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JEE Main Test 29
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JEE Main Test 29

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  • Question 1/12
    4 / -1

    One mole of ideal monoatomic gas (γ = 5/3) is mixed with one mole of diatomic gas (γ = 7/5). What is γ for the mixture? γ denotes the ratio of specific heat at constant pressure, to that at constant volume.

    Solutions

    Q = Q1 + Q2 

  • Question 2/12
    4 / -1

    The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2 s. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be

    Solutions

    As T is 2 seconds, hence the new time period will be 2/3 seconds.

  • Question 3/12
    4 / -1

    The maximum tension in the string of an oscillating pendulum is thrice the minimum tension. What is its angular amplitude

    Solutions

    The maximum tension will be at the mean position and minimum tension will be at extreme positions .

  • Question 4/12
    4 / -1

    A wire elongates by  mm when a load W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm

    Solutions

    The elongation will be l/2 on both the sides of the pulley and hence the total elongation in the wire will be l

  • Question 5/12
    4 / -1

    Four species are listed below: 

    Which one of the following is the correct sequence of their acid strength?

    Solutions

    Stability of conjugate bases can be used to determine the acidic strength of the species. 1 and 3 are already first conjugated bases of a dibasic acid. Out of 2 and 4, the conjugate base of 4 is stabilised by resonance. Hence the order is 
    i < iii < ii < iv

  • Question 6/12
    4 / -1

    In order to refine blister copper it is melted in a furnace and is stirred with green logs of wood. The purpose is

    Solutions

    The blister copper is melted in reverberatory furnace and stirred with poles of green wood. Any oxide of copper formed is reduced to metallic copper by the reducing hydrocarbons of the wood. The process is called fire refining or poling. 
    Hence, option D is correct.

  • Question 7/12
    4 / -1

    In context with the industrial preparation of hydrogen from water gas (CO + H2), which of the following is the correct statement?

    Solutions

    CO is oxidized to CO2 with steam in the presence of a catalyst followed by absorption of CO2 in alkali.

  • Question 8/12
    4 / -1

    The reaction of toluene with chlorine in the presence of FeCl3gives mainly-

    Solutions

    The correct products are o- and p- chlorotoluene. Hence, option B is correct.

  • Question 9/12
    4 / -1

    The statement p → (q → p) is equivalent to

    Solutions

    (q → p) = (p V q)
    Hence, D is the correct answer.

  • Question 10/12
    4 / -1

    How many real solutions does the equation x7 + 14x5 + 16x3 + 30x – 560 = 0 have?

    Solutions

    f(x) = x7 + 14x5 + 16x3 + 30x - 560 
    f′(x) = 7x6 + 70x4 + 48x2 + 30 > 0. Since f(x) is odd degree polynomial and is increasing. 
    ⇒ f(x) has exactly one solution.

  • Question 11/12
    4 / -1

    Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

    Solutions

    As adjA is the transpose of the matrix of cofactors of elements of A. it will have integral entries.

  • Question 12/12
    4 / -1

    Directions: Assertion–Reason type questions. Each of these questions contains two statements: statement–1 (Assertion) and Statement–2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

    In a shop there are five types of ice–creams available. A child buys six ice–creams. 
    Statement–1: 
    The number of different ways the child can buy the is ice–creams is 10C5. 
    Statement–2: 
    The number of different ways the child can buy the six ice–creams is equal to the number of different ways of arranging 6 A's and 4B's in a row.

    Solutions

    No. of different ways the child can buy six ice–creams is equal to no. of non–negative integral solution of the equation
    x1 + x2 +x3 + x4 + x5 = 6 
    which is equal to 6+5–1C4 = 10C4 
    ∴ Statement 1 is false. 

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