Free Printable MBA Factors CH 13 LD 2.4

1.

What is the maximum possible value of (21 sin X + 72 cos X)?

a)

21

b)

57

c)

63

d)

75

2.

The sum of the possible values of X in the equation |x + 7| + |x − 8| = 16 is:

a)

0

b)

1

c)

2

d)

3

3.

If |3x+5| ≤ and a and b are the minimum and maximum values of x respectively, then a + b = 68.

(a)

4.

For how many positive integer values of x, is x³ − 16x + x² + 20 ≤ 0

(a)

5.

3f (x) + 2f $\left(\frac{4x+5}{x-4}\right)$ =7 (x + 3) where x ∈ R and x ≠ 4. What is the value of f(11)?

(a)

6.

if q = p × [p] and ‘q’ is an integer such that 7 < q < 17. The number of positive real values of ‘p’ is:

(a)

7.

if q = p × [p] and ‘q’ is an integer such that 7 < q < 17. Find the product of all possible values of p

(a)

8.

If f(1) = −1, f(2x) = 4f(x) + 9, f(x + 2) = f(x) + 8(x + 1). Find the value of f(24) − f(7).

(a)

9.

In the previous question, find the value of f(1000)

(a)

10.

f(x) = (x ²+ [x]² − 2x[x])^1/2, where x is real & [x] denotes the greatest integer less than or equal to x. Find the value of f(10.08) − f(100.08).

(a)

11.

Find the sum of coefficients of the polynomial (x − 4)⁷ (x − 3)⁴ (x − 5)²

a)

2⁸ 3⁷

b)

−2⁶ .3⁸

c)

−2⁸ .3⁷

d)

2⁶ .3⁸

12.

A function f(x) is defined as $f\ \left(x\right)=\ x-\frac{1}{9-3x}-3$ If x > 3, then find the minimum possible value of f(x)

a)

$3-\frac{1}{\sqrt[]{3}}$

b)

$\frac{1}{\sqrt[]{3}}$

c)

$\sqrt[]{3}-\frac{1}{3}$

d)

$\sqrt[]{3}+\frac{1}{3}$

13.

The graph of h(x) and g(x) are given below. Then which of the following defines the relation between h(x) and g(x)?

a)

$\sqrt[]{3}$ g (x) - h (x) = a $\sqrt[]{3}$

b)

$\sqrt[]{3}$ g (x) + h (x) = a $\sqrt[]{3}$

c)

g (x) + h (x) $\sqrt[]{3}=\frac{a}{\sqrt[]{3}}$

d)

None of these

14.

Consider a function ‘f’ is such that $\frac{f\ \left(xy\right)}{f\ \left(x+y\right)}=1$ for all real values of x, y. If f(6) = 7 then the value of f(−10) + f(10) is

(a)

15.

A function f(x) is defined such that $f\ \left(\frac{x}{y}\right)=\frac{f\ \left(x\right)}{f\ \left(y\right)}$ If f(3) = 5 then f(81) = ?

(a)

16.

Find the sum of all the coefficients of the polynomial (x − 4)³ (x − 2)¹⁰ (x − 3)³

(a)

17.

$f\ \left(x\right)\left\{\frac{3^x\ when\ x\ is\ an\ odd\ number.}{3^x+4\ when\ x\ is\ an\ even\ number.}\right\}$ What is the value of $\frac{1}{4}$ [f(1) + f (2) + f (3) + f (4) + .... + f (n)] if n = 72

a)

$\frac{3}{8}$ (3⁷² - 1) + 36

b)

$\frac{3}{8}$ (3⁷² + 1) + 36

c)

$\frac{3}{8}$ (3⁷²) + 36

d)

None of these.

18.

f(x + y) = f(x.y) where x and y are real numbers and ‘f’ is a real function. If f(10) = 12 then [f(7)]¹⁴³ − [f(11)]¹⁴³ + f(5) = ?

(a)

19.

Which of the following represents the curve of |e^-|x| |?

a)

b)

c)

d)

None of these

20.

Which of the following function correctly represents the curve of |e^-x − 3|:

a)

b)

c)

d)

None of these

21.

Which of the following represents the curve of |log|x − 3||?

a)

b)

c)

d)

None of these

22.

$f\ \left(x,y\right)=x^2+y^2-x-\frac{3y}{2}\ +1$ When f(x, y) is minimum then the value of x + y = ?

(a)

23.

In the previous question, find the minimum value of f(x, y)

(a)

24.

If the graph given below represents f(x + 5) then which of the given options would represent the graph of f(–2 − x)?

a)

b)

c)

d)

25.

Which of the following options represents curve of f (−2x)?

a)

b)

c)

d)

None of these.

26.

If x, y are real numbers and function g(x) satisfies $\frac{\left(g\left(x+y\right)+g\left(x-y\right)\right)}{2}$ g(x)g(y) = and g(0) is a positive real number then which of the following options may represent graph of g(x)?

a)

b)

c)

d)

MBA Factors CH 13 LD 2.4

Total questions: 26

Worksheet time: 52mins

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