Mathematics - Class 11 Mock Test 9

10%

Question 1 of 10

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

100 is divisible by 2 and 5

A prime number is divisible by 2 and odd

All integers are positive and divisible by 2

Two and two makes four or five

Question 1 of 10

Question 2 of 10

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

true, false

false, false

false, true

true, true

Question 2 of 10

Question 3 of 10

3. If A (x₁, y₁) and B (x₂, y₂) be two points on the curve y = ax² + bx + c, then as perLagrange's mean value theorem whichof the following is correct?

At least two points where the tangent will be parallel to the chord AB

At least one point C(x₃, y₃) where the tangent will be parallel to the chord AB

At least one point C(x₃, y₃) where the tangent will be overlapping to the chord AB

At least one point C(x₃, y₃) where the tangent will be intersecting the chord AB

Question 3 of 10

Question 4 of 10

4. The compound statement with ‘Or’ is false if ________ of its component statements are __________

all, false

any, true

all, true

any, false

Question 4 of 10

Question 5 of 10

5. Square of a natural number is positive or negative.

False

True

Question 5 of 10

Question 6 of 10

6. What is the number of critical points for f(x) = max(sinx, cosx) for x belonging to (0, 2π)?

Question 6 of 10

Question 7 of 10

7. What is the value of \(\frac{d}{dx}\)(cos²⁡ x tan⁡ x) at x = 1?

-1

-2

Question 7 of 10

Question 8 of 10

8. What will be the value of dy/dx if x = asec²θ and y = atan³θ at θ = π/4?

1/2

1/4

3/4

3/2

Question 8 of 10

Question 9 of 10

9. A sentence is called statement if it is __________________

always true

either true or false but not both

always false

both true and false

Question 9 of 10

Question 10 of 10

10. Let f (x) = (x - a) (x - b) (x - c), a < b < c. Then f'(x) = 0 has two roots. At which interval does these roots belongs?

Both the roots in (b, c)

At least one root in (a, b) and at least one root in (b, c)

Neither in (a, b) nor in (b, c)

Both the roots in (a, b)

Question 10 of 10