JEE-Main - Grade 12 - Mathematics - Probability - Introduction and Snapshot of Probability - Study ref# 935

Introduction
In earlier Classes, we have studied the
probability as a measure of uncertainty of events in a random experiment. We discussed
the axiomatic approach formulated by Russian Mathematician, A.N. Kolmogorov
(1903 - 1987) and trea... read more

JEE-Main - Grade 12 - Mathematics - Probability - Introduction and Snapshot of Probability - Study ref# 936

Following sections must be covered to
understand the Probability:
1. Conditional Probability.
2. Multiplication Theorem on Probability.
3. Independent Events
4. Bayes’ Theorem
5. Random Variables and its Probability
Distributi... read more

JEE-Main - Grade 11 - Mathematics - Binomial Theorem - Importance and Snapshot of Binomial Theorem - Study ref# 623

Introduction:
We have learnt how to find the squares and cubes of
binomial like and
.
Using them, we could evaluate the numerical values of numbers like ,etc.
However, for higher powers like etc.,
the calculations become dif... read more

JEE-Main - Grade 11 - Mathematics - Binomial Theorem - Importance and Snapshot of Binomial Theorem - Study ref# 624

Following sections must be covered to understand the
Binomial Theorem:
1. Binomial Theorem for Positive Integral Indices.
2. General and Middle Terms... read more

JEE-Main - Grade 11 - Mathematics - Binomial Theorem - Target Setup for Binomial Theorem - Study ref# 625

Student requires to achieve the following milestones to get better grip over Binomial Theorem. The milestones / targets are as follows:-Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test000%Chapter Test000%Sub... read more

Using binomial theorem, indicate which number is larger
(1.1)10000 or 1000? Answer: (1.1)10000=(1+0.1)10000
…..other
terms
= 1×1+10000×0.1+…..other terms
=1+1000+other terms
=(1001+other terms) >100... read more

Prove that the coefficient of xn in the
expansion of (1+x)2n is twice the coefficient of xn in
the expansion of (1+x)2n-1. Answer: For (1 + x)2n , the general term is
Tr+1=... read more

If a and b are distinct integers, prove that (a-b) is a
factor of an-bn, whenever n is a positive integer. Answer: If we take an = (a-b+b)n
is a factor
of ... read more

Prove that the ratio of the coefficient of in and the term
independent of x in is 1:32. Answer: Coefficient of i.e. will be in 6th term =
The term
independent of x in the 2nd binomial ... read more

Find the coefficient of in and of in and find the
relation between a and b so that these coefficients are equal. Answer: Coefficient of in ... read more

If
Show that n=11 Answer: Let
Or i.e.
,the power of y is 10
For ,E
should contain or the
numerator of E should have the term of
.Hence
n=11... read more

Prove that the coefficient of the term independent of y in
the expansion of
is 210 Answer:
Where
where
The power of y is
Hence the coefficient is
... read more

Show that the coefficient of in
is 0. Answer:
The power of x will be 3r or 3r+1.
If 3r = 50 or 3r+1=50 then both do not give integral
value of r and hence no te... read more

If the sum of the coefficient in the expansion of is 4096, then prove
that the greatest coefficient in the expansion is 924. Answer: Putting x=y=1 the sum of the coefficients is
If will
be the greatest when as
n is even.Hence .... read more

If the 3rd,4th,5th, and 6th
terms in the expansion of be
respectively a, b, c, and d, prove that Answer:
Putting r=3,4,5 in the above, we get
Now dividing (1) by ... read more

Find the coefficient of in the polynomial
Where Answer: We know that factors
The coefficient of taken two at a time
represented by is equal
to Answer: We know that,
... read more

Find the coefficient of x2yz in the expansion
of Answer: If p +q +r = n then the coefficient of in is .
Here 2 +1 +1 = 4
Coefficient of
In general
Such that p +q +r = n and the summation is taken over all non-negative
integer... read more