# Quiz at GanitCharcha

Welcome to GanitCharcha's Quiz page. Our quizzes are not made to test one or to help one test how much Mathematics on a given topic he/she knows, rather it is purposefully designed to help people feel motivated to learn. Our quizzes will help to paint the construction of one's own mathematical understanding while instilling love for the subject. Under the broad name of Quiz, one can also find different types of Math problems to challenge his/her math mind.

## Quiz : Higher Secondary Level Quiz December 2014

1
If $F(n+1) = \frac{2F(n) + 1}{2},$ for $n = 1, 2, \ldots$ and $F(1) = 2$, then $F(101)$ equals to

2
The number of zeros at the end of $(101)!$ is

3
If $a^{x} = b^{y} = c^{z}$ and $a, b, c$ are in G.P., then $x$, $y$, $z$ are in

4
The last two digits of $2^{199}$ is

5
Identify the set $S$ by the following conditions:
(i) $S \cap \{3, 5, 8, 11\} = \{5, 8\}$
(ii) $S \cup \{4, 5, 11, 13\} = \{4, 5, 7, 8, 11, 13\}$
(iii) $\{8, 13\} \subset S$ and
(iv) $S \subset \{5, 7, 8, 9, 13\}$

6
The equation of lowest degree with real coefficients which has $2 + 3i$ abd $3 - 2i$ as two of its roots is,

7
The remainder when the sum $1^{5} + 2^{5} + 3^{5} + \ldots + 100^{5}$ is divided by $4$ is

8
There are two positive numbers that can be inserted between $3$ and $9$ such that the first three numbers will be in G.P. and the last three numbers will be in A.P.
Sum of these inserted positive numbers is

9
If $cos(x-y)$, $cos(x)$ and $cos(x+y)$ are in H.P., then the value of $cos(x).sec(y/2)$ is
(a) $sin(x)$     (b) -1      (c) $\sqrt{2}$     (d) $\frac{1}{2}$

10
Let, $f$ be a function satisfying $f(x + y) = f(x).f(y) \forall x, y \in R$.
If $f(1) = 3$, then the value of $f(1) + f(2) + f(3) + \ldots + f(n)$ is
(a) $3^{n+1} - 1$                        (b) $\frac{(3n + 1)}{2}$
(c) $\frac{3(3^{n} - 1)}{2}$        (d) $\frac{3(3^{n-1} - 1)}{2}$

11
Suppose $a$, $b$, and $c$ are the lengths of the sides of a triangle satisfying $(a + b + c)(a+ b - c) = 3ab$, then the angle opposite to the side of length $c$ equals to

12
The side of an equilateral triangle is $a$. A circle is inscribed in the triangle and a square is inscribed in the circle. The area of the square is
(a) $\frac{a^{2}}{24}$            (b) $\frac{a^{2}}{6}$
(c) $\frac{a^{2}}{3}$              (d) None of these

13
If for a triangle $a = 2$, $b = \sqrt{6}$ and $c = \sqrt{3} - 1$, then the angle $A$ equals to

14
A triangle is circubscribed about a circle of radius $r$ (inches). If the perimeter of the triangle is $p$ (inches) and the area is $k$ square inches then $\frac{p}{k}$ is

If $a$, $b$, $c$ are real numbers not all equal and $$a + \frac{1}{b} = b + \frac{1}{c} = c + \frac{1}{a} = p,$$ then $p$ is equal to