NCERT Exemplar

An ideal gas is permitted to grow against a consistent strain of 2 bar from 10 L to 50 L in one stage. Compute the measure of work done by the gas. In the event that a similar development were done reversibly, will the work is done be higher or lower than the prior case?

    \[\left( Considering\text{ }that\text{ }1\text{ }L\text{ }bar\text{ }=\text{ }100J \right)\]

solution:   \[\begin{array}{*{35}{l}} Measure\text{ }of\text{ }work\text{ }done\text{ }=\text{ }-\text{ }pext\text{ }V  \\ ~  \\ =\text{ }\text{ }2\text{ }bar\text{ }\times \text{ }\left(...

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The net enthalpy change of a response is the measure of energy needed to break every one of the bonds in reactant atoms less the measure of energy needed to shape every one of the bonds in the item particles. What will be the enthalpy change for the accompanying response?

    \[H2\left( g \right)\text{ }+\text{ }Br2\left( g \right)\text{ }\to \text{ }2HBr\left( g \right)\]

Considering that Bond energy of H2, Br2 and HBr is 435 kJ mol–1, 192 kJ mol–1 and 368 kJ mol–1 separately.

solution:   For the response   \[H2\left( g \right)\text{ }+\text{ }Br2\left( g \right)\text{ }\to 2HBr\left( g \right)\] \[\begin{array}{*{35}{l}} Enthalpy\text{ }change  \\ ~  \\ =\text{...

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State whether the following statements are true or false. Justify your answer. Point P (0, 2) is the point of intersection of y–axis and perpendicular bisector of line segment joining the points A (–1, 1) and B (3, 3).

Solution: The statement given in the question is false. Justification: We know that the points on the perpendicular bisector of the line segment joining two points are equidistant from the two...

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. Enthalpy is a broad property. As a rule, if the enthalpy of a general response A→B along one course is Δr H and Δr H1, ΔrH2, ΔrH3 … .. address enthalpies of middle responses prompting item B. What will be the connection between ΔrH for generally speaking response and ΔrH1, ΔrH2… .. and so forth for moderate responses.

solution:   For the response, A→B the development of B goes through a few middle of the road responses with various enthalpy esteems Δr H1, ΔrH2, ΔrH3… .., and the general enthalpy change is Δr...

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18.0 g of water totally vapourises at 100°C and 1 bar pressure and the enthalpy change in the process is 40.79 kJ mol–1. What will be the enthalpy change for vapourising two moles of water under similar conditions? What is the standard enthalpy of vapourisation for water?

solution:   Enthalpy change of vapourisation for \[1\text{ }mole\text{ }=\text{ }40.79\text{ }kJ\text{ }mol1\] enthalpy change of vapourisation for \[2\text{ }moles\text{ }of\text{ }water\text{...

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. Think about the accompanying response among zinc and oxygen and pick the right alternatives out of the choices given underneath :

    \[2\text{ }Zn\text{ }\left( s \right)\text{ }+\text{ }O2\text{ }\left( g \right)\text{ }\to \text{ }2\text{ }ZnO\text{ }\left( s \right)\text{ };\text{ }H\text{ }=\text{ }\text{ }693.8\text{ }kJ\text{ }mol1\]

(i) The enthalpy of two moles of ZnO is not exactly the absolute enthalpy of two moles of Zn and one mole of oxygen by 693.8 kJ. (ii) The enthalpy of two moles of ZnO is more than the absolute enthalpy of two moles of Zn and one mole of oxygen by 693.8 kJ. (iii) 693.8 kJ mol–1 energy is advanced in the response. (iv) 693.8 kJ mol–1 energy is caught up in the response.

solution:   Choice (I) and (iii) are the appropriate responses

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. For an optimal gas, crafted by reversible extension under isothermal condition can be determined by utilizing the articulation

    \[w\text{ }=\text{ }\text{ }nRT\text{ }ln\text{ }Vf/Vi\]

