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Question: Tick (✓) the correct answer: The number of coins, each of radius 0.75 cm and thickness 0.2 cm, to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is (a) 460 (b) 500 (c) 600 (d) 640 Solution: (d) 640 Total no. of coins $=\frac{\text { volume of cylinder }}{\text { volume of each coin }}=\frac{\pi \times 3 \times 3 \times 8}{\pi \times 0.75 \times 0.75 \times 0.2}=640$...
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Question: Tick (✓) the correct answer: The ratio of the total surface area to the lateral surface area of a cylinder whose radius is 20 cm and height 60 cm, is (a) 2 : 1 (b) 3 : 2 (c) 4 : 3 (d) 5 : 3 Solution: (c) 4 : 3 Here, $\frac{\text { Total surface area }}{\text { Lateral surface area }}=\frac{2 \pi r(h+r)}{2 \pi r h}$ $=\frac{h+r}{h}$ $=\frac{20+60}{60}$ $=\frac{4}{3}$ $=4: 3$...
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Question: $x^{2}-x+2=0$ Solution: Given: $x^{2}-x+2=0$ Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by: $x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$ $\Rightarrow x=\frac{-(-1) \pm \sqrt{(-1)^{2}-(4 \times 1 \times 2)}}{2 \times 1}$ $\Rightarrow x=\frac{1 \pm \sqrt{1-8}}{2}$ $\Rightarrow x=\frac{1 \pm \sqrt{-7}}{2}$ $\Rightarrow x=\frac{1 \pm \sqrt{7} i}{2}$ $\Rightarrow \quad x=\frac{1}{2} \pm \frac{\sqrt{7}}{2} i$ Ans: $x=\frac{1}{2}+\frac{\sqrt{7}}{2} i$ and $x...
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Question: Tick (✓) the correct answer: If the capacity of a cylindrical tank is 1848 m3and the diameter of its base is 14 m, the depth of the tank is (a) 8 m (b) 12 m (c) 16 m (d) 18 m Solution: (b) $12 \mathrm{~m}$ Diameter $=14 \mathrm{~m}$ Radius $=7 \mathrm{~m}$ Volume $=1848 \mathrm{~m}^{3}$ Now, volume $=\pi \mathrm{r}^{2} \mathrm{~h}=\frac{22}{7} \times 7 \times 7 \times \mathrm{h}=1848 \mathrm{~m}^{3}$ $\therefore \mathrm{h}=\frac{1848}{22 \times 7}=12 \mathrm{~m}$...
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Question: Following is a pie chart showing the amount spent (in Rs thousands) by a company on various modes of advertising for a product.Now, answer the following questions. (i) Which type of media advertising is the greatest amount of the total? (ii) Which type of media advertising is the least amount of the total? 1. Television 2. Newspaper 3. Magazines 4. Radio 5. Business papers 6. Direct mail 7. Yellow page 8. Outdoor 9. Miscellaneous Solution: (i) The greatest amount of the total is spent ...
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Question: Tick (✓) the correct answer: A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out? (a) 32 m3 (b) 36 m3 (c) 40 m3 (d) 44 m3 Solution: (d) $44 \mathrm{~m}^{3}$ Diameter $=2 \mathrm{~m}$ Radius $=1 \mathrm{~m}$ Height $=14 \mathrm{~m}$ $\therefore$ Volume $=\pi \mathrm{r}^{2} \mathrm{~h}=\frac{22}{7} \times 1 \times 1 \times 14=44 \mathrm{~m}^{3}$...
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Question: $x^{2}+x+1=0$ Solution: Given: $x^{2}+x+1=0$ Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by: $x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$ $\Rightarrow x=\frac{-1 \pm \sqrt{1^{2}-(4 \times 1 \times 1)}}{2 \times 1}$ $\Rightarrow x=\frac{-1 \pm \sqrt{1-4}}{2}$ $\Rightarrow x=\frac{-1 \pm \sqrt{-3}}{2}$ $\Rightarrow x=\frac{-1 \pm \sqrt{3} i}{2}$ $\Rightarrow \quad x=-\frac{1}{2} \pm \frac{\sqrt{3}}{2} i$ Ans: $x=-\frac{1}{2}+\frac{\sqrt{3}}{2} i$ and $x=...
