A grocer purchased 200 kg of rice at Rs 25 per kg.
Question: A grocer purchased 200 kg of rice at Rs 25 per kg. He sold 80 kg of it at a gain of 10% and 40 kg at a loss of 4%. At what rate per kg should he sell the remainder to gain 8% on his total investment? Solution: CP of $1 \mathrm{~kg}$ of rice $=$ Rs 25 C.P of $200 \mathrm{~kg}$ rice $=\mathrm{Rs}(200 \times 25)=\mathrm{Rs} 5000$ CP of $80 \mathrm{~kg}$ of rice=Rs $(25 \times 80)=$ Rs 2000 CP of $40 \mathrm{~kg}$ of rice $=$ Rs $(25 \times 40)=$ Rs 1000 $\mathrm{SP}$ of $80 \mathrm{~kg}$ ...
Read More →An element X of group 15 exists as diatomic molecule
Question: An element X of group 15 exists as diatomic molecule and combines with hydrogen at 773 K in presence of the catalyst to form a compound, ammonia which has a characteristic pungent smell. (a) Identify the element X. How many valence electrons does it have ? (b) Draw the electron dot structure of the diatomic molecule of X. What type of bond is formed in it ? (c) Draw the electron dot structure for ammonia. What type of bonds is formed in it ? Solution: (a) The available information sugg...
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Question: If $\tan (x+y)+\tan (x-y)=1$, find $\frac{d y}{d x}$ Solution: We are given with an equation $\tan (x+y)+\tan (x-y)=1$, we have to find $\frac{d y}{d x}$ by using the given equation, so by differentiating the equation on both sides with respect to $x$, we get, $\sec ^{2}(x+y)\left[1+\frac{d y}{d x}\right]+\sec ^{2}(x-y)\left[1-\frac{d y}{d x}\right]=0$ $\frac{d y}{d x}\left[\sec ^{2}(x+y)-\sec ^{2}(x-y)\right]+\sec ^{2}(x+y)+\sec ^{2}(x-y)=0$ $\frac{d y}{d x}=\frac{\sec ^{2}(x+y)+\sec ...
Read More →An element X which is a yellow solid at room temperature
Question: An element X which is a yellow solid at room temperature shows catenation and allotropy. X forms two oxides which are also formed during the thermal decomposition of ferrous sulphate crystals and are the major air pollutants. (a) Identify the element X. (b) Write the electronic configuration of X. (c) Write the balanced chemical equation for the thermal decomposition of ferrous sulphate crystals. (d) What would be the nature (acidic/basic) of oxides formed ? (e) Locate the position of ...
Read More →Hema bought two pairs of jeans for ₹ 1450 each.
Question: Hema bought two pairs of jeans for ₹ 1450 each. She sold one of them at a gain of 8% and the other at a loss of 4%. Find her gain or loss per cent in the whole transaction. Solution: CP of first jeans $=₹ 1,450$ Profit $=8 \%$ of $\mathrm{CP}=\frac{8}{100} \times 1450=₹ 116$ SP of first jeans $=₹ 1,450+₹ 116=₹ 1,566$ CP of second jeans $=₹ 1,450$ Loss $=4 \%$ of $\mathrm{CP}=\frac{4}{100} \times 1450=₹ 58$ SP of second jeans $=₹ 1450-₹ 58=₹ 1,392$ Total CP of two jeans $=\mathrm{CP}$ o...
Read More →(a) Electropositive nature of the element(s) increases
Question: (a) Electropositive nature of the element(s) increases down the group and decreases across the period (b) Electronegativity of the element decreases down the group and increases across the period (c) Atomic size increases down the group and decreases across a period (left to right) (d) Metallic character increases down the group and decreases across a period. On the basis of the above trends of the Periodic Table, answer the following about the elements with atomic numbers 3 to 9. (a) ...
Read More →Wasim bought two cricket bats for ₹ 840 and ₹ 360 respectively.