An example containing 1.0 mol of an ideal gas is extended isothermally and reversibly to multiple times of its unique volume, in two separate tests. The extension is completed at 300 K and 600 K separately. Pick the right alternative. (I) Work done at 600 K is multiple times the work done at 300 K. (ii) Work done at 300 K is double the work done at 600 K. (iii) Work done at 600 K is double the work done at 300 K. (iv) ∆U = 0 in the two cases.

solution:   Alternative (iii) and (iv) are the appropriate responses. work done at 600 K is double the work done at 300 K. Since each case includes isothermal extension of an optimal gas, there...

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The immediacy implies, having the capacity to continue without the help of an outer organization. The cycles which happen immediately are (I) stream of warmth from colder to hotter body. (ii) gas in a compartment contracting into one corner. (iii) gas extending to fill the accessible volume. (iv) consuming carbon in oxygen to give carbon dioxide.

solution:   Alternative (iii) and (iv) are the appropriate responses. Gas grows or diffuses in accessible space suddenly, e.g., spillage of cooking gas gives smell of ethyl mercaptan...

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. Thermodynamics essentially manages (I) interrelation of different types of energy and their change from one structure to another. (ii) energy changes in the cycles which rely just upon starting and last conditions of the minute frameworks containing a couple of particles. (iii) how and at what rate these energy changes are done. (iv) the framework in harmony state or moving from one balance state to another harmony state.

solution:   Alternative (I) and (iv) are the appropriate responses. Thermodynamics manages interrelation of different types of energy and their change into one another. It additionally manages...

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. Which of coming up next isn’t right? (I) ∆G is zero for a reversible response (ii) ∆G is positive for an unconstrained response (iii) ∆G is negative for an unconstrained response (iv) ∆G is positive for a non-unconstrained response

solution:   Alternative (ii) is the appropriate response.   ∆G gives a basis for suddenness at consistent strain and temperature.   (I) If ∆G is negative (< 0). the cycle is...

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The entropy change can be determined by utilizing the articulation

    \[S\text{ }=\text{ }qrev/T\]

At the point when water freezes in a glass container, pick the right assertion among the accompanying : (I) ∆S (framework) diminishes however ∆S (environmental factors) stays as before. (ii) ∆S (framework) increments yet ∆S (environmental elements) diminishes. (iii) ∆S (framework) diminishes yet ∆S (environmental elements) increments. (iv) ∆S (framework) diminishes and ∆S (environmental factors) likewise diminishes.

solution:   Alternative (iii) is the appropriate response. During the method involved with freezing energy is released,which is consumed by the environmental factors. Therefore,the entropy off...

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Hydrogen bonds are formed in many compounds e.g., H2O, HF, NH3. The boiling point of such compounds depends to a large extent on the strength of hydrogen bond and the number of hydrogen bonds. The correct decreasing order of the boiling points of the above compounds is : (i) HF > H2O > NH3 (ii) H2O > HF > NH3 (iii) NH3 > HF > H2O (iv) NH3 > H2O > HF

Solution: Option (ii) is the answer.

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In an adiabatic interaction, no exchange of warmth happens among framework and environmental elements. Pick the right choice with the expectation of complimentary extension of an optimal gas under adiabatic condition from the accompanying.

    \[\begin{array}{*{35}{l}}    \left( I \right)\text{ }q\text{ }=\text{ }0,\text{ }T\text{ }\ne \text{ }0,\text{ }w\text{ }=\text{ }0  \\    ~  \\    \left( ii \right)\text{ }q\text{ }\ne \text{ }0,\text{ }T\text{ }=\text{ }0,\text{ }w\text{ }=\text{ }0  \\    ~  \\    \left( iii \right)\text{ }q\text{ }=\text{ }0,\text{ }T\text{ }=\text{ }0,\text{ }w\text{ }=\text{ }0  \\    ~  \\    \left( iv \right)\text{ }q\text{ }=\text{ }0,\text{ }T\text{ }<\text{ }0,\text{ }w\text{ }\ne \text{ }0  \\ \end{array}\]

solution:   Choice (iii) is the appropriate response. With the expectation of complimentary extension w = 0 For adiabatic cycle q = 0 From first law of thermodynamics,  ...

