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JEE Mathematics Solved Question Paper 2016

Multiple Choice Questions

The sum of all real values of x satisfying the equation
$left parenthesis straight x squared minus 5 straight x space plus 5 right parenthesis to the power of straight x squared plus 4 straight x minus 60 space equals space 1 end exponent$ is:

3
-4
6
6

654 Views

2.
If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:

46^th

59^th

52^nd

52^nd

52^nd

Clearly, number of words start with A = 4!/ 2! = 12
Number of words start with L = 4! = 24
A number of words start with M = 4!/2! = 12
Number of words start with SA = 3!/2! = 3
Number of words starts with SL = 3! = 6
Note that, next word will be 'SMALL'
Hence, the position of word 'SMALL' is 58th.

394 Views

If the number of terms in the expansion of $open parentheses 1 minus 2 over straight x space plus 4 over straight x squared close parentheses to the power of straight n comma straight x not equal to 0 comma$ is 28, then the sum of the coefficients of all the terms in this expansion is

64
2187
243
243

392 Views

If the 2^nd, 5^th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

272 Views

If the sum of the first ten terms of the series,

$open parentheses 1 3 over 5 close parentheses squared space plus open parentheses 2 2 over 5 close parentheses squared space plus open parentheses 3 1 fifth close parentheses squared space plus space 4 squared space plus space open parentheses 4 4 over 5 close parentheses squared space plus.....$ is 16/5 m, the m is equal to

347 Views

Let $straight p space equals space limit as straight x rightwards arrow 0 to the power of plus of left parenthesis 1 plus tan squared square root of straight x right parenthesis to the power of 1 divided by 2 straight x end exponent comma space$ then log p is equal to

371 Views

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30^o. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60^o. Then the time taken (in minutes) by him, from B to reach the pillar, is:

182 Views

If
$straight f left parenthesis straight x right parenthesis space plus space 2 straight f open parentheses 1 over straight x close parentheses space equals space 3 straight x comma straight x space not equal to space 0 space and space straight S space equals space open curly brackets straight x space straight epsilon space straight R colon space straight f space left parenthesis straight x right parenthesis space equals space straight f left parenthesis negative straight x right parenthesis close curly brackets semicolon space then space straight S$

is an empty set
contains exactly one element.
contains exactly two elements.
contains exactly two elements.

251 Views

A value of θ for which $fraction numerator 2 space plus space 3 straight i space sin space straight theta over denominator 1 minus 2 straight i space sin space straight theta end fraction$ is purely imaginary is

π/3
π/6
$sin to the power of negative 1 end exponent open parentheses fraction numerator square root of 3 over denominator 4 end fraction close parentheses$
$sin to the power of negative 1 end exponent open parentheses fraction numerator square root of 3 over denominator 4 end fraction close parentheses$

207 Views

10.

If A = $open square brackets table row cell 5 straight a end cell cell negative straight b end cell row 3 2 end table close square brackets$ and A adj A = AA^T, then 5a +b is equal to