Question: Wasim bought two cricket bats for ₹ 840 and ₹ 360 respectively. He sells the first bat at a gain of 15% and the second one at a loss of 5%. Find his gain or loss per cent in the whole transaction. Solution: CP of the first bat = ₹840 Profit% on the first bat = 15% $\therefore$ Profit $=15 \%$ of ₹ $840=\frac{15}{100} \times 840=₹ 126$ SP of the first bat = ₹840 + ₹126 = ₹966 CP of the second bat = ₹360 Loss $=5 \%$ of ₹ $360=\frac{5}{100} \times 360=₹ 18$ SP of the second bat = ₹360 ₹1...
Read More →Find the domain and the range of each of the following real
Question: Find the domain and the range of each of the following real function: $f(x)=\frac{1}{2-\sin 3 x}$ Solution: Given: $f(x)=\frac{1}{2-\sin 3 x}$ Need to find: Where the functions are defined. The maximum value of an angle is $2 \pi$ So, the maximum value of $x=2 \pi / 3$. Whereas, the minimum value of $x$ is 0 Therefore, the domain of the function, $\mathrm{D} \mathrm{f}(\mathrm{x})=(0,2 \pi / 3)$. Now, the minimum value of $\sin \theta=0$ and the maximum value of $\sin \theta=1 .$ So, t...
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Question: If $\sin (\mathrm{xy})+\frac{\mathrm{y}}{\mathrm{x}}=\mathrm{x}^{2}-\mathrm{y}^{2}$, find $\frac{\mathrm{dy}}{\mathrm{dx}}$. Solution: We are given with an equation $\sin (x y)+\frac{y}{x}=x^{2}-y^{2}$, we have to find $\frac{d y}{d x}$ by using the given equation, so by differentiating the equation on both sides with respect to $x$, we get, $\cos (x y)\left[(1) y+x \frac{d y}{d x}\right]+\frac{x \frac{d y}{d x}-y(1)}{x^{2}}=2 x-2 y \frac{d y}{d x}$ $y \cos (x y)+x \cos (x y) \frac{d y...
Read More →Mendeleev predicted the existence of certain
Question: Mendeleev predicted the existence of certain elements not known at that time and named two of them as Eka-silicon and Eka-aluminium. (a) Name the elements which have taken the place of these elements. (b) Mention the group and the period of these elements in the Modern Periodic Table. (c) Classify these elements as metals, non-metals or metalloids. (d) How many valence electrons are present in each one of them ? Solution: (a) Germanium (Ge) for Eka-silicon and gallium (Ga) for Eka-alum...
Read More →Sonu buys 40 kg of wheat at ₹ 12.50 per kg and 30 kg of wheat at ₹ 14 per kg.
Question: Sonu buys 40 kg of wheat at ₹ 12.50 per kg and 30 kg of wheat at ₹ 14 per kg. At what rate per kg should he sell the mixture to gain 5% on the whole? Solution: 40 kg of wheat is bought for ₹12.50/kg. CP of 40 kg of wheat = 40 12.50 = ₹500 30 kg of wheat is bought for ₹14/kg. CP of 30 kg of wheat = 30 14 = ₹420 Total CP = ₹500 + ₹420 = ₹920 Profit $=5 \%$ of $\mathrm{CP}=5 \%$ of ₹ $920=\frac{5}{100} \times 920=₹ 46$ Let the SP be ₹x. Profit = SP CP ⇒x 920 = 46 ⇒x= ₹966 SP of 70 kg whea...
Read More →Find the domain and the range of each of the following real
Question: Find the domain and the range of each of the following real function: $f(x)=\frac{x^{2}-9}{x-3}$ Solution: Given: $f(x)=\frac{x^{2}-9}{x-3}$ Need to find: Where the functions are defined. To find the domain of the function $f(x)$ we need to equate the denominator of the function to 0 . Therefore $x-3=0$ $\Rightarrow x=3$ It means that the denominator is zero when $x=3$ So, the domain of the function is the set of all the real numbers except 3 . The domain of the function, $\mathrm{D}_{...
