ICSE

At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is 5/12. On walking 192 meters towards the tower, the tangent of the angle is found to be 3/4. Find the height of the tower.

SOLUTION: Let  AB to be the vertical tower and C and D be the two points such that CD = 192 m. And let ∠ACB = θ and ∠ADB = α \[\begin{array}{*{35}{l}} tan\text{ }\theta \text{ }=\text{ }5/12  \\...

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The angle of elevation of the top of a tower is observed to be 60o. At a point, 30 m vertically above the first point of observation, the elevation is found to be 45o. Find: (i) the height of the tower, (ii) its horizontal distance from the points of observation.

Let AB to be the tower of height h meters and let the two points be C and D be such that CD = 30 m, ∠ADE = 45o and ∠ACB = 60o (i) In ∆ADE, \[\begin{array}{*{35}{l}} AE/DE\text{ }=\text{ }tan\text{...

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Two pillars of equal heights stand on either side of a roadway, which is 150 m wide. At a point in the roadway between the pillars the elevations of the tops of the pillars are 60o and 30o; find the height of the pillars and the position of the point.

Let AB and CD be the two towers of height h m each and let P be a point in the roadway BD such that BD = 150 m, ∠APB = 60o and ∠CPD = 30o In ∆ABP, \[\begin{array}{*{35}{l}} AB/BP\text{ }=\text{...

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From the top of a light house 100 m high, the angles of depression of two ships are observed as 48o and 36o respectively. Find the distance between the two ships (in the nearest metre) if: (i) the ships are on the same side of the light house. (ii) the ships are on the opposite sides of the light house.

Let AB to be the lighthouse and the two ships be C and D such that ∠ADB = 36o and ∠ACB = 48o In ∆ABC, \[\begin{array}{*{35}{l}} AB/BC\text{ }=\text{ }tan\text{ }{{48}^{o}}  \\ BC\text{ }=\text{...

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A ladder is placed along a wall such that its upper end is resting against a vertical wall. The foot of the ladder is 2.4 m from the wall and the ladder is making an angle of 68o with the ground. Find the height, up to which the ladder reaches.

Let the height upto which the ladder reaches as ‘h’ meters. the angle of elevation is 68o \[\begin{array}{*{35}{l}} =>\text{ }tan\text{ }{{68}^{o}}~=\text{ }h/\text{ }2.4  \\ 2.475\text{ }=\text{...

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Glycogen is a branched-chain polymer of α-D-glucose units in which chain is formed by C1—C4 glycosidic linkage whereas branching occurs by the formation of C1-C6 glycosidic linkage. Structure of glycogen is similar to __________.
(i) Amylose
(ii) Amylopectin
(iii) Cellulose
(iv) Glucose

Option (ii) is the answer. Glycogen has a similar structure to amylopeptin. It's an a-D glucose unit branched chain polymer with C1-C4 glycosidic linkage for chain formation and C1-C6 glycosidic...

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Proteins are found to have two different types of secondary structures viz. α-helix and β-pleated sheet structure. α-helix structure of the protein is stabilised by : (i) Peptide bonds (ii) van der Waals forces (iii) Hydrogen bonds (iv) Dipole-dipole interactions

Option ( iii) is the answer. Hydrogen bonding help to keep the -helix structure of proteins stable. By twisting into a right-handed helix and hydrogen bonding the -NH group of each amino acid...

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Which of the following reactions of glucose can be explained only by its cyclic structure?
(i) Glucose forms pentaacetate.
(ii) Glucose reacts with hydroxylamine to form an oxime.
(iii) Pentaacetate of glucose does not react with hydroxylamine.
(iv) Glucose is oxidised by nitric acid to gluconic acid

Option (iii) is the answer. The absence of a free -CHO group is indicated by the fact that glucose pentaacetate does not react with hydroxylamine. Only the cyclic nature of glucose may explain this...

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Structure of a disaccharide formed by glucose and fructose is given below. Identify anomeric carbon atoms in monosaccharide units.
(i) ‘a’ carbon of glucose and ‘a’ carbon of fructose.
(ii) ‘a’ carbon of glucose and ‘e’ carbon of fructose.
(iii) ‘a’ carbon of glucose and ‘b’ carbon of fructose.
(iv) ‘f’ carbon of glucose and ‘f ’ carbon of fructose.

Option (iii) is the answer. Anomeric carbon is carbon that is next to an oxygen atom in the cyclic structure of glucose or fructose. 'a' and 'b' are next to the oxygen atom, as illustrated in the...

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Three structures are given below in which two glucose units are linked. Which of these linkages between glucose, units are between C1 and C4 and which linkages are between C1 and C6?
(i) (A) is between C1 and C4, (B) and (C) is between C1 and C6
(ii) (A) and (B) are between C1 and C4, (C) is between C1 and C6
(iii) (A) and (C) is between C1 and C4, (B) is between C1 and C6
(iv) (A) and (C) is between C1 and C6, (B) is between C1 and C4

Option (iii) is the answer (A) and (C) are in the Cl-C4 range, while (B) is in the Cl-C6 range.

