Math Answers

Draw all possible distinct sample of size 3 from the population 2 ,4, 6, 8, 10, 12,

Construct the sampling distribution of the sample mean X and calculate it's means and variance meauX and sigma X

Payment of 700.00 every month for one (1) year that will start at the end of the third month. What is the period of deferral?

f(x)= x^4 +8x^3+16x^2

g(x) = -4x^2 -16x +5

using algebraic method, find the points of intersection of the graphs f(x) and g(x).

which of the solutions are reflected on the graphs

1) A man sells his car for $749 at a loss of 25/2% of what he paid for it. Find his actual loss

2) An article which costs $3.20 in 1940 now costs $9.12. Find the percentage increase in cost.

3) If a dealer charges $2.75 for a chair, he gains 75/2%, at what price must he sell it to gain 45%?

Q13.

Suppose T, S : R^2 "\\to" R^2 are linear defined by T (u, v) = (3u + v, u + 2v) and S (x, y) = (2x - y, x + y).

Also the matrices of T and S with respect to the standard bases of R^2 and R^2 are given as M (T) ="\\begin{bmatrix}\n 3 & 1 \\\\\n 1 & 2\n\\end{bmatrix}"

and M (S) ="\\begin{bmatrix}\n 2 & - 1 \\\\\n 1 & 1\n\\end{bmatrix}". Then M(T S) =

(1) "\\begin{bmatrix}\n 1 & 0 \\\\\n 0 & 1\n\\end{bmatrix}"

(2) "\\begin{bmatrix}\n 3 & 1 \\\\\n 1 & 5\n\\end{bmatrix}"

(3) "\\begin{bmatrix}\n 3 & 1 \\\\\n 4 & 1\n\\end{bmatrix}"

4) None of the given answers is true

Q10.

For a given matrix A = "\\begin{bmatrix}\n 1 & 0 & 2 & -3 \\\\\n 2 & 0 & 4 & - 6 \\\\\n -3 & 0 & - 6& 9\n\\end{bmatrix}". Which of the following is true

(1) rank (A) = 3, nullity (A) = 1

(2) rank (A) = 2, nullity (A) = 2

(3) rank (A) = 1, nullity (A) = 3

(4) None of the given answers is true.

Q11.

For a, b "\\in" R, the transformation T : R^2 "\\to" R^3 defined byT (x, y) = (2x - y, 3x + y + 3A, 5x - 2y + bxy) is linear if

(1) a = b = 1

(2) a = 0; b = 1

(3) a = 1; b = 0

(4) None of the given answers is true.

Q12.

Suppose T : R^3 "\\to" R^2

is a linear defined by

T (x, y) = (4x + 3y + Z, x - 2y). Then which of the following is basis of range T is

(1) (4, 1, 3), (1, 2, 0)

(2) (1, 0), (0, 1), (1, 1)

(3) (4, 1), (3, 2), (1, 0)

(4) None of the given answers is true.

Q7.

The vectors (1, 2, 0), (0, -4, 2), (1, 0, 1) are

(1) Span R^3

(2) linearly dependent

(3) linearly independent

(4) None of the given answers is true.

Q8.

Let W be the subspace of R^5 defined by

W = {(x base 1; x base 2; x base 3; x base 4; x base 5) 2 R^5 : x base 1 = 3x base 2 and x base 3 = 7x base 4}

Then the basis of W is

(1) (3,1,0,0,1), (3,1,3,0,0), (3,1,0,0,1)

(2) (3,1,0,1,1), (0,0,3,0,1), (0,0,1,3,1)

(3) (3,1,1,0,1), (0,1,1,0,3), (0,0,1,0,1)

(4) None of the given answers is true.

Q9.

The basis for a solution space of given homogenous linear system

x base 1 + x base 2 - x base 3 = 0

x base 1 + x base 2 - x base 3 = 0

x base 1 - x base 3=0

- x base 1 + x base 3=0 "\\implies"x base 2 = 0 "\\implies"x base 2 = 0

- 2x base 1 - x base 2 + 2x base 3 = 0

- 2x base 1 - x base 2 + 2x base 3= 0

- 2x base 1 + 2x base 3 = 0 is

(1) {(1, 0, 1)}

(2) {(1, 0, 1), (0, 1, 0)}

(3) f(1; 1; 1);(1; 0; 1), (2, 1, 2)}

(4) None of the given answers is true.

A six-sided die is rolled three times independently. Which is more likely: a sum of 11 or a sum of 12?

Q4.

The value of x "\\in" R^4

such that (4, 3, - 3, 2) + 3x = (7, -3, 3, 2) is

(1) x = (4, -4, 3, 0)

(2) x = (4, - 4, 3, 0)

(3) x = (1, -2, 0, 0)

(4) None of the given answers is true.

Q5.

Let W be a subset of R^3 defined as

W = (x, y, z) "\\in" R^3: 2x + y - z - 1 = 0.

Then

(1) W is a subspace of R^3

(2) W is closed under scalar multiplication

(3) W is not a subspace of R^3

(4) None of the given answers is true.

Q6.

The set of differentiable real-valued functions f on the interval (0,3) such that f'(2) = "\\alpha" is a subspace of R^(0,3). The value of must be

(1) negative

(2) positive

(3) zero

(4) None of the given answers is true.

Q1.

Consider the sets

A = {x "\\in" Z : x = 2 (y - 2) for some

y "\\in" Z} and B = {x "\\in" Z : x = 2z for some z "\\in" Z}. Then

(i) A and B are equal,

(ii) A {\displaystyle \subsetneq } B,

(iii) B {\displaystyle \subsetneq } A

(1) (i) only

(2) (ii) only.

(3) (iii) only

(4) None of the given answers is true.

Q2.

Consider a function f: R → R^+ defined as f(x) =e^x: Then the image of S ={x ∈ R: 0 ≤ x^2 - 9} is

(i) (-∞; e^-3]U[e^3;∞);

(ii) [e^-3; e3^];

(iii)[e^3;∞)

(4) None of the given answers is true.

Q3.

The two distinct square roots of i is

(1) √2 + √2i and -√2 - √2i

(2) 2√2 + 2√2i and - 2√2 - 2√2i

(3)√2/2 + √2/2(I) and - √2/2 - √2/2(I)

(4) None of the given answers is true.