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Question: Tick (✓) the correct answer: Five equal cubes, each of edge 5 cm, are placed adjacent to each other. The volume of the cuboid so formed, is (a) 125 cm3 (b) 375 cm3 (c) 525 cm3 (d) 625 cm3 Solution: (d) $625 \mathrm{~cm}^{3}$ Length of the cuboid so formed $=25 \mathrm{~cm}$ Breadth of the cuboid $=5 \mathrm{~cm}$ Height of the cuboid $=5 \mathrm{~cm}$ $\therefore$ Volume of cuboid $=25 \times 5 \times 5=625 \mathrm{~cm}^{3}$...
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Question: Tick (✓) the correct answer: Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. The edge of the new cube formed is (a) 12 cm (b) 14 cm (c) 16 cm (d) 18 cm Solution: (a) $12 \mathrm{~cm}$ Total volume $=6^{3}+8^{3}+10^{3}=216+512+1000=1728 \mathrm{~cm}^{3}$ $\therefore$ Edge of the new cube $=\sqrt[3]{1728}=12 \mathrm{~cm}$...
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Question: Solution: Total quantity obtained from the given three colours $=192+228+180=600$ Also, $\quad 600=100 \%$ or $1=\frac{100}{600} \%=\frac{1}{6} \%$ or $192=\frac{1}{6} \times 192=32 \%$ or $228=\frac{1}{6} \times 228=38 \%$ or $180=\frac{1}{6} \times 180=30 \%$...
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Question: Tick (✓) the correct answer: If each side of a cube is doubled, its surface area (a) is doubled (b) becomes 4 times (c) becomes 6 times (d) becomes 8 times Solution: (b) becomes 4 times. Let the side of the cube be a units. Surface area = 6a2sq units Now, new side = 2aunits New surface area = 6(2a2) sq units = 24a2sq units. Thus, the surface area becomes 4 times the original area....
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Question: Tick (✓) the correct answer: If each side of a cube is doubled then its volume (a) is doubled (b) becomes 4 times (c) becomes 6 times (d) becomes 8 times Solution: (d) If each side of the cube is doubled, its volume becomes 8 times the original volume. Let the original side be aunits. Then original volume =a3cubic units Now, new side = 2aunits Then new volume = (2a)3sq units = 8a3cubic units Thus, the volume becomes 8 times the original volume....
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Question: Tick $(\checkmark)$ the correct answer: The diagonal of a cube measures $4 \sqrt{3} \mathrm{~cm}$. Its volume is (a) $8 \mathrm{~cm}^{3}$ (b) $16 \mathrm{~cm}^{3}$ (c) $27 \mathrm{~cm}^{3}$ (d) $64 \mathrm{~cm}^{3}$ Solution: (d) $64 \mathrm{~cm}^{2}$ Diagonal of the cube $=a \sqrt{3}=4 \sqrt{3} \mathrm{~cm}$ i.e., $a=4 \mathrm{~cm}$ $\therefore$ Volume $=a^{3}=4^{3}=64 \mathrm{~cm}^{3}$...
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Question: Tick (✓) the correct answer: The area of the cardboard needed to make a box of size 25 cm 15 cm 8 cm will be (a) 390 cm2 (b) 1390 cm2 (c) 2780 cm2 (d) 1000 cm2 Solution: (b) $1390 \mathrm{~cm}^{2}$ Surface area $=2(25 \times 15+15 \times 8+25 \times 8)=2(375+120+200)=1390 \mathrm{~cm}^{2}$...
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Question: Solution: Total Quantity obtained from the given four symbols $=800+700+550+450=2500$ From the pie chart, $28 \%$ of $2500=\frac{28}{100} \times 2500=700$ $22 \%$ of $2500=\frac{22}{100} \times 2500=550$ $18 \%$ of $2500=\frac{18}{100} \times 2500=450$ $32 \%$ of $2500=\frac{32}{100} \times 2500=800$...
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Question: Tick (✓) the correct answer: A rectangular water tank is 3 m long, 2 m wide and 5 m high. How many litres of water can it hold? (a) 30000 (b) 15000 (c) 25000 (d) 35000 Solution: (a) 30000 Volume $=3 \times 2 \times 5=30 \mathrm{~m}^{3}=30000 \mathrm{~L}$...
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Question: Sonia picks up a card from the given cards Find the probability of getting (a) an odd number (b) a Y card (c) a G card (d) a B card bearing number greater than 7. Solution: (a) The probability of getting an odd number $=\frac{\text { Number of events getting an odd number }}{\text { Total number of events }}=\frac{5}{10}=\frac{1}{2}$ (b) The probability of getting a $Y$ card $=\frac{\text { Number of events getting a } Y \text { card }}{\text { Total number of events }}=\frac{3}{10}$ (...
