alleryStart learning →If $f(x) = kx^2(1 - x)$ for $0 < x < 1$ is the p.d.f. of $X$, the value of $k$ is:
- 10
- 12
- 6
- 8
Show answer and solution
Correct answer: B. 12
$\int_0^1 k(x^2 - x^3)\,dx = k[x^3/3 - x^4/4]_0^1 = k(1/3 - 1/4) = k/12 = 1$ ⇒ $k = 12$.
Indian Navy 10+2 B.Tech Cadet Correlation and Regression — practice questions
Explore 36 free Correlation and Regression questions in Indian Navy 10+2 B.Tech Cadet Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–30 of 36.
If $f(x) = kx^2(1 - x)$ for $0 < x < 1$ is the p.d.f. of $X$, the value of $k$ is:Read the answer and worked solution →sec θ is defined as:Read the answer and worked solution →General solution of cos θ = 0:Read the answer and worked solution →Probability of a certain event:Read the answer and worked solution →The probability of drawing a king from a standard pack of 52 cards is:Read the answer and worked solution →The probability of getting a number greater than 4 on a single throw of a die is:Read the answer and worked solution →In radian measure, $\pi$ radians equals:Read the answer and worked solution →The point dividing the segment from $(1,1)$ to $(4,7)$ in the ratio 1:2 is:Read the answer and worked solution →Find x such that the distance from (x, 1) to (2, 3) is √8.Read the answer and worked solution →The exact value of cos 60° is:Read the answer and worked solution →Complete the definition of conditional probabilityRead the answer and worked solution →True or false: conditional probabilityRead the answer and worked solution →Independent or mutually exclusive?Read the answer and worked solution →Match each rule to its nameRead the answer and worked solution →IndependenceRead the answer and worked solution →Order the steps for a Bayes' theorem questionRead the answer and worked solution →Complete the conditions for a partitionRead the answer and worked solution →True or false: independence versus exclusivityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Tap every statement that follows from independenceRead the answer and worked solution →The multiplication ruleRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead the answer and worked solution →Which theorem answers which question?Read the answer and worked solution →True or false: total probability and BayesRead the answer and worked solution →Match each historical figure to their contributionRead the answer and worked solution →The Historical NoteRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →
Worked practice questions
sec θ is defined as:
- 1/sin θ
- sin θ/cos θ
- 1/tan θ
- 1/cos θ
Show answer and solution
Correct answer: D. 1/cos θ
sec θ = 1/cos θ (cosecant: csc θ = 1/sin θ; cotangent: cot θ = 1/tan θ).
General solution of cos θ = 0:
- θ = π/2 + nπ
- θ = nπ
- θ = π/4 + nπ
- θ = 0 + 2nπ
Show answer and solution
Correct answer: A. θ = π/2 + nπ
cos θ = 0 at θ = π/2 and 3π/2 (i.e., 90° and 270°).
**General:** θ = π/2 + nπ where n ∈ ℤ. (Every π apart.)
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