MathJax TeX Test Page

# Browsing Archive: April, 2015

## Counting

Posted by vinod on Tuesday, April 14, 2015, In : IIT,WBJEE,AIEEE
MathJax TeX Test Page If the integers $m$ and $n$ are chosen at random from $1$ to $100$, then find the probability that the number of the form $7^n+7^m$ is divisible by $5$. $$.$$ Number of numbers of the form $7^n+7^m$ is 100×100= $100^2$ , since m,n ∈{1 ,…………,100}. Now $7^1=7,7^2=49,7^3=343$ and $7^4=2401$ , the digits at the unit places are 7,9,3 and 1. $$.$$ For n ≥5 the digit at the unit place for the number $7^n$ will be one of among the num...

## Counting

Posted by vinod on Tuesday, April 14, 2015, In : IIT,WBJEE,AIEEE
Evaluate: $\int_{-n}^n max \{x+|x|,x-[x]\} \mathrm{d}x$ where $[x]$ is the floor function  When $x > 0$ we see that $x+|x| = 2x$.  Let $k \leq x < k+1, k = 0,1,2,.........,n-1$ $\Rightarrow [x] = k, therefore, x-[x] = x-k$  $So, x+|x| = 2x > x - k = x-[x] \Rightarrow max \{x+|x|,x-[x]\} = 2x$  $\int_{0}^n max \{x+|x|,x-[x]\} \mathrm{d}x = 2 \int_{0}^n x \mathrm{d}x = x^2|_{0}^{n^2} = n^2 \dots (A)$  When $x < 0$ we see that \(x+|x| = x-...

## JEE MAIN MATHEMATICS SOLVED PAPER 2015

Posted by vinod on Tuesday, April 14, 2015, In : IIT,WBJEE,AIEEE
JEE (MAIN)-2015

MATHEMATICS
Important Instructions:

1.  The test is of 3 hours duration.

2. The Test Booklet consists of 90 questions. The maximum marks are 360.

3. There are three parts in the question paper A, B, C consisting of Mathematics, Physics and

Chemistry having 30 questions in each part of equal weightage. Each question is allotted 4 (four)

marks for each correct response.

4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct res...

## ISC Mathematics Question Paper Solved 2015

Posted by vinod on Tuesday, April 14, 2015, In : IIT,WBJEE,AIEEE

Get the solved ISC Mathematics Question paper for the year 2015. The solutions are short need not to be considered as the way of answering in board exams. Click Below
ISC MATHS PAPER 2015

## Bayes' Theorem: Solved Problems

Posted by vinod on Tuesday, April 14, 2015, In : IIT,WBJEE,AIEEE
Solved Problems on Bayes' Theorem. NCERT Solutions

Question 1.

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

Question 2.

Of the students in a college, it is known that 60% reside in hostel and 40% are

day scholars (not residing in hostel). Previous year results report that 30% ...