Sequences and S...

With the help of match-sticks, Zalak prepared a pattern as shown below. When $$97$$ matchsticks are used, the serial number of the figure will be ...........

Ten points lie in a plane so that no three of them are collinear. The number of lines passing through exactly two of these points are dividing the plane into two regions each containing four of the remaining points is 

Area of the triangle formed by the points $$(0,0),(2,0)$$ and $$(0,2)$$ is

Find the value of $$a$$ if area of the triangle is $$17$$ square units whose vertices are $$(0,0), (4,a), (6,4)$$.                         

Out of $$7$$ consonants and $$4$$ vowels, words are formed each having $$3$$ consonants and $$2$$ vowels. The number of such words that can be formed is

Find the term independent of $$x$$ in $${ \left( \cfrac { 3 }{ 2 } { x }^{ 2 }-\cfrac { 1 }{ 3x }  \right)  }^{ 9 }$$.

Choose $$3, 4, 5$$ points other than vertices respectively on the sides $$AB, BC$$ and $$CA$$ of a $$\triangle ABC$$. The number of triangles that can be formed by using only these points as vertices, is

If $$f(x)=\left| \log { \left| x \right|  }  \right| $$, then

Three bells commenced to toll at the same time and tolled at intervals of $$20, 30, 40$$ seconds respectively. If they toll together at $$6$$ am, then which of the following is the time at which they can toll together

The first term of an AP is $$148$$ and the common difference is $$-2$$. If the AM of first $$n$$ terms of the AP is $$125$$, then the value of $$n$$ is