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Which of the accompanying assertions is right? (I) The presence of responding species in a covered measuring utencil is an illustration of an open framework. (ii) There is a trade of energy just as a matter between the framework also, the environmental elements in a shut framework. (iii) The presence of reactants in a shut vessel made down of copper is an illustration of a shut framework. (iv) The presence of reactants in a canteen jar or some other shut protected vessel is an illustration of a shut framework.

solution: Alternative (iii) is the appropriate response. For a shut vessel made down of copper, regardless of can be traded between the framework and the environmental elements however energy trade...

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Form the pair of linear equations for the following problems and find their solution by substitution method.(i) The difference between two numbers is 26 and one number is three times the other. Find them.(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Arrangement (i): Leave the two numbers alone x and y individually, to such an extent that y > x. As indicated by the inquiry, \[y\text{ }=\text{ }3x\text{ }\ldots \text{ }\ldots \text{ }\ldots...

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Choose the correct answer from the given four options in the following questions: AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is (A) 5 (B) 3 (C) √34 (D) 4

Solution: Option (C) √34 is the correct answer. The three vertices are: $A\text{ }=\text{ }\left( 0,\text{ }3 \right)$, $O\text{ }=\text{ }\left( 0,\text{ }0 \right)$ , $B\text{ }=\text{ }\left(...

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For going to a city B from city A, there is a route via city C such that AC⊥CB, AC = 2 x km and CB = 2 (x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.

Solution: According to the given question, AC⊥CB, $AC\text{ }=\text{ }2x\text{ }km$, $CB=2\left( x+7 \right)km$ and $AB=26\text{ }km$ As a result, we get triangle ACB right angled at C. Now, using...

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A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.

Solution: Let 5 m be the length of the ladder AC. Let 4m be the height of the wall on which ladder is placed is BC From right angled triangle EBD, Now using the Pythagoras Theorem,...

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Thermodynamics isn’t worried about______. (I) energy changes associated with a substance response. (ii) the degree to which a substance response continues. (iii) the rate at which a response continues. (iv) the practicality of a synthetic response.

solution: Choice (iii) is the appropriate response. This is because Thermodynamics informs us concerning the practicality, energy changes and degree of compound response. It doesn't informs us...

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The monthly income of 100 families are given as below : Income (in Rs) Number of families 0-5000 8 5000-10000 26 10000-15000 41 15000-20000 16 20000-25000 3 25000-30000 3 30000-35000 2 35000-40000 1 Calculate the modal income.

  As per the information given, The most elevated recurrence = 41, 41 lies in the stretch 10000 – 15000. Here, l = 10000, fm = 41,f1 = 26,f2 = 16 and h = 5000 \[=\text{ }10000\text{ }+\text{...

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The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follows: Speed (km/h) 85-100 100-115 115-130 130-145 Number of players 11 9 8 5 Calculate the median bowling speed.

First we develop the combined recurrence table Speed ( in km/h)               Number of players           Cumulative recurrence 85 – 100              11           11 100 – 115           ...

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Weekly income of 600 families is tabulated below : Weekly income Number of families (in Rs) 0-1000 250 1000-2000 190 2000-3000 100 3000-4000 40 4000-5000 15 5000-6000 5 Total 600 Compute the median income.

Week by week Income   Number of families (fi)   Cumulative recurrence (cf) 0-1000  250        250 1000-2000           190        250 + 190 = 400 2000-3000           100        440 + 100 = 540...

