Tick (✓) the correct answer
Question: If $\left(x-\frac{1}{x}\right)=4$, find the value of (i) $\left(x^{2}+\frac{1}{x^{2}}\right)$. (ii) $\left(x^{4}+\frac{1}{x^{4}}\right)$. Solution: (i) Given, $\left(x-\frac{1}{x}\right)=4$ Squaring both the sides: $\left(x-\frac{1}{x}\right)^{2}=4^{2}$ $\Rightarrow(x)^{2}-2 \times(x) \times\left(\frac{1}{x}\right)+\left(\frac{1}{x}\right)^{2}=16$ $\Rightarrow x^{2}-2+\frac{1}{x^{2}}=16$ $\Rightarrow x^{2}+\frac{1}{x^{2}}=16+2$ $\therefore\left(x^{2}+\frac{1}{x^{2}}\right)=18$ (ii) Fro...
Read More →Let A = (1, 2, 3} and B = {4}
Question: Let A = (1, 2, 3} and B = {4} How many relations can be defined from A to B. Solution: The number of relations from set A to set B = $2^{n(A) \times n(B)}$ n(A) = Number of elements in set A n(B) = Number of elements in set B Here, n(A) = 3 n(B) = 1 Total number of relations = $2^{3 \times 1}$ = 8...
Read More →Which of the following oxide(s)
Question: Which of the following oxide(s) of iron would be obtained on prolonged reaction of iron with steam ? (a)FeO (b)Fe2O3 (c)Fe3O4 (d)Fe2O3and Fe3O4 Solution: (c). 3Fe (s) + 4H2O (g) Fe3O4(s) + 4H2(g)...
Read More →Which one of the following metals
Question: Which one of the following metals does not react with cold as well as hot water ? (a)K (b)Ca (c)Mg (d)Fe. Solution: (d)Fe....
Read More →Aluminium is used for making cooking utensils.
Question: Aluminium is used for making cooking utensils. Which of the following properties of the metal are responsible for the same ? (i) Good thermal conductivity (ii) Good electrical conductivity (iii) Ductility (iv) High melting point (a)(i) and (ii) (b)(i) and (iii) (c)(ii) and (iii) (d)(i) and (iv) Solution: (d).In order that a metal may be used for making cooking utensils, it must be good conductor of heat and also must have high melting point....
Read More →Solve this
Question: Let $R=\left\{\left(x, x^{2}\right): x\right.$ is a prime number less than 10$\} .$ (i) Write $\mathbf{R}$ in roster form. (ii) Find dom (R) and range (R). Solution: i) $\left\{\left(x, x^{2}\right): x\right.$ is a prime number less than 10$\}$. Roster form: $R=\{(1,1),(2,4),(3,9),(5,25),(7,49)\}$ ii) The domain of $R$ is the set of first co-ordinates of $R$ Dom(R) = {1, 2, 3, 5, 7} The range of $R$ is the set of second co-ordinates of $R$ Range $(R)=\{1,4,9,25,49\}$...
Read More →The ability of metals to be drawn
Question: The ability of metals to be drawn into thin sheets is known as (a)ductility (b)malleability (c)sonorosity (d)conductivity. Solution: (b)malleability...
Read More →Which of the following properties is generally
Question: Which of the following properties is generally not shown by metals ? (a)Electrical conduction (b)Sonorous nature (c)Dullness (d)Ductility. Solution: (c).Metals have shining lustre and they mostly do not show any dullness....
Read More →Divide
Question: Divide (5a3 4a2+ 3a+ 18) by (a2 2a+ 3). Solution: Therefore, $(5 a+6)$ is the quotient....
Read More →If A = {5} and B = {5, 6}, write down all possible subsets of A × B.
Question: If A = {5} and B = {5, 6}, write down all possible subsets of A B. Solution: A = {5} B = {5, 6} A B = {(5, 5), (5, 6)} All the possible subsets of A B are, {} {(5, 5)} {(5, 6)} {(5, 6), (5, 6)}...