Read More →Complete the following cross word puzzle
Question: Complete the following cross word puzzle Across : (1) An element with atomic number 12. (3) Metal used in making cans and member of Group 14. (4) A lustrous non-metal which has 7 electrons in its outermost shell. Down : (2) Highly reactive and soft metal which imparts yellow colour when subjected to flame and is kept in kerosene. (5) The first element of second period (6) An element which is used in making fluorescent bulbs and is second member of group 18 in the Modern Periodic Table....
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Question: If $y \sqrt{x^{2}+1}=\log \left(\sqrt{x^{2}+1}-x\right)$, show that $\left(x^{2}+1\right) \frac{d y}{d x}+x y+1=0$ Solution: We are given with an equation $y \sqrt{x^{2}+1}=\log \left(\sqrt{x^{2}+1}-x\right)$, we have to prove that $\left(x^{2}+1\right) \frac{d y}{d x}+x y+1=0$ by using the given equation we will first find the value of $\frac{d y}{d x}$ and we will put this in the equation we have to prove, so by differentiating the equation on both sides with respect to $x$, we get, ...
Read More →A cycle was sold at a gain of 10%. Had it been sold for ₹ 260 more,
Question: A cycle was sold at a gain of 10%. Had it been sold for ₹ 260 more, the gain would have been 14%. Find the cost price of the cycle. Solution: Let the CP be ₹x. SP when gain is $10 \%=x+\frac{10}{100} x=₹ \frac{110}{100} x$ SP when gain is $14 \%=x+\frac{14}{100} x=₹ \frac{114}{100} x$ Difference in SP = SP when gain is 14% SP when gain is 10% = ₹260 $\therefore \frac{114 x}{100}-\frac{110 x}{100}=260$ $\Rightarrow \frac{4 x}{100}=260$ $\Rightarrow x=6500$ Hence, the CP of the cycle is ...
Read More →(a) In this ladder symbols of elements are jumbled up.
Question: (a) In this ladder symbols of elements are jumbled up. Rearrange these symbols of elements in the increasing order of their atomic number in the Periodic Table. (b) Arrange them in the order of their group also. Solution: (a) H, He, Li, Be, B, C, N, O, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K, Ca, Br. (b) Group 1 H, Li, Na, K Group 2 Be, Mg, Ca Group 13 B, A1 Group 14 C, Si Group 15 N, P Group 16 O, S Group 17 Cl, Br Group 18 He, Ne, Ar...
Read More →Find the domain and the range of each of the following real
Question: Find the domain and the range of each of the following real function: $f(x)=\frac{|x-4|}{x-4}$ Solution: Given: $f(x)=\frac{|x-4|}{x-4}$ Need to find: Where the functions are defined. To find the domain of the function f(x) we need to equate the denominator of the function to 0. Therefore, $x-4=0$ $\Rightarrow x=4$ It means that the denominator is zero when $x=4$ So, the domain of the function is the set of all the real numbers except 4 . The domain of the function, $\mathrm{D} \mathrm...
Read More →A dealer gets Rs 56 less if instead of selling a chair at a gain of 15%,
Question: A dealer gets Rs 56 less if instead of selling a chair at a gain of 15%, it is sold at a gain of 8%. Find the cost price of the chair. Solution: Let $R s x$ be the CP. Gain $_{1}$ percentage $=\left(\frac{\operatorname{gain}_{1}}{\mathrm{CP}} \times 100\right) \%$ $\Rightarrow 15=\frac{\text { gain }_{1}}{x} \times 100$ $\Rightarrow$ Gain $_{1}=$ Rs $\frac{15 x}{100}$ Again, gain $_{2}$ percentage $=\left(\frac{\mathrm{gain}_{2}}{\mathrm{CP}} \times 100\right) \%$ $\Rightarrow 8=\frac{...
