Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X
Concept: Mean of a Random Variable
The total cost of manufacturing x articles is C = 47x + 300x^{2} − x^{4}. Find x, for which average cost is increasing.
Concept: Increasing and Decreasing Functions
Choose the correct alternative :
If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is
Concept: Truth Value of Statement
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If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is
Concept: Truth Value of Statement
State whether the following statement is True or False :
x^{2} = 25 is true statement.
Concept: Truth Value of Statement
Form the differential equation from the relation x^{2 }+ 4y^{2 }= 4b^{2}
Concept: Differential Equations
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(5x + 7)/(2x - 13)`
Concept: Derivatives of Composite Functions - Chain Rule
Find the equation of tangent to the curve y = `sqrt(x - 3)` which is perpendicular to the line 6x + 3y – 4 = 0.
Concept: Introduction of Derivatives
Evaluate the following definite integrals: `int_1^3 logx.dx`
Concept: Fundamental Theorem of Integral Calculus
A retailer sold a suit for ₹ 8,832 after allowing 8% discount on marked price and further 4% cash discount. If he made 38% profit, find the cost price and the marked price of the suit.
Concept: Commission and Brokerage Agent
The rate of premium is 2% and other expenses are 0.75%. A cargo worth ₹ 3,50,100 is to be insured so that all its value and the cost of insurance will be recovered in the event of total loss.
Concept: Concept of Insurance
Choose the correct alternative:
Regression analysis is the theory of
Concept: Regression
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We can estimate the value of one variable with the help of other known variable only if they are
Concept: Regression
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In the regression equation of X on Y
Concept: Regression
Find the equation of the line of regression of Y on X for the following data:
n = 8, `sum(x_i - barx).(y_i - bary) = 120, barx = 20, bary = 36, sigma_x = 2, sigma_y = 3`
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
Choose the correct alternative :
The assignment problem is said to be balanced if it is a ______.
Concept: Assignment Problem
Solve the following problem :
A dairy plant has five milk tankers, I, II, III, IV and V. These milk tankers are to be used on five delivery routes A, B, C, D and E. The distances (in kms) between the dairy plant and the delivery routes are given in the following distance matrix.
I | II | III | IV | V | |
A | 150 | 120 | 175 | 180 | 200 |
B | 125 | 110 | 120 | 150 | 165 |
C | 130 | 100 | 145 | 160 | 175 |
D | 40 | 40 | 70 | 70 | 100 |
E | 45 | 25 | 60 | 70 | 95 |
How should the milk tankers be assigned to the chilling center so as to minimize the distance travelled?
Concept: Assignment Problem
A sample of 4 bulbs is drawn at random with replacement from a lot of 30 bulbs which includes 6 defective bulbs. Find the probability distribution of the number of defective bulbs.
Concept: Random Variables and Its Probability Distributions
A random variable X has the following probability distribution:
x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(x) | k | 2k | 2k | 3k | k^{2} | 2k^{2} | 7k^{2} + k |
Determine P(X > 4)
Concept: Random Variables and Its Probability Distributions
A die is thrown 4 times. If ‘getting an odd number’ is a success, find the probability of 2 successes
Concept: Random Variables and Its Probability Distributions