CUET · MATHS · PYQ PAPER 2025
The probability distribution of a random variable \(x\) is, \(P(x)=\frac{k}{2^x}, x=0,1,2,3\). Then
Match List-I with List-II
| List-I | List-II |
| (A) k | (I) \(\frac{2}{15}\) |
| (B) \(P ( x =1)\) | (II) \(\frac{1}{5}\) |
| (C) \(P (1<x<3)\) | (III) \(\frac{8}{15}\) |
| (D) \(P(x \geq 2)\) | (IV) \(\frac{4}{15}\) |
- A (A) - (III), (B) - (II), (C) - (I), (D) - (IV)
- B (A) - (IV), (B) - (II), (C) - (III), (D) - (I)
- C (A) - (IV), (B) - (III), (C) - (I), (D) - (II)
- D (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
Answer & Solution
Correct Answer
(D) (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
Step-by-step Solution
Detailed explanation
\(\sum P(x) = 1 \Rightarrow k(\frac{1}{2^0} + \frac{1}{2^1} + \frac{1}{2^2} + \frac{1}{2^3}) = 1\) \(k(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}) = 1\) \(k(\frac{8+4+2+1}{8}) = 1 \Rightarrow k(\frac{15}{8}) = 1 \Rightarrow k = \frac{8}{15}\) (A) - (III)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- The value of the determinant \(\left|\begin{array}{lll}a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1\end{array}\right|\) is:CUET 2023 Hard
- If \(A\) is a square matrix, then \(\left(A^T-A\right)\) is-CUET 2025 Easy
- The point on the curve \(y=(x-2)^2\) at which the tangent is parallel to the chord joining the points \((2,0)\) and \((4,4) \) is :CUET 2025 Easy
- Which of the following statements are correct?
(A) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a triangle, then its area is \(\frac{1}{2}|\vec{a} \times \vec{b}|\)
(B) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a parallelogram, then its area is \(|\vec{a} \times \vec{b}|\)
(C) \(|\vec{a} \times \vec{b}|=|\vec{a}||\vec{b}| \cos \theta\)
(D) If \(\vec{a}\) and \(\vec{b}\) represent the 'diagonals' of a parallelogram, then its area is \(\frac{1}{2}|\vec{a} \times \vec{b}|\)
Choose the correct answer from the options given below :CUET 2025 Easy - The sale of ice creams is higher in summer than in winter is an example of:CUET 2025 Easy
- A machine costing ₹ \(36000\) has an effective life of 5 years with scrap value of ₹ \( 5000\) following a linear method of depreciation. Which are correct?
(A) The value of the machine after 1 year is ₹ \(31000\)
(B) The value of the machine after 2 years is ₹ \(23600\)
(C) The value of the machine after 3 years is ₹ \(18400\)
(D) The value of the machine after 4 years is ₹ \(11200\)
Choose the correct answer from the options given below :CUET 2025 Hard
More PYQs from CUET
- What are the two types of isomerism that exist in \(\text{[Pt(Cl)}_2\text{(NO}_2)_2]\) ?CUET 2023 Medium
- The de-Broglie wavelength of neutron at \( 127^\circ \text{C} \) is : (Given Boltzmann constant, \( k = 1.38 \times 10^{-23} \text{ J mole}^{-1} \text{K}^{-1}, h = 6.63 \times 10^{-34} \text{ Js} \), mass of neutron \( m = 1.66 \times 10^{-27} \text{ kg} \))CUET 2023 Medium
- Match List-I with List-II
Choose the correct answer from the options given below:List-I (Physical property) List-II (Expression) (A) G (conductance) (I) \(1/(RA)\) (B) R (resistance) (II) \(A/(\rho l)\) (C) \(\kappa\) (Specific conductance) (III) \(\kappa/c\) (D) \(\Lambda_m\) (molar conductance) (IV) \(l/(\kappa A)\) CUET 2025 Medium - "The random variable \(X\) has a probability distribution \(P ( X )\) of the following form, where \(k\) is some number.
\(P(X=x)=\left\{\begin{array}{ll}k, & \text { if } x=0 \\2 k, & \text { if } x=1 \\3 k, & \text { if } x=2 \\0, & \text { otherwise }\end{array}\right.\)
Then \(P(x \leq 2)\) is :"CUET 2023 Medium - The simplest form of \(\tan ^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)\) is, where \(-a < x < a\).CUET 2023 Hard
- Which of the following statement is incorrect about fructose?CUET 2023 Hard