CUET · MATHS · PYQ PAPER 2025
Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is : [Given \(e^{-2}=0.135\)]
- A 0.5
- B 1
- C 0.135
- D 0.27
Answer & Solution
Correct Answer
(D) 0.27
Step-by-step Solution
Detailed explanation
\(\lambda = n \times p = 100 \times 0.02 = 2\) \(P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}\) \(P(X=2) = \frac{2^2 e^{-2}}{2!} = \frac{4 \times 0.135}{2} = 2 \times 0.135 = 0.27\)
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
- \(\int \frac{x \sin ^{-1} x}{\sqrt{1-x^2}} d x=\)CUET 2023 Medium
- The demand function P for maximising a profit monopolist is given by \(P = 274 -\) \(x^2\), while the marginal cost is \(4+3x\) for \(x\) units of commodity. The consumer surplus isCUET 2025 Easy
- The shortest wavelengths in the hydrogen spectrum, in decreasing order, for spectral series Pfund, Balmer, Brackett, and Lyman are :CUET 2024 Medium
- If \(X\) is a random variable and \(a, b\) are real numbers, then which of the following statements are correct?
(A) \(E[a X+b]=a E(X)+b\)
(B) \(\operatorname{Var}(a X+b)=a^2 \operatorname{Var}(X)+b\)
(C) \(\operatorname{Var}(a X+b)=a \operatorname{Var}(X)\)
(D) \(\operatorname{Var}(X)=E\left(X^2\right)-[E(X)]^2\)
Choose the correct answer from the options given below:CUET 2025 Hard - A die is thrown again and again until three sixes are obtained. The probability of obtaining third six in sixth throw of the die is:CUET 2023 Medium
- The sum of the minor and the cofactor of the element 6 in the determinant \(\Delta=\left|\begin{array}{lll}2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right|\) is:CUET 2023 Medium
More PYQs from CUET
- Match List - I (reagent) with List - II (Transformations)
List - I (Reducing Agent) List - II (Transformations) (A) Sodium Borohydride (I) Aldehyde to alkane (B) \(SnCl _2\) and HCl (II) aldehydes to Primary alcohols (C) Zn-Hg and conc. HCl (III) Nitriles to Imine (D) DIBAL-H (IV) Ester to aldehyde
Choose the correct answer.CUET 2025 Medium - According to the Biot- Savart law, the magnetic field due to a current element is
(A) inversely proportional to the square of the distance from the current element to the point of interest.
(B) produced by a vector source.
(C) perpendicular to the plane containing the displacement vector and the current element.
(D) non-zero at any point in the direction of the current element.
Choose the correct answer from the options given below:CUET 2025 Hard - Which of the following reagents convert an alcohol into an alkyl chloride?
(A) Conc. Hydrogen Chloride
(B) Phosphorus trichloride
(C) Phosphorus pentachloride
(D) Thionyl Chloride
Choose the correct answer from the options given below:CUET 2025 Hard - The product obtained, when starch is hydrolyzed with dilute sulphuric acid at 393 K under pressure, is\[ \left(C_6 H_{10} O_5\right)_n+n H_2 O \frac{H^{+}}{393 K ; 2-3 atm} ? \]CUET 2023 Easy
- Which is not the limitation of valence bond theory involving coordination compound.CUET 2023 Medium
- Arrange the following in correct sequence with respect to the events of menstrual cycle:
(A) Development of primary follicle to graafian follicle
(B) Attainment of peak level in luteinising hormone
(C) Release of ovum by graafian follicle
(D) Formation of corpus luteum
Choose the correct answer from the options given below:CUET 2023 Hard