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Test: Functions- 3 - CUET Commerce MCQ


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15 Questions MCQ Test General Test Preparation for CUET - Test: Functions- 3

Test: Functions- 3 for CUET Commerce 2024 is part of General Test Preparation for CUET preparation. The Test: Functions- 3 questions and answers have been prepared according to the CUET Commerce exam syllabus.The Test: Functions- 3 MCQs are made for CUET Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Functions- 3 below.
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Test: Functions- 3 - Question 1

Find the domain of the definition of the function y = lxl

Detailed Solution for Test: Functions- 3 - Question 1

Test: Functions- 3 - Question 2

If f(x) is an even function, then the graph y = f(x) will be symmetrical about

Detailed Solution for Test: Functions- 3 - Question 2

y — axis by definition.

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Test: Functions- 3 - Question 3

The function f(x) = x2 + 4x + 4 is

Detailed Solution for Test: Functions- 3 - Question 3

Given: f(x) = x2 + 4x + 4

Replace x by -x,

⇒ f(-x) = (-x)2 + 4(-x) + 4

= x2 - 4x + 4                       (∵ (-x)2 = x2)

⇒ f(-x) ≠ ± f(x)

Hence function is neither odd nor even.

Test: Functions- 3 - Question 4

Find the minimum value of the function fix) = log2 (x2 - 2x + 5).

Detailed Solution for Test: Functions- 3 - Question 4

The minimum value of the function would occur at the minimum value of (x2 - 2x + 5) as this quadratic function has imaginary roots.

Thus, minimum value of the argument of the log is 4. So minimum value of the function is log2 4 = 2.

Test: Functions- 3 - Question 5

Which of the following is an even function?

Detailed Solution for Test: Functions- 3 - Question 5

x–8 is even since f(x) = f(–x) in this case.

Test: Functions- 3 - Question 6

For what value of x, x2 + 10x + 11 will give the minimum value?

Detailed Solution for Test: Functions- 3 - Question 6

dy/dx = 2x + 10 = 0 fi x = –5.

Test: Functions- 3 - Question 7

Find the maximum value of the function 1/(x2 – 3x + 2).

Detailed Solution for Test: Functions- 3 - Question 7

Since the denominator x2 – 3x + 2 has real roots, the maximum value would be infinity.

Test: Functions- 3 - Question 8

Read the instructions below and solve.
f(x) = f(x – 2) – f(x – 1), x is a natural number
f(1) = 0, f(2) = 1

The value of f(8) is

Detailed Solution for Test: Functions- 3 - Question 8

f(1) = 0, f(2) = 1,
f(3) = f(1) – f(2) = –1
f(4) = f(2) – f(3) = 2
f(5) = f(3) – f(4) = –3
f(6) = f(4) – f(5) = 5
f(7) = f(5) – f(6) = –8
f(8) = f(6) – f(7) = 13
f(9) = f(7) – f(8) = –21

13

Test: Functions- 3 - Question 9

Read the instructions below and solve.
f(x) = f(x – 2) – f(x – 1), x is a natural number
f(1) = 0, f(2) = 1

What will be the domain of the definition of the function f(x) = 8–xC 5–x for positive values of x?

Detailed Solution for Test: Functions- 3 - Question 9

f(1) = 0, f(2) = 1,
f(3) = f(1) – f(2) = –1
f(4) = f(2) – f(3) = 2
f(5) = f(3) – f(4) = –3
f(6) = f(4) – f(5) = 5
f(7) = f(5) – f(6) = –8
f(8) = f(6) – f(7) = 13
f(9) = f(7) – f(8) = –21

For any nCr, n should be positive and r ≥ 0.
Thus, for positive x, 5 – x ≥ 0
fi x = 1, 2, 3, 4, 5.

Test: Functions- 3 - Question 10

Ajesh saves Rs 50,000 every year and deposits the money in a bank at compound interest of 10%(compunded annually).What would be his total saving at the end of the 5th year?

Detailed Solution for Test: Functions- 3 - Question 10

 

At the end of the 1st year, he will get Rs 50000, it will give him interest for 4 years compounded annually
Hence at the end of 5 years, this amount will become 50000(1.1)4
Similarly, the amount deposited in the 2nd year will give interest for 3 years. Hence it will become 50000(1.1)3
Similarly, we can calculate for the remaining years.
The total saving at the end of the 5th year would be a GP, given by
Net saving = 50000(1.1)+  50000(1.1)3  ..... 50000
Thus net saving = =  Rs 3,05,255

Test: Functions- 3 - Question 11

Define the following functions:
(a) (a M b) = a – b (b) (a D b) = a + b
(c) (a H b) = (ab) (d) (a P b) = a/b

Q.

Which of the following functions will represent a2 – b2?

Detailed Solution for Test: Functions- 3 - Question 11

Option a = (a – b) (a + b) = a2 – b2

Test: Functions- 3 - Question 12

Define the following functions:
(a) (a M b) = a – b (b) (a D b) = a + b
(c) (a H b) = (ab) (d) (a P b) = a/b

Q.

What is the value of (3M4H2D4P8M2)?

Detailed Solution for Test: Functions- 3 - Question 12

3 – 4 × 2 + 4/8 – 2 = 3 – 8 + 0.5 – 2 = – 6.5
(using BODMAS rule)

Test: Functions- 3 - Question 13

Define the following functions:
(a) (a M b) = a – b (b) (a D b) = a + b
(c) (a H b) = (ab) (d) (a P b) = a/b

Q.

Which of the four functions defined has the minimum value?

Detailed Solution for Test: Functions- 3 - Question 13

The minimum would depend on the values of a and b. Thus, cannot be determined.

Test: Functions- 3 - Question 14

If 0 < a <1 and 0 < b < 1 and if a < b, which of the following expressions will have the highestvalue?

Detailed Solution for Test: Functions- 3 - Question 14

Again (a + b) or a/b can both be greater than each other depending on the values we take for a and b.
E.g. for a = 0.9 and b = 0.91, a + b > a/b.
For a = 0.1 and b = 0.11, a + b < a/b

Test: Functions- 3 - Question 15

The number of real-valued solutions of the equation 2x+ 2-x = 2 - (x - 2)is:

Detailed Solution for Test: Functions- 3 - Question 15

We notice that the minimum value of the term in the LHS will be greater than or equal to 2 {at x=0; LHS = 2}. However, the term in the RHS is less than or equal to 2 {at x=2; RHS = 2}. The values of x at which both the sides become 2 are distinct; hence, there are zero real-valued solutions to the above equation.

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