There are $100$ students in a class. In an examination, $50$ of them failed in Mathematics, $45$ failed in Physics, $40$ failed in Biology and $32$ failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects.
- is 12
- is 4
- is 2
- cannot be determined from the given information
The Correct Option is C
Solution and Explanation
$a + b + c + d + e + f + g + h=100$ ...(i)
$h=1$ ...(ii)
$a + b + d +e=50$ ...(iii)
Venn diagram shows failed students
$b + c + d +f=45$ ...(iv)
$d + e + f +g=40$ ...(v)
$b + e +f=32$ ...(vi)
On solving, the above equations, we get $d=2$
Top Questions on Sets
Let \[ A = \{x : |x^2 - 10| \le 6\} \quad \text{and} \quad B = \{x : |x - 2| > 1\}. \] Then
- Let \(S\) be the set of the first 11 natural numbers. Then the number of elements in \[ A = \{ B \subseteq S : n(B) \ge 2 \text{ and the product of all elements of } B \text{ is even} \} \] is ____________.
- Given the sets $ A = \{ x \mid |x - 2|<3 \} $ and $ B = \{ x \mid |x + 1| \leq 4 \} $, find $ A \cap B $.
- If \(A=\{1,2,3\}\), \(B=\{3,4\}\), then \(A\cup B\) is:
- If $A = \{x \in \mathbb{R} \mid \sin^{-1}(\sqrt{x^2+x+1}) \in [-\frac{\pi}{2}, \frac{\pi}{2}]\}$ and $B = \{y \in \mathbb{R} \mid y = \sin^{-1}(\sqrt{x^2+x+1}), x \in A\}$, then
Questions Asked in WBJEE exam
What are the charges stored in the \( 1\,\mu\text{F} \) and \( 2\,\mu\text{F} \) capacitors in the circuit once current becomes steady?
- WBJEE - 2026
- Capacitors and Capacitance
Which one among the following compounds will most readily be dehydrated under acidic condition?
- WBJEE - 2026
- Organic Reactions
Manufacturers supply a zener diode with zener voltage \( V_z=5.6\,\text{V} \) and maximum power dissipation \( P_{\max}=\frac14\,\text{W} \). This zener diode is used in the circuit shown. Calculate the minimum value of the resistance \( R_s \) so that the zener diode will not burn when the input voltage is \( V_{in}=10\,\text{V} \).
- WBJEE - 2026
- Zener Diodes
Two charges \( +q \) and \( -q \) are placed at points \( A \) and \( B \) respectively which are at a distance \( 2L \) apart. \( C \) is the midpoint of \( AB \). The work done in moving a charge \( +Q \) along the semicircle CSD (\( W_1 \)) and along the line CBD (\( W_2 \)) are
- WBJEE - 2026
- electrostatic potential and capacitance
A piece of granite floats at the interface of mercury and water. If the densities of granite, water and mercury are \( \rho, \rho_1, \rho_2 \) respectively, the ratio of volume of granite in water to that in mercury is
- WBJEE - 2026
- Buoyancy and Floatation
Concepts Used:
Sets
In mathematics, a set is a well-defined collection of objects. Sets are named and demonstrated using capital letter. In the set theory, the elements that a set comprises can be any sort of thing: people, numbers, letters of the alphabet, shapes, variables, etc.
Read More: Set Theory
Elements of a Set:
The items existing in a set are commonly known to be either elements or members of a set. The elements of a set are bounded in curly brackets separated by commas.
Read Also: Set Operation
Cardinal Number of a Set:
The cardinal number, cardinality, or order of a set indicates the total number of elements in the set.
Read More: Types of Sets