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Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced


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9 Questions MCQ Test Maths 35 Years JEE Main & Advanced Past year Papers | Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced

Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced for JEE 2022 is part of Maths 35 Years JEE Main & Advanced Past year Papers preparation. The Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced questions and answers have been prepared according to the JEE exam syllabus.The Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced below.
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*Multiple options can be correct
Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 1

If the first and the (2n – 1)st terms of an A.P., a G.P. and an H.P. are equal and their n-th terms are a, b and c respectively, th en (1988 - 2 Marks)

Detailed Solution for Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 1

 Let x be the first term and y the (2n–1)th terms of AP, GP and HP whose nth terms are a, b, c  respectively.
For AP, y = x + (2n – 2) d

  ....(1)

For  G.P. 

....(2)

For H.P.

....(3)
Thus from (1), (2) and (3), a, b, c are A.M., G.M. and H.M. respectively of x and y

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 2

For 0 < φ < π/2, if          then: (1993 -  2 Marks)

Detailed Solution for Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 2

 We have for 

                  ....(1)

[Using sum of infinite G.P. cos2α being < 1]

....(2)

...(3)

Substituting the values of cos2φ and sin2φ in (3), from (1) and (2), we  get

 

Thus (b) and (c) both are correct.

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 3

Let n be an odd integer. If  for every value of q, then (1998 - 2 Marks)

Detailed Solution for Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 3

Putting  θ = 0, we get b0= 0

 

= b1 + b2 sinθ+ b3 sin 2θ + ...... +bn sin n-1θ

Taking limit as θ → 0, we obtain

Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 4

Let Tr be the rth  term of an A.P., for r = 1, 2, 3, .... If for some positive  integers m, n we have  equals (1998 - 2 Marks)

Detailed Solution for Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 4


*Multiple options can be correct
Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 5

If x > 1, y > 1, z > 1 are in G.P., then      are in (1998 - 2 Marks)

Detailed Solution for Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 5

If   x, y, z are in G.P. (x,  y,  z  > 1); log x, log y, log z will be in A.P.
⇒ 1 + log x, 1 + log y, 1 + log z will also be in A.P.

will be in H.P..

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 6

For a positive integer n, let  . Then (1999 - 3 Marks)

Detailed Solution for Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 6

We have

Thus, a (100) < 100

Also

Thus, a (200) > 

i.e. a (200) > 100.

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 7

A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then (2008)

Detailed Solution for Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 7

We know by geometry   PS × ST = QS × SR ...(1)

∵  S is not the centre of circulm circle,

PS ≠ ST
And we know that for two unequal real numbers.
H.M. < G.M

[using eqn (1)]    ...(2)

∴ (b) is the correct option.

Also 

From equations (2) and (3) we get  

∴ (d) is also the correct option.

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 8

Let     = 1, 2, 3, ............ Then,     (2008)

Detailed Solution for Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 8

We have 

and 

For n = 1 we get

Also  = 0.34 × 1.73 = 0.58

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 9

Let  Then Sn can take value(s)  (JEE Adv. 2013)  

Detailed Solution for Test: MCQs (One or More Correct Option): Sequences and Series | JEE Advanced - Question 9

= 8n2 + 8n2 + 4n = 16n2 + 4n
For n = 8,  16n2 + 4n = 1056
and for n = 9, 16n2 + 4n = 1332

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