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Given below is a cumulative frequency distribution showing the marks secured by 50 students of a class: Marks Below 20 Below 40 Below 60 Below 80 Below 100 Number of students 17 22 29 37 50 Form the frequency distribution table for the data.

The recurrence circulation table for given information. Marks    Number of understudies 0 – 20    12 20 – 40  22 – 17 = 5 40 – 60  29 – 22 = 7 60 – 80  37 – 29 = 8 80 – 100              50 – 37 =...

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The following are the ages of 300 patients getting medical treatment in a hospital on a particular day: Age (in years) 10-20 20-30 30-40 40-50 50-60 60-70 Number of patients 60 42 55 70 53 20 Form: ALess than type cumulative frequency distribution. More than type cumulative frequency distribution

  (I) Less than type Age (in year)       Number of patients Under 10             0 Under 20             60 + 0 = 60 Under 30             60 + 42 = 102 Under 40             102 + 55 = 157 Under...

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Find the unknown entries a, b, c, d, e, f in the following distribution of heights of students in a class: Height Frequency Cumulative frequency (in cm) 150-155 12 a 155-160 b 25 160-165 10 c 165-170 d 43 170-175 e 48 175-180 2 f Total 50

  Tallness (in cm)  Frequency           Cumulative recurrence given       Cumulative recurrence 150 – 155            12           a             12 155 – 160            b            ...

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Form the frequency distribution table from the following data : Marks (out of 90) Number of candidates More than or equal to 80 4 More than or equal to 70 6 More than or equal to 60 11 More than or equal to 50 17 More than or equal to 40 23 More than or equal to 30 27 More than or equal to 20 30 More than or equal to 10 32 More than or equal to 0 34

The recurrence dissemination table for the given information is: Class Interval      Number of understudies 0-10       34 – 32 = 2 10-20     32 – 30 = 2 20-30     30 – 27 = 3 30-40     27 – 23 = 4...

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The following table shows the cumulative frequency distribution of marks of 800 students in an examination: Marks Number of students Below 10 10 Below 20 50 Below 30 130 Below 40 270 Below 50 440 Below 60 570 Below 70 670 Below 80 740 Below 90 780 Below 100 800 Construct a frequency distribution table for the data above.

The recurrence circulation table for the given information is: Class Interval      Number of understudies 0-10       10 10-20     50 – 10 = 40 20-30     130 – 50 = 80 30-40     270 – 130 = 140...

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The following is the distribution of weights (in kg) of 40 persons : Weight (in kg) 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 Number of persons 4 4 13 5 6 5 2 1 Construct a cumulative frequency distribution (of the less than type) table for the data above.

Weight (in kg)    Cumulative recurrence Under 45             4 Under 50             4 + 4 = 8 Under 55             8 + 13 = 21 Under 60             21 + 5 = 26 Under 65             26 + 6 = 32 Under...

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The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below : Mileage (km/l) 10-12 12-14 14-16 16-18 Number of cars 7 12 18 13 Find the mean mileage. The manufacturer claimed that the mileage of the model was 16 km/litre. Do you agree with this claim?

Mileage (km L-1)              Class – Marks (xi)             Number of vehicles (fi)   fixi 10 – 12  11           7             77 12 – 14  13           12           156 14 – 16  15          ...

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The weights (in kg) of 50 wrestlers are recorded in the following table : Weight (in kg) 100-110 110-120 120-130 130-140 140-150 Number of wrestlers 4 14 21 8 3 Find the mean weight of the wrestlers.

Weight (in kg)    Number of Wrestlers (fi)               Class Marks (xi)  Deviation (di = xi – a) fidi 100 – 110            4             105        –20        –80 110 – 120            14          ...

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An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table : Number of seats 100-104 104-108 108-112 112-116 116-120 Frequency 15 20 32 18 15 Determine the mean number of seats occupied over the flights.

  Class Interval      Class Marks (xi)  Frequency (fi)     Deviation (di = xi – a)      fidi 100 – 104            102        15           –8           –120 104 – 108            106       ...

