1
MCQ (Single Correct Answer)

JEE Main 2018 (Online) 15th April Evening Slot

The coefficien of x10 in the expansion of (1 + x)2(1 + x2)3(1 + x3)4 is equal to :
A
52
B
56
C
50
D
44

Explanation

$$ \because $$$$\,\,\,$$ (1 + x)2 = 1 + 2x + x2,

(1 + x2)3 = 1 + 3x2 + 3x4 + x6

and (1 + x3)4 = 1 + 4x3 + 6x6 + 4x9 + x12

So, the possible combination for x10 are :

x . x9,   x . x6.  x3,  x2 . x2 . x6 , x4 . x6

Corresponding coefficients are 2 $$ \times $$ 4, 2$$ \times $$ 1 $$ \times $$4, 1 $$ \times $$3$$ \times $$ 6,

3 $$ \times $$ 6   or   8, 8, 18, 18.

$$\therefore\,\,\,$$ Sum of the coefficient is 8 + 8 + 18 + 18 = 52

Therefore, the coefficient of x10 in the expansion of

(1 + x)2 (1 + x2)3 (1 + x3)4 is 52.
2
MCQ (Single Correct Answer)

JEE Main 2018 (Online) 16th April Morning Slot

The coefficient of x2 in the expansion of the product
(2$$-$$x2) .((1 + 2x + 3x2)6 + (1 $$-$$ 4x2)6) is :
A
107
B
106
C
108
D
155

Explanation

Given,

(2 $$-$$ x2) . (1 + 2x + 3x2) 6 + (1 $$-$$ 4x2)6)

Let, a = ((1 + 2x + 3x2)6 + (1 $$-$$ 4x2)6)

$$\therefore\,\,\,\,$$ Given statement becomes,

(2 $$-$$ x2) . (a)

=    2a $$-$$ x2 (a)

Here coefficients of x2 is

=    2 (coefficient of x2 in a ) $$-$$ 1 (constant in a)

(1 + 2x + 3x2) 6  =   6C0 + 6C1 (2x + 3x2) + 6C2 (2x + 3x2)2

      + . . . . . .+ (2x + 3x2)6

(1 $$-$$ 4x2)6 = 6C0 $$-$$ 6C1 (4x2) + 6C2 (4x2)2

      + . . . . .+ (4x2)6

Coefficient of x2 in (1 + 2x + 3x2)6

= 6C1 $$ \times $$ 3 + 6C2 $$ \times $$ 4

= 18 + 60

Coefficient of x2 in (1 $$-$$ 4x2)6

= $$-$$ 6C1 $$ \times $$ 4

= $$-$$ 24

Coefficient of x2 in ((1 + 2x + 3x2)6 + (1 $$-$$ 4x2)6)

= 60 + 18 $$-$$ 24

= 54

Constant term in (1 + 2x + 3x2)6 = 6C0 = 1

Constant term in (1 $$-$$ 4x)6 = 6C0 = 1

$$\therefore\,\,\,\,$$ Constant term in ((1 + 2x + 3x2)6 + (1 $$-$$ 4x)6)

= 1 + 1 = 2

$$\therefore\,\,\,\,$$ Coefficient of x2 in (2 $$-$$ x2) ((1 + 2x + 3x2)6 + (1 $$-$$ 4x2)6)

= 2 (54) $$-$$ 1 (2)

= 108 $$-$$ 2

= 106
3
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 9th January Morning Slot

If the fractional part of the number $$\left\{ {{{{2^{403}}} \over {15}}} \right\} is \, {k \over {15}}$$, then k is equal to :
A
8
B
14
C
6
D
1

Explanation

$${{{2^{403}}} \over {15}}$$

$$ = {{{2^3}\, \cdot \,{2^{400}}} \over {15}}$$

$$ = {8 \over {15}}{\left( {16} \right)^{100}}$$

$$ = {8 \over {15}}{\left( {15 + 1} \right)^{100}}$$

$$ = {8 \over {15}}\left( {{}^{100}{C_0} + {}^{100}{C_1}\,15 + {}^{100}{C_2}{{\left( {15} \right)}^2} + .....{{\left( {15} \right)}^{100}}} \right)$$

$$ = {8 \over {15}} + 8\left( {{}^{100}{C_1} + {}^{100}{C_2}\,\left( {15} \right) + ..... + {{\left( {15} \right)}^{99}}} \right)$$

$$ = {8 \over {15}} + 8$$ (integer)

$$ \therefore $$  Fractional part $$ = {8 \over {15}}$$

According to the question,

$${k \over {15}} = {8 \over {15}}$$

$$ \Rightarrow $$   K $$=$$ 8
4
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 9th January Evening Slot

The coefficient of t4 in the expansion of $${\left( {{{1 - {t^6}} \over {1 - t}}} \right)^3}$$ is :
A
14
B
15
C
10
D
12

Explanation

$${\left( {{{1 - {t^6}} \over {1 - t}}} \right)^3}$$

= (1 $$-$$ t6)3 (1 $$-$$ t)$$-$$3

= (1 $$-$$ 3C1t6 + 3C2t12 $$-$$ 3C3t18) $$ \times $$ (1 $$-$$ t)$$-$$3

coefficient of t4 is 1 $$ \times $$ coefficient of t4 in (1 $$-$$ t)$$-$$3

= 1 $$ \times $$ 3+4$$-$$1C4 (By multinomial theorem)

= 6C4 = 15

Questions Asked from Mathematical Induction and Binomial Theorem

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Name Indicates No of Questions
AIEEE 2002 (5)
keyboard_arrow_right
AIEEE 2003 (2)
keyboard_arrow_right
AIEEE 2004 (4)
keyboard_arrow_right
AIEEE 2005 (5)
keyboard_arrow_right
AIEEE 2006 (2)
keyboard_arrow_right
AIEEE 2007 (2)
keyboard_arrow_right
AIEEE 2008 (1)
keyboard_arrow_right
AIEEE 2009 (1)
keyboard_arrow_right
AIEEE 2010 (1)
keyboard_arrow_right
AIEEE 2011 (1)
keyboard_arrow_right
AIEEE 2012 (1)
keyboard_arrow_right
JEE Main 2013 (Offline) (1)
keyboard_arrow_right
JEE Main 2014 (Offline) (1)
keyboard_arrow_right
JEE Main 2015 (Offline) (1)
keyboard_arrow_right
JEE Main 2016 (Offline) (1)
keyboard_arrow_right
JEE Main 2016 (Online) 10th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2017 (Offline) (1)
keyboard_arrow_right
JEE Main 2017 (Online) 8th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2017 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2018 (Offline) (1)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2018 (Online) 16th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Evening Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th April Evening Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 7th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 7th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 8th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 9th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 2nd September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 4th September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 4th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 6th September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 6th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 24th February Morning Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 24th February Evening Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 26th February Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 16th March Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 17th March Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 17th March Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 18th March Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th July Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th July Evening Shift (3)
keyboard_arrow_right
JEE Main 2021 (Online) 27th July Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 26th August Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th August Morning Shift (1)
keyboard_arrow_right

EXAM MAP

Joint Entrance Examination

JEE Advanced JEE Main

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE ME GATE PI GATE EE GATE CE GATE IN

Medical

NEET