Match the important chemicals given
Question: Match the important chemicals given in Column (A) with the chemical formulae given in Column (B) Solution: (a)-(ii) ; (b)-(iii) ; (c)-(iv) ; (d)-(i)...
Read More →Match the acids given in column (A) with
Question: Match the acids given in column (A) with their correct sources given in column (B) Solution: (a)-(iv) (b)-(iii) (c)-(ii) (d)-(i)...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\cos ^{-1}\left\{\frac{\cos x+\sin x}{\sqrt{2}}\right\}, \frac{\pi}{4}x\frac{\pi}{4}$ Solution: $y=\cos ^{-1}\left\{\frac{\cos x+\sin x}{\sqrt{2}}\right\}$ Now $y=\cos ^{-1}\left\{\cos x \frac{1}{\sqrt{2}}+\sin x \frac{1}{\sqrt{2}}\right\}$ $y=\cos ^{-1}\left\{\cos x \cos \left(\frac{\pi}{4}\right)+\sin x \sin \left(\frac{\pi}{4}\right)\right\}$ Using $\cos (A-B)=\cos A \cos B+\sin A \sin B$ $y=\cos ^{-1}\left\{\cos \left(x-\...
Read More →Identify the correct representation of reaction
Question: Identify the correct representation of reaction occurring during chloralkali process (а)2NaCl(l) + 2H2O(l) 2NaOH(s) + Cl2(g) + H2(g) (b)2NaCI(aq) + 2H2O (aq)2NaOH(aq) + Cl2(g) + H2(aq) (c)2NaCl(aq) + 2H2O(l) 2NaOH(aq) + Cl2(aq) + H2(g) (d)2NaCl (aq) + 2H2O (l)2NaOH (aq) + Cl2(g) + H2(g) Solution: (d).It is the correct answer since the physical states of all the species involved are correct....
Read More →Half of a herd of deer are grazing in the field and three-fourths of the remaining are playing nearby.
Question: Half of a herd of deer are grazing in the field and three-fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find thenumber of deer in the herd. Solution: Let the number of deer in the herd be $\mathrm{x}$. The number of deer grazing in the field is $\left(\frac{1}{2}\right) \mathrm{x}$. Remaining deer $=x-\frac{x}{2}=\frac{x}{2}$ $N$ umber of deer playing nearby $=\frac{3}{4}\left(\frac{x}{2}\right)=\frac{3}{8} x$ The number of deer drinking wate...
Read More →Which of the following are present in a dilute
Question: Which of the following are present in a dilute aqueous solution of hydrochloric acid ? (a)H3O++ Cl (b)H3O++ OH (c)Cl+ OH (d)unionised HCl Solution: (a).HCl will react with water as follows : HCl (l) + H2O(l) H3O+(aq) + Cl(aq)...
Read More →Which of the following statements is true for acids ?
Question: Which of the following statements is true for acids ? (a)Bitter and change red litmus to blue (b)Sour and change red litmus to blue (c)Sour and change blue litmus to red (d)Bitter and change blue litmus to red Solution: (c).Both are the characteristics of acids....
Read More →Which of the following is(are) true when HCl (g) is passed through water ?
Question: Which of the following is(are) true when HCl (g) is passed through water ? (i) It does not ionise in the solution as it is a covalent compound. (ii) It ionises in the solution (iii) It gives both hydrogen and hydroxyl ions in the solution (iv) It forms hydronium ion in the solution due to the combination of hydrogen ion with water molecule (a)(i) only (b)(iii) only (c)(ii) and (iv) (d)(iii) and (iv) Solution: (c).Both are true....
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\sin ^{-1}\left\{\frac{\sin x+\cos x}{\sqrt{2}}\right\},-\frac{3 \pi}{4}x\frac{\pi}{4}$ Solution: $y=\sin ^{-1}\left\{\frac{\sin x+\cos x}{\sqrt{2}}\right\}$ Now $y=\sin ^{-1}\left\{\sin x \frac{1}{\sqrt{2}}+\cos x \frac{1}{\sqrt{2}}\right\}$ $y=\sin ^{-1}\left\{\sin x \cos \left(\frac{\pi}{4}\right)+\cos x \sin \left(\frac{\pi}{4}\right)\right\}$ Using $\sin (A+B)=\sin A \cos B+\cos A \sin B$ $y=\sin ^{-1}\left\{\sin \left(x...