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Question: $2 x^{2}+1=0$ Solution: $2 x^{2}+1=0$ $\Rightarrow 2 x^{2}=-1$ $\Rightarrow^{x^{2}}=-\frac{1}{2}$ $\Rightarrow x=\pm \sqrt{-\frac{1}{2}}$ $\Rightarrow x=\pm \sqrt{\frac{1}{2}} i$ $\Rightarrow x=\pm \frac{i}{\sqrt{2}}$ Ans: $x=\pm \frac{i}{\sqrt{2}}$...
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Question: Tick (✓) the correct answer: The dimensions of a room are (10 m 8 m 3.3 m). How many men can be accommodated in this room if each man requires 3 m3of space? (a) 99 (b) 88 (c) 77 (d) 75 Solution: (b) 88 Volume of the room $=10 \times 8 \times 3.3=264 \mathrm{~m}^{3}$ One person requires $3 \mathrm{~m}^{3}$. $\therefore$ Total no. of people that can be accommodated $=\frac{264}{3}=88$...
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Question: Tick (✓) the correct answer: A rectangular water reservoir contains 42000 litres of water. If the length of reservoir is 6 m and its breadth is 3.5 m, the depth of the reservoir is (a) 2 m (b) 5 m (c) 6 m (d) 8 Solution: (a) $2 \mathrm{~m}$ $42000 \mathrm{~L}=42 \mathrm{~m}^{3}$ Volume $=l b h$ $\therefore$ Height $(h)=\frac{\text { volume }}{l b}=\frac{42}{6 \times 3.5}=\frac{6}{6 \times 0.5}=2 \mathrm{~m}$...
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Question: Tick (✓) the correct answer: An iron beam is 9 m long, 40 cm wide and 20 cm high. If 1 cubic metre of iron weighs 50 kg, what is the weight of the beam? (a) 56 kg (b) 48 kg (c) 36 kg (d) 27 kg Solution: (c) $36 \mathrm{~kg}$ Volume of the iron beam $=9 \times 0.4 \times 0.2=0.72 \mathrm{~m}^{3}$ $\therefore$ Weight $=0.72 \times 50=36 \mathrm{~kg}$...
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Question: $x^{2}+5=0$ Solution: Given: $x^{2}+5=0$ $\Rightarrow x^{2}=-5$ $\Rightarrow x=\pm \sqrt{(}-5)$ $\Rightarrow x=\pm \sqrt{5} i$ Ans: $x=\pm \sqrt{5} i$...
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Question: Tick (✓) the correct answer: The surface area of a (10 cm 4 cm 3 cm) brick is (a) 84 cm2 (b) 124 cm2 (c) 164 cm2 (d) 180 cm2 Solution: (c) $164 \mathrm{sq} \mathrm{cm}$ Surface area $=2(10 \times 4+10 \times 3+4 \times 3)=2(40+30+12)=164 \mathrm{~cm}^{2}$...
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Question: Tick (✓) the correct answer: Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is (a) 1 : 3 (b) 1 : 9 (c) 1 : 27 (d) none of these Solution: (b) $1: 9$ $\frac{\text { Volume } 1}{\text { Volume } 2}=\frac{1}{27}=\frac{a^{3}}{b^{3}}$ $\Rightarrow a=\frac{b}{\sqrt[3]{27}}=\frac{b}{3}$ or $b=3 a$ or $\frac{b}{a}=3$ Now, $\frac{\text { surface area } 1}{\text { surface area } 2}=\frac{6 \mathrm{a}^{2}}{6 \mathrm{~b}^{2}}=\frac{\mathrm{a}^{2}}{\mathrm{~b}^{2...
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Question: $x^{2}+2=0$ Solution: This equation is a quadratic equation Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by: $x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$ Given: $\Rightarrow \mathrm{x}^{2}+2=0$ $\Rightarrow \mathrm{x}^{2}=-2$ $\Rightarrow \mathrm{x}=\pm \sqrt{(-2)}$ But we know that $\sqrt{(-1)}=\mathrm{i}$ $\Rightarrow x=\pm \sqrt{2} i$ Ans: $x=\pm \sqrt{2} i$...
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