Read More →Find each of the following products:
Question: Find each of the following products: (i) (4a+ 5b) (5a 6b) (ii) (6x2 x + 8) (x2 3) Solution: (i) $(4 a+5 b) \times(5 a-6 b)$ $=20 a^{2}-24 a b+25 a b-30 b^{2}$ $=20 a^{2}+a b-30 b^{2}$ (ii) (6x2 x + 8) (x2 3) $=6 x^{4}-18 x^{2}-x^{3}+3 x+8 x^{2}-24$ $=6 x^{4}-x^{3}-18 x^{2}+8 x^{2}+3 x-24$ $=6 x^{4}-x^{3}-10 x^{2}+3 x-24$...
Read More →Identify the compound ‘Y’ on the basis
Question: Identify the compound Y on the basis of the reactions given below. Also write the name and chemical formulae of A, B and C. Solution: The compound Y is sodium hydroxide. It forms A, B and C as follows :...
Read More →Subtract
Question: Subtract 4a2+ 5b2 6c2+ 8 from 2a2 3b2 4c2 5. Solution: $2 a^{2}-3 b^{2}-4 c^{2}-5-\left(4 a^{2}+5 b^{2}-6 c^{2}+8\right)$ $=2 a^{2}-3 b^{2}-4 c^{2}-5-4 a^{2}-5 b^{2}+6 c^{2}-8$ $=2 a^{2}-4 a^{2}-3 b^{2}-5 b^{2}-4 c^{2}+6 c^{2}-5-8$ $=-2 a^{2}-8 b^{2}+2 c^{2}-13$...
Read More →A sulphate salt of Group 2 element of the Periodic Table is a white,
Question: A sulphate salt of Group 2 element of the Periodic Table is a white, soft substance which can be moulded into different shapes by making its dough. When this compound is left in open for some time, it becomes a solid mass and cannot be used for moulding purposes. Identify the sulphate salt. Why does it show such a behaviour ? Give the reaction involved. Solution: The available information suggests that the element present in group 2 of the Periodic Table* is calcium (Ca) and the sulpha...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: Number of boys and girls in a class are in the ratio 7 : 5. The number of boys is 8 more than the number of girls. The total class strength is (a) 56 (b) 52 (c) 48 (d) 36 Solution: (c) 48 Let the number of boys in the class be $\mathrm{x}$. Then, the number of girls will be $(\mathrm{x}-8)$. The equation becomes: $\frac{x}{x-8}=\frac{7}{5}$ $\Rightarrow 5 x=7 x-56$ $\Rightarrow 5 x-7 x=-56$ $\Rightarrow-2 x=-56$ $\Rightarrow x=\frac{-56}{-2}=28$ Therefore, ...
Read More →A dry pellet of a common base ‘B’,
Question: A dry pellet of a common base B, when kept in open absorbs moisture and turns sticky. The compound is also formed by chloralkali process. Identify B. What type of reaction occurs when B is treated with an acidic oxide ? Write a balanced chemical equation for one such solution. Solution: The available information suggests that the base B is sodium hydroxide (NaOH). It is a deliquescent substance and becomes sticky on absorbing moisture from atmosphere. It is commercially formed by the e...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: The sum of two numbers is 95. If one exceeds the other by 15, then the smaller of the two is (a) 40 (b) 35 (c) 45 (d) 55 Solution: (a) 40 Let the numbers be $x$ and $x+15$. $\therefore x+x+15=95$ $\Rightarrow 2 x+15=95$ $\Rightarrow 2 x=95-15$ $\Rightarrow 2 x=80$ $\Rightarrow x=40$ The smaller number is 40 ....