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In nucleoside, a base is attached at 1C position of the sugar moiety. A nucleotide is formed by linking the phosphoric acid unit to the sugar unit of a nucleoside. At which position of sugar unit is the phosphoric acid linked in a nucleoside to give a nucleotide?

When a nitrogenous base is connected to the 1' position of a five-carbon sugar, a nucleoside is produced. The 5' carbon of the sugar in a nucleoside molecule is bonded to the 5' carbon of the sugar...

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Monosaccharides contain carbonyl group hence are classified, as aldose or ketose. The number of carbon atoms present in the monosaccharide molecule is also considered for classification. In which class of monosaccharide will you place fructose?

Carbonyl groups can be found in monosaccharides. As a result, they're categorised as either aldose or ketose. Aldose refers to monosaccharides that contain an aldehyde group. Ketose refers to...

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The letters ‘D’ or ‘L’ before the name of a stereoisomer of a compound indicates the correlation of configuration of that particular stereoisomer. This refers to their relationship with one of the isomers of glyceraldehyde. Predict whether the following compound has ‘D’ or ‘L’ configuration.

On the left side of the C5 carbon atom, the –OH group is connected. As a result, the provided compound is in the 'L' configuration.

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Protein found in a biological system with a unique three-dimensional structure and biological activity is called a native protein. When a protein in its native form, is subjected to a physical change like change in temperature or a chemical change like change in pH, denaturation of protein takes place. Explain the cause.

Hydrogen bonds and other intermolecular interactions connect the amino acid residues in proteins. The hydrogen bonds are disrupted when a physical or chemical change occurs, and the native protein...

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Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels 5 km/hr faster than the second train. If after 2 hours, they are 50 km apart, find the speed of each train.

Let the speed of the second train be \[~x\text{ }km/hr.\] Then, the speed of the first train is \[\left( x\text{ }+\text{ }5 \right)\text{ }km/hr\] Let O be the position of the railway station,...

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A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.

Let the usual speed of the plane to be \[x\text{ }km/hr\] The distance to travel \[=\text{ }1500km\] since, Time = Distance/ Speed As the ques suggests, \[{{x}^{2}}~+\text{ }250x\text{ }\text{...

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An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for: (i) the onward journey; (ii) the return journey. If the return journey took 30 minutes less than the onward journey, write down an equation in x and find its value.

According to ques, Distance \[=\text{ }400\text{ }km\] Average speed of the airplane \[=\text{ }x\text{ }km/hr\] Also, speed while returning \[=\text{ }\left( x\text{ }+\text{ }40 \right)\text{...

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A hotel bill for a number of people for overnight stay is Rs 4800. If there were 4 people more, the bill each person had to pay, would have reduced by Rs 200. Find the number of people staying overnight.

Let the number of people staying overnight as x. According to ques, total hotel bill \[~=\text{ }Rs\text{ }4800\] Now,hotel bill for each person \[=\text{ }Rs\text{ }4800/x\] therefore,...

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A trader buys x articles for a total cost of Rs 600. (i) Write down the cost of one article in terms of x. If the cost per article were Rs 5 more, the number of articles that can be bought for Rs 600 would be four less. (ii) Write down the equation in x for the above situation and solve it for x.

According to ques, Number of articles \[=\text{ }x\] And, the total cost of articles \[=\text{ }Rs\text{ }600\] Again, (i) Cost of one article \[=\text{ }Rs\text{ }600/x\] (ii) also,...

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The distance by road between two towns A and B is 216 km, and by rail it is 208 km. A car travels at a speed of x km/hr and the train travels at a speed which is 16 km/hr faster than the car. Calculate: (iii) If the train takes 2 hours less than the car, to reach town B, obtain an equation in x and solve it. (iv) Hence, find the speed of the train.

(iii) According to the question, \[4x\text{ }+\text{ }1728\text{ }=\text{ }{{x}^{2}}~+\text{ }16x\] Or, \[{{x}^{2}}~+\text{ }12x\text{ }\text{ }1728\text{ }=\text{ }0\] Or, \[{{x}^{2}}~+\text{...

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The distance by road between two towns A and B is 216 km, and by rail it is 208 km. A car travels at a speed of x km/hr and the train travels at a speed which is 16 km/hr faster than the car. Calculate: (i) the time taken by the car to reach town B from A, in terms of x; (ii) the time taken by the train to reach town B from A, in terms of x.

According to ques, Speed of car = \[x\text{ }km/hr\] Speed of train = \[\left( x\text{ }+\text{ }16 \right)\text{ }km/hr\] Time = \[Distance/\text{ }Speed\] (i)Time taken by the car to reach town B...

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