Determine the probability that the student studied for at most 2 hours.
Show Hint
Solution and Explanation
Step 1: The probability that the student studied for at most 2 hours is given by: \[ P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2). \] Step 2: Substitute the given values: \[ P(X \leq 2) = 0.1 + k(1) + k(2). \] Step 3: Substitute \( k = 0.15 \): \[ P(X \leq 2) = 0.1 + 0.15(1) + 0.15(2). \] Step 4: Compute the value: \[ P(X \leq 2) = 0.1 + 0.15 + 0.3 = 0.55. \] Thus, the probability that the student studied for at most 2 hours is 0.55.
Top Questions on Vectors
- Let \( \mathbf{a} \), \( \mathbf{b} \), and \( \mathbf{c} \) be vectors of magnitude 2, 3, and 4 respectively. If: - \( \mathbf{a} \) is perpendicular to \( (\mathbf{b} + \mathbf{c}) \), - \( \mathbf{b} \) is perpendicular to \( (\mathbf{c} + \mathbf{a}) \), - \( \mathbf{c} \) is perpendicular to \( (\mathbf{a} + \mathbf{b}) \), then the magnitude of \( \mathbf{a} + \mathbf{b} + \mathbf{c} \) is equal to:
- If the sum of two vectors is a unit vector, then the magnitude of their difference is:
- Number of functions \( f: \{1, 2, \dots, 100\} \to \{0, 1\} \), that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to:
- Let \( \vec{a} \) be a position vector whose tip is the point (2, -3). If \( \overrightarrow{AB} = \vec{a} \), where coordinates of A are (–4, 5), then the coordinates of B are:
The respective values of \( |\vec{a}| \) and} \( |\vec{b}| \), if given \[ (\vec{a} - \vec{b}) \cdot (\vec{a} + \vec{b}) = 512 \quad \text{and} \quad |\vec{a}| = 3 |\vec{b}|, \] are:
Questions Asked in CBSE CLASS XII exam
Draw a rough sketch for the curve $y = 2 + |x + 1|$. Using integration, find the area of the region bounded by the curve $y = 2 + |x + 1|$, $x = -4$, $x = 3$, and $y = 0$.
- CBSE CLASS XII - 2025
- Integration
- In the circuit shown, the charge on the left plate of the 20 µF capacitor is \( -50\,\mu C \). The charge on the right plate of the 12 µF capacitor is:
- CBSE CLASS XII - 2025
- Electrostatics
- Nita, Vidur and Mita were partners in a firm sharing profits and losses in the ratio of 3 : 4 : 1. On 1st April 2024, they decided to admit Samir as a new partner. The new profit sharing ratio between Nita, Vidur, Mita and Samir will now be 1 : 1 : 1 : 1. The balance sheet of Nita, Vidur and Mita before Samir’s admission showed machinery at ₹ 6,00,000. On the date of admission, it was found that the machinery is overvalued by 20%. The value of machinery shown in the new Balance Sheet after Samir’s admission will be :
- CBSE CLASS XII - 2025
- Admission of a Partner
In a Linear Programming Problem (LPP), the objective function $Z = 2x + 5y$ is to be maximized under the following constraints:
\[ x + y \leq 4, \quad 3x + 3y \geq 18, \quad x, y \geq 0. \] Study the graph and select the correct option.- CBSE CLASS XII - 2025
- Linear Programming Problem
- The corner points of the feasible region of a Linear Programming Problem are $(0, 2)$, $(3, 0)$, $(6, 0)$, $(6, 8)$, and $(0, 5)$. If $Z = ax + by; \, (a, b>0)$ be the objective function, and maximum value of $Z$ is obtained at $(0, 2)$ and $(3, 0)$, then the relation between $a$ and $b$ is :
- CBSE CLASS XII - 2025
- Linear Programming Problem and its Mathematical Formulation