Read More →A metal carbonate (X) on reacting with an acid gives
Question: A metal carbonate (X) on reacting with an acid gives a gas which when passed through a solution (Y) gives the carbonate back. On the other hand, a gas (G) that is obtained at anode during electrolysis of brine is passed on dry substance (Y). It gives a compound (Z), used for disinfecting drinking water. Identity X, Y, G and Z. Solution: The gas (G) obtained at anode during the electrolysis of brine is chlorine. The compound (Z) used for disinfecting drinking water is bleaching powder. ...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: Sum of three consecutive integers is 51. The middle one is (a) 14 (b) 15 (c) 16 (d) 17 Solution: (d) 17 Let the three consecutive integers be $x, x+1$ and $x+2$. Equation $=x+x+1+x+2=51$ $\Rightarrow 3 x+3=51$ $\Rightarrow 3 x=51-3$ $\Rightarrow 3 x=48$ $\Rightarrow x=\frac{48}{3}=16$ Middle integer $=x+1=16+1=17$...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: The base of an isosceles triangle is 6 cm and its perimeter is 16 cm. Length of each of the equal sides is (a) 4 cm (b) 5 cm (c) 3 cm (d) 6 cm Solution: (b) 5 cm Let the equal side of the isosceles triangle be $\mathrm{x}$. Then, the perimeter of the triangle would be $(x+x+6)$. $\therefore 2 x+6=16$ $\Rightarrow 2 x=16-6$ $\Rightarrow 2 x=10$ $\Rightarrow x=\frac{10}{2}=5$ $\therefore$ Length of each equal side $=5 \mathrm{~cm}$...
Read More →For making cake, baking powder is taken.
Question: For making cake, baking powder is taken. If at home your mother uses baking soda instead of baking powder in cake, (a) how will it affect the taste of the cake and why ? (b) how can baking soda be converted into baking powder ? (c) what is the role of tartaric acid added to baking soda ? Solution: Baking powder is a mixture of baking soda and tartaric acid. Out of the two, only baking soda is actually used for making bread or cake fluffy. The role of tartaric acid is to neutralise sodi...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: The ages of A and B are in the ratio 5 : 7. Four years from now the ratio of their ages will be 3 : 4. The present age of B is (a) 20 years (b) 28 years (c) 15 years (d) 21 years Solution: (b) 28 years Let $\mathrm{x}$ be the common multiple of the ages of $\mathrm{A}$ and $\mathrm{B}$. Then. the age $s$ of $\mathrm{A}$ and $\mathrm{B}$ would be $5 \mathrm{x}$ and $7 \mathrm{x}$, respectively. $\therefore \frac{5 x+4}{7 x+4}=\frac{3}{4}$ $\Rightarrow 4(5 x+...
Read More →In the following schematic diagram for the preparation
Question: In the following schematic diagram for the preparation of hydrogen gas as shown in the figure, what would happen if following changes are made ? (a) In place of zinc granules, same amount of zinc dust is taken in the test tube (b) Instead of dilute sulphuric acid, dilute hydrochloric acid is taken (c) In place of zinc, copper turnings are taken (d) Sodium hydroxide is taken in place of dilute sulphuric acid and the tube is heated. Solution: (a) Hydrogen gas would evolve at a greater sp...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: Four-fifths of a number is greater than three-fourths of the number by 4. The number is (a) 12 (b) 64 (c) 80 (d) 102 Solution: (c) 80 Let the number be $\mathrm{x}$. $\therefore \frac{4}{5} x=\frac{3}{4} x+4$ $\Rightarrow \frac{4 x}{5}=\frac{3 x+16}{4}$ $\Rightarrow 16 x=15 x+80$ $\Rightarrow 16 x-15 x=80$ $\Rightarrow x=80$...
Read More →When zinc metal is treated with a dilute solution of a strong acid,
Question: When zinc metal is treated with a dilute solution of a strong acid, a gas is evolved which is utilised in the hydrogenation of oils. Name the gas evolved. Write the chemical equation of the reaction involved and also write a test to detect the gas formed. Solution: The gas evoloved is hydrogen. The gas burns brightly with a pop sound when a burning splinter is brought in its contact. This causes the hydrogenation of edible liquid oils to form solid fats also called Vanaspati ghee....
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