caused by the ant sting. Solution: The acid present in ant sting is methanoic acid or formic acid. Its chemical formula is HCOOH. Being poisonous in nature, it causes pain and irritation. Even blisters may appear on the stung area. One should immediately rub the stung area with a mild base like baking soda (NaHCO3). It will react with formic acid to form salt ...
Read More →What will be the action of the following
Question: What will be the action of the following substances on blue litmus paper ? Solution: Dry HCl gas, Moistened NH3gas, Lemon juice, Carbonated soft drink, Curd, Soap solution. It will become red, will remain blue, will become red, will become red, will become red, will remain blue....
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