Mathematics - Class 12 Mock Test 4

10%

Question 1 of 10

1. If log₁₀3 = 0.4771 and log₁₀e = 0.4343, then what is the value of log₁₀30.5?

1.484

1.4

1.5

1.43

Question 1 of 10

Question 2 of 10

2. If y=log⁡(2x³), find \(\frac{d^2 y}{dx^2}\).

\(\frac{2}{x^2}\)

-\(\frac{3}{x^2}\)

-\(\frac{2}{x^2}\)

\(\frac{3}{x^2}\)

Question 2 of 10

Question 3 of 10

3. Find \(\frac{dy}{dx}\), if x=3a² cos²⁡θ and y=4a sin²⁡θ.

\(\frac{4}{3a}\)

-\(\frac{3}{4a}\)

\(\frac{3}{4a}\)

-\(\frac{4}{3a}\)

Question 3 of 10

Question 4 of 10

4. The edge of a cube is increasing at a rate of 7 cm/s. Find the rate of change of area of the cube when x=6 cm.

578 cm²/s

498 cm²/s

688 cm²/s

504 cm²/s

Question 4 of 10

Question 5 of 10

5. Find the interval in which function f(x) = x² – 4x + 5 is increasing.

(3, ∞)

(2, ∞)

(-∞, ∞)

(-∞, 2)

Question 5 of 10

Question 6 of 10

6. Find the interval in which function f(x) = sinx+cosx, 0 ≤ x ≤ 2π is decreasing.

(π/4, 5π/4)

(π/4, -5π/4)

(-π/4, 5π/4)

(-π/4, π/4)

Question 6 of 10

Question 7 of 10

7. The total cost N(x) in rupees, associated with the production of x units of an item is given by N(x)=0.06x³-0.01x²+10x-43. Find the marginal cost when 5 units are produced.

Rs. 14.4

Rs. 144.00

Rs. 56.2

Rs. 1.44

Question 7 of 10

Question 8 of 10

8. Is the function f(x) = 3x+10 is increasing on R?

True

False

Question 8 of 10

Question 9 of 10

9. The length of a side of a cube is 10cm; if an error of 0.05cm is made in measuring the side, then what is the value of approximate error in calculating its volume?

15.5 cu cm

16 cu cm

15 cu cm

14 cu cm

Question 9 of 10

Question 10 of 10

10. What will be the estimate error made in calculating the area of the triangle ABC in which the sides a and b are measured accurately as 25 cm and 16 cm, while the angle C is measured as 60° but (1/2)° in error?

53/63 sq cm

Data not sufficient

55/63 sq cm

55/67 sq cm

Question 10 of 10