IIT JEE Practice Question and Answer

Q: India is a Tropical country but has a Monsoonal climate because 2494 1

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    Its real extent is vast
    Correct
    Wrong
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    It is surrounded by the sea
    Correct
    Wrong
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    The Himalayas provide the barrier effect
    Correct
    Wrong
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    Land and sea breeze create monsoons
    Correct
    Wrong
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Answer : 3. "The Himalayas provide the barrier effect"
Explanation :

Answer: C) The Himalayas provide the barrier effect Explanation: The whole of India, south of the Himalayas can be climatically treated as a tropical country as the Himalayas provide the barrier effect.    Indian subcontinent is separated from the rest of Asia by the lofty Himalayan ranges which block the cold air masses moving southwards from Central Asia.     As a result, during winters, the northern half of India is warmer by 3°C to 8°C than other areas located on same latitudes.    During summer, due to over the head position of the sun, the climate in the southern parts resemble equatorial dry climate.   The seasonal reversal of winds in Arabian Sea and Bay of Bengal give India a typical tropical monsoon climate.   So Indian climate, to be precise, is Tropical monsoon type (a distinct wet and dry climate) rather than just a tropical or half temperate climate.

Q: C U B A E D E D A B E B A U C D B C A D B D U B C A C B E D A    If all the A's are dropped from the above arrangement, which of the following will be eleventh from the left end of the above arrangement? 2579 0

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    E
    Correct
    Wrong
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    C
    Correct
    Wrong
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    D
    Correct
    Wrong
  • 4
    U
    Correct
    Wrong
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Answer : 4. "U"
Explanation :

Answer: D) U Explanation: If all the A's are dropped from the above arrangement, we get   C U B E D E D B E B U C D B C D B D U B C C B E D.    Here the eleventh from the left end of the above arrangement is U

Q: 5 men and 4 women are to be seated in a row so that the women occupy the even places . How many such arrangements are possible? 1728 1

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    2880
    Correct
    Wrong
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    1440
    Correct
    Wrong
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    720
    Correct
    Wrong
  • 4
    2020
    Correct
    Wrong
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Answer : 1. "2880"
Explanation :

Answer: A) 2880 Explanation: There are total 9 places out of which 4 are even and rest 5 places are odd.   4 women can be arranged at 4 even places in 4! ways.   and 5 men can be placed in remaining 5 places in 5! ways.   Hence, the required number of permutations  = 4! x 5! = 24 x 120 = 2880

Q: How many 7 digit numbers can be formed using the digits 1, 2, 0, 2, 4, 2, 4? 2775 0

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    120
    Correct
    Wrong
  • 2
    360
    Correct
    Wrong
  • 3
    240
    Correct
    Wrong
  • 4
    424
    Correct
    Wrong
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Answer : 2. "360"
Explanation :

Answer: B) 360 Explanation: There are 7 digits 1, 2, 0, 2, 4, 2, 4 in which 2 occurs 3 times, 4 occurs 2 times.    Number of 7 digit numbers = 7!3!×2! = 420   But out of these 420 numbers, there are some numbers which begin with '0' and they are not 7-digit numbers. The number of such numbers beginning with '0'.   =6!3!×2! = 60   Hence the required number of 7 digits numbers = 420 - 60 = 360

Q: A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady? 1483 0

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    123
    Correct
    Wrong
  • 2
    113
    Correct
    Wrong
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    246
    Correct
    Wrong
  • 4
    945
    Correct
    Wrong
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Answer : 3. "246"
Explanation :

Answer: C) 246 Explanation: A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking.    (i) 1 lady out of 4 and 4 gentlemen out of 6  (ii) 2 ladies out of 4 and 3 gentlemen out of 6  (iii) 3 ladies out of 4 and 2 gentlemen out of 6  (iv) 4 ladies out of 4 and 1 gentlemen out of 6    In case I the number of ways = C14×C46 = 4 x 15 = 60  In case II the number of ways = C24×C36 = 6 x 20 = 120  In case III the number of ways = C34×C26 = 4 x 15 = 60 In case IV the number of ways = C44×C16 = 1 x 6 = 6    Hence, the required number of ways = 60 + 120 + 60 + 6 = 246

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Answer : 2. "2 x (18!)"
Explanation :

Answer: B) 2 x (18!) Explanation: A person can be chosen out of 18 people in 18 ways to be seated between Musharraf and Manmohan. Now consider Musharraf, Manmohan, and the third person, sitting between them, as a single personality, we can arrange them in 17! ways but Musharraf and Manmohan can also be arranged in 2 ways.    Required number of permutations = 18 x (17!) x 2 = 2 x 18!

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Answer : 2. "535"
Explanation :

Answer: B) 535 Explanation: The number of points of intersection of 37 lines is C237. But 13 straight lines out of the given 37 straight lines pass through the same point A.   Therefore instead of getting C213 points, we get only one point A. Similarly 11 straight lines out of the given 37 straight lines intersect at point B. Therefore instead of getting C211 points, we get only one point B.    Hence the number of intersection points of the lines is C237-C213-C211 +2 = 535

Q: A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved? 1345 0

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    1/4
    Correct
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    1/2
    Correct
    Wrong
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    3/4
    Correct
    Wrong
  • 4
    7/12
    Correct
    Wrong
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Answer : 3. "3/4"
Explanation :

Answer: C) 3/4 Explanation: Let A, B, C be the respective events of solving the problem and A , B, C be the respective events of not solving the problem. Then A, B, C are independent event ∴A, B, C are independent events Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4  PA=12, PB=23, PC= 34 ∴ P( none  solves the problem) = P(not A) and (not B) and (not C)                     = PA∩B∩C                    = PAPBPC         ∵ A, B, C are Independent                                          =  12×23×34                     = 14   Hence, P(the problem will be solved) = 1 - P(none solves the problem)                  = 1-14= 3/4

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