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The daily income of a sample of 50 employees are tabulated as follows : Income (in Rs) 1-200 201-400 401-600 601-800 Number of employees 14 15 14 7 Find the mean daily income of employees.

C.I          xi            di = (xi – a)          Fi            fidi 1 – 200  100.5     –200      14           –2800 201 – 400            300.5     0             15           0 401 – 600           ...

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The following tabe gives the number of pages written by Sarika for completing her own book for 30 days : Number of pages written per day 16-18 19-21 22-24 25-27 28-30 Number of days 1 3 4 9 13 Find the mean number of pages written per day.

Class Marks         Mid – Value (xi) Number of days (fi)         fixi 15.5 – 18.5          17           1             17 18.5 – 21.5          20           3             60 21.5 – 24.5         ...

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In calculating the mean of grouped data, grouped in classes of equal width, we may use the formula where a is the assumed mean. a must be one of the mid-points of the classes. Is the last statement correct? Justify your answer.

No, the assertion isn't right. It isn't required that expected mean ought to be the mid – mark of the class span. a can be considered as any worth which is not difficult to work on it.

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Apoorv throws two dice once and computes the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36? Why?

Apoorv toss two dice on the double. Thus, the all out number of results = 36 Number of results for getting item 36 = 1(6×6) ∴ Probability for Apoorv = 1/36 Peehu tosses one kick the bucket, Thus,...

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Consider the following distribution : Marks obtained Number of students More than or equal to 0 63 More than or equal to 10 58 More than or equal to 20 55 More than or equal to 30 51 More than or equal to 40 48 More than or equal to 50 42 The frequency of the class 30-40 is (A) 3 (B) 4 (C) 48 (D) 51

(A) 3 Clarification: Imprints Obtained            Number of students        Cumulative Frequency 0-10       (63 – 58) = 5       5   10-20     (58 – 55) = 3       3   20-30     (55 – 51) =...

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The times, in seconds, taken by 150 athletes to run a 110 m hurdle race are tabulated below Class 13.8-14 14-14.2 14.2-14.4 14.4-14.6 14.6-14.8 14.8-15 Frequency 2 4 5 71 48 20 The number of athletes who completed the race in less than 14.6 seconds is : A11 (B) 71 (C) 82 (D) 130

(C) 82 Clarification: The quantity of competitors who finished the race in under 14.6 second= 2 + 4 + 5 + 71 = 82 Subsequently, choice (C) is right

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Consider the data : Class 65-85 85-105 105-125 125-145 145-165 165-185 185-205 Frequency 4 5 13 20 14 7 4 The difference of the upper limit of the median class and the lower limit of the modal class is A0 (B) 19 (C) 20 (D) 38

(C) 20 Clarification: Class      Frequency           Cumulative Frequency   65-85     4             4   85-105  5             9   105-125               13           22  ...

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For the following distribution: Marks Number of students Below 10 3 Below 20 12 Below 30 27 Belo w 40 57 Below 50 75 Below 60 80 The modal class is (A)10-20 (B) 20-30 (C) 30-40 (D) 50-60

(C) 30-40 Clarification: Marks    Number of students        Cumulative Frequency   Underneath 10  3=3        3   10-20     (12 – 3) = 9         12   20-30     (27 – 12) = 15     27...

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For the following distribution : Class 0-05 5-10 10-15 15-20 20-25 Frequency 10 15 12 20 9 the sum of lower limits of the median class and modal class is (A)15 (B) 25 (C) 30 (D) 35

(B) 25 Clarification: Class      Frequency           Cumulative Frequency   0-5         10           10   5-10       15           25   10-15     12           37   15-20    ...

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While computing mean of grouped data, we assume that the frequencies are (A) Evenly distributed over all the classes (B) Centred at the class marks of the classes (C) Centred at the upper limits of the classes (D) Centred at the lower limits of the classes

(B) Centered at the class characteristics of the classes Clarification: In figuring the mean of assembled information, the frequencies are focused at the class signs of the classes. Subsequently,...