Read More →Atomic number of a few elements are : 10, 20, 7, 14
Question: Atomic number of a few elements are : 10, 20, 7, 14 (a) Identify the elements (b) Identify the Group number of these elements in the Periodic Table (c) Identify the Periods of these elements in the Periodic Table (d) What would be the electronic configuration for each of these elements ? (e) Determine the valency of these elements. Solution: (a) The elements are : Neon (Z = 10), Calcium (Z = 20), Nitrogen (Z = 7) and Silicon (Z = 14) (b) Group numbers : Neon (18), Calcium (2), Nitrogen...
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Question: If $y-x \sin y$, prove that $\frac{d y}{d x}=\frac{\sin y}{(1-x \cos y)}$ Solution: We are given with an equation $y=x \sin y$, we have to prove that $\frac{d y}{d x}=\frac{\sin y}{1-x \cos y}$ by using the given equation we will first find the value of $\frac{d y}{d x}$ and we will put this in the equation we have to prove, so by differentiating the equation on both sides with respect to $x$, we get, $\frac{d y}{d x}=\sin y+x \cos y \frac{d y}{d x}$ $\frac{d y}{d x}[1-x \cos y]=\sin y...
Read More →An element X (atomic number 17) reacts
Question: An element X (atomic number 17) reacts with an element Y (atomic number 20) to form a divalent halide. (a) Where in the Periodic Table are elements X and Y placed ? (b) Classify X and Y as metal(s), non-metal(s) or metalloid(s). (c) What will be the nature of oxide of element Y ? Identify the nature of bonding in the compound formed (d) Draw the electron dot structure of the divalent halide. Solution: Element X (Z = 17) is chlorine while element Y (Z = 20) is calcium. (a) Chlorine (Cl)...
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Question: If $x \sin (a+y)+\sin a \cos (a+y)=0$, prove that $\frac{d y}{d x}=\frac{\sin ^{2}(a+y)}{\sin a}$ Solution: We are given with an equation $x \sin (a+y)+\sin a \cos (a+y)=0$, we have to prove that $\frac{d y}{d x}=\frac{\sin ^{2}(a+y)}{\sin a}$ by using the given equation we will first find the value of $\frac{d y}{d x}$ and we will put this in the equation we have to prove, so by differentiating the equation on both sides with respect to $x$, we get, $\tan (a+y)=\frac{-\sin a}{x}$ $\se...
Read More →Find the domain and the range of each of the following real function:
Question: Find the domain and the range of each of the following real function: f(x) =$1-|x-2|$ Solution: Given: $f(x)=1-|x-2|$ Need to find: Where the functions are defined. Since $|x-2|$ gives real no. for all values of $x$, the domain set can possess any real numbers. So, the domain of the function, $\operatorname{Df}(x)=(-\infty, \infty)$. Now the given function is $f(x)=1-|x-2|$, where $|x-2|$ is always positive. So, the maximum value of the function is 1 . Therefore, the range of the funct...
Read More →A dealer gets ₹ 940 more if instead of selling a table at a loss of 10%,
Question: A dealer gets ₹ 940 more if instead of selling a table at a loss of 10%, it is sold at a gain of 10%. Find the cost price of the table. Solution: Let the cost price be ₹x. Loss $=10 \%$ of $₹ x=\frac{10}{100} x=₹ \frac{x}{10}$ SP in case of loss $=$ CP $-$ Loss $=x-\frac{x}{10}=₹ \frac{9 x}{10}$ Gain $=10 \%$ of $₹ x=\frac{10}{100} x=₹ \frac{x}{10}$ SP in case of profit $=$ CP $+$ Profit $=x+\frac{x}{10}=₹ \frac{11 x}{10}$ It is given that dealer gets ₹940 more if sold at a profit of 1...
Read More →An element placed in 2nd group and 3rd Period of the Periodic Table,
Question: An element placed in 2nd group and 3rd Period of the Periodic Table, burns in the presence of oxygen to form a basic oxide. (a) Identify the element (b) Write the electronic configuration (c) Write the balanced equation when it burns in the presence of air (d) Write a balanced equation when this oxide is dissolved in water (e) Draw the electron dot structure for the formation of this oxide Solution: (a) The element is magnesium (Mg). (b) The electronic configuration is 2, 8, 2. (c) Mag...
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