IIT JEE Practice Question and Answer

Q: If x = 2 + 223 + 213 then find the value of x3-6x2+6x ? 1070 0

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    1
    Correct
    Wrong
  • 2
    2
    Correct
    Wrong
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    3
    Correct
    Wrong
  • 4
    4
    Correct
    Wrong
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Answer : 2. "2"
Explanation :

Answer: B) 2 Explanation: Given that x = 2+ 223 + 213   So x - 2 = 223 + 213   Now cubing on both sides, we get     => x3-8-6x2+12x = 4 + 2 + 6(x-2)   Therefore, x3-6x2+6x = -6 + 8 = 2

Q: A goods truck travels from a place at a certain time and at fixed speed. After 6hrs another truck leaves the same place and move in same direction of uniform speed of 90kmph. The truck catches up the goods truck in 4hrs. Find the speed of the goods truck ? 1127 0

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    36 kmph
    Correct
    Wrong
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    32 kmph
    Correct
    Wrong
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    28 kmph
    Correct
    Wrong
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    34 kmph
    Correct
    Wrong
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Answer : 1. "36 kmph"
Explanation :

Answer: A) 36 kmph Explanation: Let the speed of goods truck be 'p' kmphDistance covered by goods truck in 10hrs (4+6) = Distance covered by other truck in 4 hrs. 10p = 4 x 90p = 36kmph.Therefore, the speed of the goods truck is p = 36 kmph.

Q: Choose Odd one out of the options ? 8385 0

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    PSRQ
    Correct
    Wrong
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    SVUT
    Correct
    Wrong
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    MNPO
    Correct
    Wrong
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    KNML
    Correct
    Wrong
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Answer : 3. "MNPO"
Explanation :

Answer: C) MNPO Explanation: PSRQ --> {16, 19, 18, 17} - next 3 alphabets of "P" is written in reverse orderSVUT --> {19, 22, 21, 20} - next 3 alphabets of "S" is written in reverse order MNPO --> {13, 14, 16, 15} KNML --> {11, 14, 13, 12} - next 3 alphabets of "K" is written in reverse order Except "MNPO", others are not in consecutive order.

Q: In a party there are male and female members. If 15 female quit then the number of females will become double the number of males. If 45 males quit no. of female becomes five times the number of males. Find the number of females ? 1608 0

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    175
    Correct
    Wrong
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    145
    Correct
    Wrong
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    165
    Correct
    Wrong
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    135
    Correct
    Wrong
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Answer : 1. "175"
Explanation :

Answer: A) 175 Explanation: Let the number of males be 'M'Let the number of females be 'F'From the given conditions,(F-15)=2M.....(i)F=5(M-45).....(ii)By solving the equations (1) & (2) we get M = 80 Then substitute M = 80 in (1)F = 2M + 15F = 2 x 80 + 15=> F = 175Therefore, number of males = 80 and females = 175 in the party.

Q: Dot cabs company provides cabs for software employees. The company has 8 Swift dzires, 6 Scorpios, 7 Innovas and few small cars. If Swift dzire makes one fourth of the total fleet, how many small cars are there in the company ? 1857 0

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    9
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    10
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    11
    Correct
    Wrong
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    12
    Correct
    Wrong
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Answer : 3. "11"
Explanation :

Answer: C) 11 Explanation: Given the company has 8 SD + 6 SRP + 7 IN = 21 cars + 'x' small cars.Given SD makes 1/4 th of the total fleet.=> 8 = 1/4 (21 + x)=> 32 = 21 + x=> x = 11 Therefore, the company has 11 small cars.

Q: K is 50% faster than L. If L starts at 9 A.M. and K starts at 10 A.M. L travels at a speed of 50 km/hr. If L and K are 300 kms apart, The time when they meet when they travel in opposite direction is ? 1921 0

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    12 pm
    Correct
    Wrong
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    1 pm
    Correct
    Wrong
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    11 am
    Correct
    Wrong
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    11:30 am
    Correct
    Wrong
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Answer : 1. "12 pm"
Explanation :

Answer: A) 12 pm Explanation: let 't' be the time after which they met since L starts. Given K is 50% faster than L 50 t + 1.5*50(t-1) = 300 50 t +75 t = 300 + 75 t = 375 / 125 = 3 hrs past the time that L starts So they meet at (9 + 3)hrs = 12:00 noon.

Q: How many zeros are there from 1 to 10000 ? 2198 0

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    2893
    Correct
    Wrong
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    4528
    Correct
    Wrong
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    6587
    Correct
    Wrong
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    4875
    Correct
    Wrong
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Answer : 1. "2893"
Explanation :

Answer: A) 2893 Explanation: For solving this problem first we would break the whole range in 5 sections 1) From 1 to 9Total number of zero in this range = 0 2) From 10 to 99Total possibilities = 9*1 = 9 ( here 9 is used for the possibilities of a non zero integer) 3) From 100 to 999 - three type of numbers are there in this range a) x00 b) x0x c) xx0 (here x represents a non zero number)Total possibilities for x00 = 9*1*1 = 9, hence total zeros = 9*2 = 18for x0x = 9*1*9 = 81, hence total zeros = 81similarly for xx0 = 81 total zeros in three digit numbers = 18 + 81 +81 = 180 4) From 1000 to 9999 - seven type of numbers are there in this rangea)x000 b)xx00 c)x0x0 d)x00x e)xxx0 f)xx0x g)x0xxTotal possibilities for x000 = 9*1*1*1 = 9, hence total zeros = 9*3 = 27 for xx00 = 9*9*1*1 = 81, hence total zeros = 81*2 = 162 for x0x0 = 9*1*9*1 = 81, hence total zeros = 81*2 = 162for x00x = 9*1*1*9 = 81, hence total zeros = 81*2 = 162 for xxx0 = 9*9*9*1 = 729, hence total zeros = 729*1 = 729for xx0x = 9*9*1*9 = 729, hence total zeros = 729*1 = 729for x0xx = 9*1*9*9 = 729, hence total zeros = 729*1 = 729total zeros in four digit numbers = 27 + 3*162 + 3*729 = 2700thus total zeros will be 0+9+180+2700+4 (last 4 is for 4 zeros of 10000)= 2893

Q: There are 600 Kabaddi players 4% wear knee band on one leg. Of the remaining, 25% wear knee bands on both legs. How many players don't wear a knee band ? 1783 0

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    426
    Correct
    Wrong
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    428
    Correct
    Wrong
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    415
    Correct
    Wrong
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    432
    Correct
    Wrong
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Answer : 4. "432"
Explanation :

Answer: D) 432 Explanation: There are 600 Kabaddi players4% wear knee band on one legRemaining players = 600 x 0.96 = 576Of the remaining, 25% wear knee bands on both leg and Of the remaining, 75% do not wear knee bands .So players not wearing knee bands = 0.75 x 576 = 576 x 3/4 = 144 x 3 = 432.

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