Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
Concept: Statement Patterns and Logical Equivalence
Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
Concept: Statement Patterns and Logical Equivalence
If the population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 60 thousand in 40 years, what will be the population in another 20 years? `("Given" sqrt(3/2) = 1.2247)`
Concept: Application of Differential Equations
If x = a sin 2t (1 + cos2t) and y = b cos 2t (1 – cos 2t), find the values of `dy/dx `at t = `pi/4`
Concept: Derivatives of Functions in Parametric Forms
A bill of Rs.7,500 was discounted for Rs. 7,290 at a bank on 28th October 2006. If the rate of interest was 14% p.a., what is the legal due date ?
Concept: Commission, Brokerage and Discount
From the following table which relates to the number of animals of a certain
species at age x. complete the life table :
| x | 0 | 1 | 2 | 3 | 4 | 5 |
| lx | 1000 | 850 | 760 | 360 | 25 | 0 |
Concept: Life Tables
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(p ∧ ~ q) → (~ p ∧ ~ q)
Concept: Statement Patterns and Logical Equivalence
Use quantifiers to convert the following open sentences defined on N, into a true statement.
n2 ≥ 1
Concept: Quantifier and Quantified Statements in Logic
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(p ∧ ~ q) → (~ p ∧ ~ q)
Concept: Statement Patterns and Logical Equivalence
The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.
Concept: Increasing and Decreasing Functions
Choose the correct alternative:
`int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x`, then p = ?
Concept: Methods of Integration: Integration Using Partial Fractions
The equations given of the two regression lines are 2x + 3y - 6 = 0 and 5x + 7y - 12 = 0.
Find:
(a) Correlation coefficient
(b) `sigma_x/sigma_y`
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
Find k, if the function f is continuous at x = 0, where
`f(x)=[(e^x - 1)(sinx)]/x^2`, for x ≠ 0
= k , for x = 0
Concept: Continuous Function of Point
If x=a sin 2t(1+cos 2t) and y=b cos 2t(1−cos 2t), find `dy/dx `
Concept: Derivatives of Functions in Parametric Forms
The cost C of producing x articles is given as C = x3-16x2 + 47x. For what values of x, with the average cost is decreasing'?
Concept: Derivatives of Functions in Parametric Forms
The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.
Concept: Increasing and Decreasing Functions
Cost of assembling x wallclocks is `( x^3/3 - 40x^2)` and labour charges are 500x. Find the number of wall clocks to be manufactured for which average cost and marginal cost attain their respective minimum.
Concept: Maxima and Minima
Evaluate : `int_3^9 [root(3)(12-x)]/[ root(3)(x) + root(3)(12 - x)]`
Concept: Applications of Definite Integrals
If f(x) = `("e"^(2"x") - 1)/"ax"` , for x < 0 , a ≠ 0
= 1 for x = 0
= `("log" (1 + 7"x"))/"bx"` , for x > 0 , b ≠ 0
is continuous at x = 0, then find a and b.
Concept: Applications of Definite Integrals
Find the volume of a solid obtained by the complete revolution of the ellipse `x^2/36 + y^2/25 = 1` about X-axis.
Concept: Applications of Definite Integrals
