Quiz at GanitCharcha


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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

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

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

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

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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) $S \subset \{5, 7, 8, 9, 13\}$

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

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

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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

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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) $\frac{1}{2}$

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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) $\frac{3(3^{n-1} - 1)}{2}$

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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

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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

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

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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

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15
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

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