Search found 25 matches

by Mahfuz Sobhan
Sat Dec 12, 2015 7:31 pm
Forum: Secondary Level
Topic: Maymensingh divisional 2014 Q.no.- 4
Replies: 1
Views: 767

Re: Maymensingh divisional 2014 Q.no.- 4

first term, a = 7
common difference, d = 8
number of term, n = 100
a + (n - 1)*d = 7 + (100 - 1)*8 = 7 + 99*8 = 7 + 792 = 799
in 800th position, 5 is situated
therefore in 799th position 4 is situated.
ans is 4
by Mahfuz Sobhan
Sat Dec 12, 2015 7:27 pm
Forum: Secondary Level
Topic: Maymensingh divisional 2014 Q.no.- 4
Replies: 1
Views: 767

Maymensingh divisional 2014 Q.no.- 4

In the given diagram a square is marked with circle. Which number will be inside the square 100th position upper than this one?
by Mahfuz Sobhan
Sat Dec 12, 2015 6:58 pm
Forum: Secondary Level
Topic: coxbazar divisional 2014 Q.no.-5
Replies: 0
Views: 654

coxbazar divisional 2014 Q.no.-5

The first number in an arithmetic progression is 23 and the last number is 52. Difference between successive terms is rational. The progression contains no more than 291 terms. How many such sequences can be formed?
by Mahfuz Sobhan
Sat Dec 12, 2015 6:31 pm
Forum: Secondary Level
Topic: coxbazar divisional 2014 Q.no.-2
Replies: 2
Views: 851

coxbazar divisional 2014 Q.no.-2

Hasib went to the kite festival with five friends and bought 12 kites. They were all of different colors. He and his friend Tahmid took 2 kites and told the others to pick any one among other kites. In how many ways can they do it?
by Mahfuz Sobhan
Sat Dec 12, 2015 6:27 pm
Forum: Secondary Level
Topic: coxbazar divisional 2014 Q.no.-1
Replies: 1
Views: 830

coxbazar divisional 2014 Q.no.-1

Avik runs twice as fast as Tusher. Kamrul runs 4 times slower than Tusher. They started running together. After some time if the distance between Kamrul and Avik is 105 meters than find the total of the distances they covered individually.
by Mahfuz Sobhan
Sun Nov 22, 2015 7:10 pm
Forum: Secondary Level
Topic: Inequality
Replies: 0
Views: 645

Inequality

The inequality \[ \frac{x|x-2|(x-4)|x-6|...|x-2014|}{(x-1)|x-3|(x-5)|x-7|...|x-2015|} > 0\] does not hold for a finite number of intervals on the real number line. What is the sum of the length between the points 0 and 1 is 1 unit long.
by Mahfuz Sobhan
Tue Nov 17, 2015 5:56 pm
Forum: Number Theory
Topic: prove it!!!
Replies: 2
Views: 638

prove it!!!

Let $$a_1, ........., a_n$$ be any non-zero integers whose g.c.d is $$d$$. Then there exist integers
$$x_1, ....., x_n$$ such that $$a_1 x_1 ++.....+a_n x_n = d$$.
by Mahfuz Sobhan
Wed Nov 04, 2015 8:56 pm
Forum: Secondary Level
Topic: geometry
Replies: 3
Views: 1028

geometry

In $$ΔABC$$, $$∠B = 90$$. A circle is drawn taking $$AB$$ as a chord. $$O$$ is the center of the circle. $$O$$ and $$C$$ isn't on the same side of $$AB$$. $$BD$$ is perpendicular to $$AC$$. Prove that, $$BD$$ will be a tangent to the circle if and only if $$∠BAO = ∠BAC$$.
by Mahfuz Sobhan
Thu Sep 03, 2015 3:41 pm
Forum: Secondary Level
Topic: If x is very very very small........
Replies: 0
Views: 576

If x is very very very small........

If $$x$$ is very very very small $$sin x » x$$. An operator $$S_n$$ is defined such that
$$S_n(x)= sin sin sin .... x $$(a total of $$n$$ $$sin$$ operators are included here). For
sufficiently large $$n$$, $$S_n(x) » S_(n-1)(x)$$. In that case, express cos $$(S_n(x))$$ as the
nearest rational value.
by Mahfuz Sobhan
Thu Aug 06, 2015 9:35 pm
Forum: Secondary Level
Topic: chittagong-divisional-2014
Replies: 1
Views: 698

chittagong-divisional-2014

If $$a$$,$$b$$ are co-prime and $$a$$ $$=$$ $$259$$, find gcd of $$a^2$$ $$-$$ $$ab$$ $$–$$ $$b^2$$ and $$a$$ $$+$$ $$b$$. :oops: