MCQ_SINGLE

The number of elements in the set {$x \in R : (|x| - 3) |x + 4| = 6$} is equal to :

MCQ_SINGLE

If the probability that the random variable $X$ takes the value $x$ is given by $P(X=x) = k(x+1)3^{-x}, x = 0, 1, 2, 3 \dots$, where $k$ is a constant, then $P(X \geq 3)$ is equal to

MCQ_SINGLE

Consider the sets $A = \{(x, y) \in R \times R : x^2 + y^2 = 25\}$, $B = \{(x, y) \in R \times R : x^2 + 9y^2 = 144\}$, $C = \{(x, y) \in Z \times Z : x^2 + y^2 \le 4\}$ and $D = A \cap B$. The total number of one-one functions from the set $D$ to the set $C$ is:

MCQ_SINGLE

Let $\bigcup_{i=1}^{50} X_i = \bigcup_{i=1}^{n} Y_i = T$ where each $X_i$ contains $10$ elements and each $Y_i$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_i$'s and exactly $6$ of sets $Y_i$'s, then $n$ is equal to:

NUMERICAL

For $n \geq 2$, let $S_n$ denote the set of all subsets of $\{1,2, \ldots, n\}$ with no two consecutive numbers. For example $\{1,3,5\} \in S_6$, but $\{1,2,4\} \notin S_6$. Then $n\left(S_5\right)$ is equal to ________

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