Read More →Equal volumes of hydrochloric acid and sodium
Question: Equal volumes of hydrochloric acid and sodium hydroxide solutions of same concentration are mixed and the pH of the resulting solution is checked with a pH paper. What would be the colour obtained ? (a)Red (b)Yellow (c)Green (d)Blue Solution: (c).pH paper will acqure green colour which indicates that the solution is of neutral nature....
Read More →The difference between the ages of two cousins is 10 years.
Question: The difference between the ages of two cousins is 10 years. 15 years ago, if the elder one was twice as old as the younger one, find their present ages. Solution: Let the age of the younger cousin be $\mathrm{x}$. Then, the age of the elder cousin will be $(\mathrm{x}+10)$. 15 years ago : Age of the younger cousin $=(\mathrm{x}-15)$ Age of elder $\operatorname{cousin}=(\mathrm{x}+10-15)$ $=(x-5)$ $\therefore(x-5)=2(x-15)$ $\Rightarrow x-5=2 x-30$ $\Rightarrow x-2 x=-30+5$ $\Rightarrow-...
Read More →Match the chemical substances given in Column
Question: Match the chemical substances given in Column (A) with their appropriate application given in Column (B) (a)1(ii), 2(i), 3(iv), 4(iii) (b)1(iii), 2(ii), 3(iv), 4(i) (c)1(iii), 2(iv), 3(i), 4(ii) (d)1(ii), 2(iv), 3(i), 4(iii) Solution: (c) 1(iii), 2(iv), 3(i), 4(ii)...
Read More →A man is 10 times older than his grandson.
Question: A man is 10 times older than his grandson. He is also 54 years older than him. Find their present ages. Solution: Let the age of the grandson be $\mathrm{x}$ years. Then, his grandfather's age will be $10 \mathrm{x}$. Also, the grandfather is 54 years older than his grandson. $\therefore$ Age of the grandson $=\mathrm{x}+54$ $10 x=x+54$ $\Rightarrow 10 x-x=54$ $\Rightarrow 9 x=54$ $\Rightarrow x=\frac{54}{9}=6$ Therefore, the grandson's age is 6 years. Grandfather's age $=10(\mathrm{x}...
Read More →Which of the following statements is not correct ?
Question: Which of the following statements is not correct ? (a)All metal carbonates react with acid to give a salt, water and carbon dioxide (b)All metal oxides react with water to give salt and acid (c)Some metals react with acids to give salt and hydrogen (d)Some non metal oxides react with water to form an acid Solution: (b).The statement is not correct as the metal oxide reacts with water to form metal hydroxide....
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\cos ^{-1}\left\{\frac{x}{\sqrt{x^{2}+a^{2}}}\right\}$ Solution: $y=\cos ^{-1}\left\{\frac{x}{\sqrt{x^{2}+a^{2}}}\right\}$ Let $x=a \cot \theta$ Now $y=\cos ^{-1}\left\{\frac{\operatorname{acot} \theta}{\sqrt{a^{2} \cot ^{2} \theta+a^{2}}}\right\}$ Using $1+\cot ^{2} \theta=\operatorname{cosec}^{2} \theta$ $y=\cos ^{-1}\left\{\frac{\operatorname{acot} \theta}{a \sqrt{\cot ^{2} \theta+1}}\right\}$ $y=\cos ^{-1}\left\{\frac{\op...
Read More →Monu's father is 26 years younger than Monu's grandfather and 29 years older than Monu.
Question: Monu's father is 26 years younger than Monu's grandfather and 29 years older than Monu. The sum of the ages of all the three is 135 years. What is the age of each one of them? Solution: Let the age of Monu's father be x years. The age of Monu's grandfather will be $(x+26)$. Then, the age of Monu will be $(\mathrm{x}-29)$. $\therefore x+(x+26)+(x-29)=135$ $\Rightarrow x+x+26+x-29=135$ $\Rightarrow 3 x-3=135$ $\Rightarrow 3 x=135+3$ $\Rightarrow 3 x=138$ $\Rightarrow x=\frac{138}{3}=46$ ...