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Choose the correct answer from the given four options: 1. In the formula For finding the mean of grouped data di’s are deviations from a of (A) Lower limits of the classes (B) Upper limits of the classes (C) Mid points of the classes (D) Frequencies of the class marks

(C) Mid marks of the classes Clarification: We know, \[di\text{ }=\text{ }xi\text{ }\text{ }a\] Where, xi are information and 'a' is the expected to be mean In this way, di are the deviations from...

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A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at Rs 0.05 per dm2.

The state of pencil = chamber. Let the sweep of base = r cm Outline of base = 1.5 cm Boundary of circle is 2πr = 1.5 cm r = 1.5/2π cm As per the inquiry, Tallness, h = 25 cm We realize that, Bended...

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The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used up on writing 3300 words on an average. How many words can be written in a bottle of ink containing one fifth of a litre?

Allow us first to work out the volume of barrel of pen that is of round and hollow shape Think about barrel, Since 1cm = 10 mm Base width = 5 mm = 0.5 cm Base span, r = 0.25 cm Stature, h = 7 cm We...

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How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm. If one cubic cm of iron weighs 7.5 g, find the weight of the box.

Let the length (l), breath (b), and stature (h) be the outside element of an open box and thickness be x. The volume of metal utilized in box = Volume of outer box – Volume of inner box Think about...

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A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8cm. The height of the cone is (A) 12cm (B) 14cm (C) 15cm (D) 18cm

(B) 14cm Volume of circular shell = Volume of cone recast by liquefying For Spherical Shell, Inside measurement, d1 = 4 cm Inside range, r1 = 2 cm [ as range = 1/2 diameter] Outer measurement, d2 =...

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A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 1/8 space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is (A) 142296 (B) 142396 (C) 142496 (D) 142596

(A) 142296   As indicated by the inquiry,   Volume of block =223=10648cm3   Volume of block that stays unfilled \[=1/8\times 10648=1331cm3\]   volume involved by circular marbles...

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A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called (A) a frustum of a cone (B) cone (C) cylinder (D) sphere

(A) a frustum of a cone At the point when a cone is isolated into two sections by a plane through any point on its pivot corresponding to its base, the upper and lower parts got are cone and a...

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Choose the correct answer from the given four options: A cylindrical pencil sharpened at one edge is the combination of (A) a cone and a cylinder (B) frustum of a cone and a cylinder (C) a hemisphere and a cylinder (D) two cylinders.

(A) a cone and a cylinder The Nib of a sharpened pencil = conical shape The rest of the part of a sharpened pencil = cylindrical Therefore, a pencil is a combination of cylinder and a cone.

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In figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°. Then, ∠PBA is equal to (a) 50° (b) 30° (c) 60° (d) 100°

Solution: (d) 100° Explanation: From triangles APB and CPD, $\angle APB\text{ }=~\angle CPD\text{ }=\text{ }50{}^\circ $ (as they are vertically opposite angles) $AP/PD\text{ }=\text{ }6/5$ … (i)...

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From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

As per the inquiry, From an outside point P, two digressions, PA and PB are attracted to a circle with focus O. At a point E on the circle digression is drawn which crosses PA and PB at C and D,...

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A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are α and β, respectively. Prove that the height of the tower is [h tan α/(tan β – tan α)].

Considering that an upward banner staff of stature h is overcomed on an upward pinnacle of tallness H(say), with the end goal that FP = h and FO = H. The point of height of the base and top of the...

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A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are α and β, respectively. Prove that the height of the tower is [h tan α/(tan β – tan α)].

Considering that an upward banner staff of stature h is overcomed on an upward pinnacle of tallness H(say), with the end goal that FP = h and FO = H. The point of height of the base and top of the...

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