A square with side $a$ is revolved about its centre through $45^\circ$. What is the area common to both the squares?

1

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

2

If $ \theta = \tan^{-1}\dfrac{1}{1+2} + \tan^{-1}\dfrac{1}{1+2\cdot3} + \tan^{-1}\dfrac{1}{1+3\cdot4} + \ldots + \tan^{…

Topic: NIMCET 2009

1

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

2

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

3

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

4

If $\sin^{-1}x + \cos^{-1}(1-x) = \sin^{-1}(1-x)$ then $x$ satisfies the equation:

Topic: NIMCET 2009

5

A and B are independent witnesses. Probability A speaks the truth = $x$, Probability B speaks the truth = $y$. If both…

Topic: NIMCET 2009

6

If $A$ is a $3\times 3$ matrix with $\det(A)=3$, then $\det(\operatorname{adj}A)$ is:

Topic: NIMCET 2009

7

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

8

The total number of relations that exist from a set $A$ with $m$ elements into the set $A \times A$ is:

Topic: NIMCET 2009

9

Water runs into a conical tank of radius $5$ ft and height $10$ ft at a constant rate of $2\text{ ft}^3/\text{min}$. Ho…

Topic: NIMCET 2009

10

The probability that a man who is 85 yrs old will die before attaining the age of 90 is $1/3$. $A_1, A_2, A_3, A_4$ are…

Topic: NIMCET 2009