Read More →Which of the following is not a base ?
Question: Which of the following is not a base ? (a)NaOH (b)KOH (c)NH4OH (d)C2H5OH. Solution: (d).Ethyl alcohol (C2H5OH) is not a base. It is an alcohol and is very weakly acidic in nature....
Read More →Which of the following is not a mineral acid ?
Question: Which of the following is not a mineral acid ? (a)Hydrochloric acid (b)Citric acid (c)Sulphuric acid (d)Nitric acid. Solution: (b).Citric acid is an organic acid present in citrus fruits. It is not a mineral acid....
Read More →Rakhi's mother is four times as old as Rakhi.
Question: Rakhi's mother is four times as old as Rakhi. After 5 years, her mother will be three times as old as she will be then. Find their present ages. Solution: Let the present age of Rakhi be $\mathrm{x}$. Then, the present age of Rakhi's mother will be $4 \mathrm{x}$. After five years, Rakhi 's age will be $(\mathrm{x}+5)$. After five years, her mother's age will be $(4 \mathrm{x}+5)$. $4 x+5=3(x+5)$ $\Rightarrow 4 x+5=3 x+15$ $\Rightarrow 4 x-3 x=15-5$ $\Rightarrow x=10$ Present age of Ra...
Read More →Which of the following is used
Question: Which of the following is used for dissolution of gold ? (a)Hydrochloric acid (b)Sulphuric acid (c)Nitric acid (d)Aqua regia. Solution: (d).For the details of aqua regia....
Read More →In an attempt to demonstrate electrical conductivity
Question: In an attempt to demonstrate electrical conductivity through an electrolyte, the apparatus set up is given. Which among the following statement(s) is(are) correct ? (i) Bulb will not glow because electrolyte is not acidic (ii) Bulb will glow because HCl is a strong acid and furnishes ions for conduction. (iii) Bulb will not glow because circuit is incomplete (iv) Bulb will not glow because it depends upon the type of electrolytic solution (a)(i) and (iii) (b)(ii) and (iv) (c)(ii) only ...
Read More →Divide 4500 into two parts such that 5%
Question: Divide 4500 into two parts such that 5% of the first part is equal to 10% of the second part. Solution: Let the first part be $\mathrm{x}$. Let the second part be $(4500-\mathrm{x})$. $\therefore 5 \%$ of $x=10 \%$ of $(4500-x)$ $\Rightarrow\left(\frac{5}{100}\right) x=\left(\frac{10}{100}\right)(4500-x)$ $\Rightarrow \frac{5 x}{100}=\frac{45000-10 x}{100}$ $\Rightarrow 5 x=45000-10 x \quad$ (by cancellation of same denominators from both the sides) $\Rightarrow 5 x+10 x=45000$ $\Right...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\sin ^{-1}\left(1-2 x^{2}\right), 0x1$ Solution: $y=\sin ^{-1}\left\{1-2 x^{2}\right\}$ let $x=\sin \theta$ Now $y=\sin ^{-1}\left\{\sqrt{1-2 \sin ^{2} \theta}\right\}$ Using $1-2 \sin ^{2} \theta=\cos 2 \theta$ $y=\sin ^{-1}(\cos 2 \theta)$ $y=\sin ^{-1}\left\{\sin \left(\frac{\pi}{2}-2 \theta\right)\right\}$ Considering the limits, $0x1$ $0\sin \theta1$ $0\theta\frac{\pi}{2}$ $02 \theta\pi$ $0-2 \theta-\pi$ $\frac{\pi}{2}\f...
Read More →Which of the following is
Question: Which of the following is acidic in nature ? (a)Lime juice (b)Human blood (c)Lime water (d)Antacid Solution: (a).Lime juice is of acidic nature. It contains citric acid....
Read More →Which of the following substances
Question: Which of the following substances will not give carbon dioxide on treatment with dilute acid ? (a)Marble (b)Lime stone (c)Baking soda (d)Lime Solution: (d).Since lime (CaO) does not contain carbon, it will not give any carbon dioxide gas....
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