List of practice Questions

If $ A = \{1,2,3,4,5,6\} $ and $ B = \{1,2,3,\ldots,9\} $, then the number of strictly increasing functions $ f : A \to B $ such that $ f(i) \neq i $ for all $ i = 1,2,3,4,5,6 $ is:

The speed-density relation on a one-way, single lane road is shown in the figure, where speed $ u $ is in km/hour and density $ k $ is in vehicles/km. The maximum flow (in vehicles/hour) on this road is

Consider the following relation $ R = \{(4,5), (5,4), (7,6), (6,7)\} $ on set $ I = \{4,5,6,7\} $. Which of the following properties relation $ R $ does not have? (A) Reflexive property
(B) Symmetric property
(C) Transitive property
(D) Antisymmetric property
Choose the correct answer from the options given below:

In a group of 50 people, 30 like tea, 25 like coffee, and 10 like neither. How many like both tea and coffee?

Let $ A = \{-3, -2, -1, 0, 1, 2, 3\} $. A relation $ R $ is defined such that $ xRy $ if $ y = \max(x, 1) $. The number of elements required to make it reflexive is $ l $, the number of elements required to make it symmetric is $ m $, and the number of elements in the relation $ R $ is $ n $. Then the value of $ l + m + n $ is equal to:

How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?

If the set $R = {(a, b) : a + 5b = 42, a, b \in \mathbb{N}}$ has $m$ elements and $\sum_{n=1}^m (1 + i^n) = x + iy$, where $i = \sqrt{-1}$, then the value of $m + x + y$ is:

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then how many received medals in exactly two of three events?

Let $A = \{x \in \mathbb{R}: |x+3| + |x+4| \le 3\}$,} \[ B = \left\{ x \in \mathbb{R} : 3 \cdot \sum_{r=1}^{\infty} \frac{3^{x-3}}{10^r} < 3^{-3x} \right\}, \] where $[x]$ denotes the greatest integer function. Then,

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :

Let $ Z $ be the set of all integers,
$ A = \{(x, y) \in Z \times Z : (x - 2)^2 + y^2 \leq 4\} $,
$ B = \{(x, y) \in Z \times Z : x^2 + y^2 \leq 4\} $ and
$ C = \{(x, y) \in Z \times Z : (x - 2)^2 + (y - 2)^2 \leq 4\} $
If the total number of relations from $ A \cap B $ to $ A \cap C $ is $ 2^p $, then the value of $ p $ is :

If $A = \{x \in \mathbb{R} : |x-2|>1\}$, $B = \{x \in \mathbb{R} : \sqrt{x^2-3}>1\}$, $C = \{x \in \mathbb{R} : |x-4| \geq 2\}$ and $\mathbb{Z}$ is the set of all integers, then the number of subsets of the set $(A \cap B \cap C)^c \cap \mathbb{Z}$ is _________.

Let S = 1, 2, 3, 4, 5, 6, 9. Then the number of elements in the set T={A $\subseteq$ S: A $\neq \emptyset$ and the sum of all the elements of A is not a multiple of 3} is _________.