Mathematics - Class 11 Mock Test 9

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Question 1 of 10

1. Which of the following compound statement has both true component statements?

A prime number is divisible by 2 and odd

All integers are positive and divisible by 2

100 is divisible by 2 and 5

Two and two makes four or five

Question 1 of 10

Question 2 of 10

2. Which of the following limits does not yield 1?

\(\lim\limits_{x \rightarrow 0}\frac{⁡tan x}{cot x}\)

\(\lim\limits_{x \rightarrow 0}\) x cosec x

\(\lim\limits_{x \rightarrow 0}(\frac{1}{e^x}+cos⁡ x)\)

\(\lim\limits_{x \rightarrow 0}\frac{⁡sin x}{x}\)

Question 2 of 10

Question 3 of 10

3. f(x) is a polynomial of degree 4, vanishes at x = -1 and has local minimum/maximum at x = 1, x = 2, and x = 3. If, _-2∫² f(x) dx = -1348/15. Then what is the value of f(x)?

x⁴ – 8x³ + 22x² – 24x – 55

x⁴ – 8x³ + 22x² – 24x + 55

Data not sufficient

x⁴ – 8x³ – 22x² – 24x – 55

Question 3 of 10

Question 4 of 10

4. If p then q means if p is ________ then q must be ______________

true, false

false, false

false, true

true, true

Question 4 of 10

Question 5 of 10

5. Is Rolle’s theorem valid for f(x) = x² - 3x + 4 in the interval [1, 2]?

Yes

Data not sufficient

Depends on x

Question 5 of 10

Question 6 of 10

6. The function y = f(x) is represented parametrically by x = t⁵ - 5t³ – 20t + 7 and y = 4t³ – 3t² – 18t + 3 (-2 < t < 2). At which point does y = f(x) has a minimum value?

t = 3/2

t = -1

t = 0

t = 1/2

Question 6 of 10

Question 7 of 10

7. A sentence is called statement if it is __________________

always false

always true

both true and false

either true or false but not both

Question 7 of 10

Question 8 of 10

8. “All integers are positive or negative”. Is this ‘or’ is inclusive?

True

False

Question 8 of 10

Question 9 of 10

9. Identify the type of Or and whether the statement “2 is a prime number or even number” is true or not?

Inclusive Or, true

Exclusive Or, false

Exclusive Or, true

Inclusive Or, false

Question 9 of 10

Question 10 of 10

10. What is the value of \(\frac{d}{dx}(\frac{sec⁡x}{cosec\, x \,tan⁡x}\))?

sin ⁡x

cos ⁡x

Question 10 of 10