If $ \theta = \tan^{-1}\dfrac{1}{1+2} + \tan^{-1}\dfrac{1}{1+2\cdot3} + \tan^{-1}\dfrac{1}{1+3\cdot4} + \ldots + \tan^{-1}\dfrac{1}{1+n(n+1)} $, then $\tan\theta$ is equal to:
Next 10 Questions — NIMCET 2009
Ascending by ID
1
2
3
4
5
6
7
8
9
10
If
$(1 + x - 2x^2)^6 = 1 + a_1 x + a_2 x^2 + \ldots + a_{12} x^{12}$,
then the value of $a_2 + a_4 + a_6 + \ldots + a_{…
Topic: NIMCET 2009
A square with side $a$ is revolved about its centre through $45^\circ$.
What is the area common to both the squares?
Topic: NIMCET 2009
A and B throw a die in succession to win a bet with A starting first.
Whoever throws ‘1’ first wins Rs. 110.
What are t…
Topic: NIMCET 2009
How many different paths in the $xy$-plane are there from $(1,3)$ to $(5,6)$,
if a path proceeds one step at a time eit…
Topic: NIMCET 2009
If the distance of $(x,y)$ from the origin is defined as
$d(x,y) = \max(|x|,|y|)$,
then the locus of points where $d(x,…
Topic: NIMCET 2009
If
$\sin^{-1}x + \cos^{-1}(1-x) = \sin^{-1}(1-x)$
then $x$ satisfies the equation:
Topic: NIMCET 2009
A and B are independent witnesses.
Probability A speaks the truth = $x$,
Probability B speaks the truth = $y$.
If both…
Topic: NIMCET 2009
If $A$ is a $3\times 3$ matrix with $\det(A)=3$, then $\det(\operatorname{adj}A)$ is:
Topic: NIMCET 2009
A set contains $(2n+1)$ elements. If the number of subsets that contain at most $n$ elements is $4096$, then the value …
Topic: NIMCET 2009
The total number of relations that exist from a set $A$ with $m$ elements into the set $A \times A$ is:
Topic: NIMCET 2009
