Correct Answer: D. Organic Evolution

Correct Answer: (A) at 6 in the evening yesterday

Correct Answer: D. post-purchase decision

Correct Answer: c) Vegetables

Explanation

(a) \(p = \begin{pmatrix} 3 \\ -1 \end{pmatrix} = 3i - j ; q = \begin{pmatrix} 3 \\ 4 \end{pmatrix} = 3i + 4j\)

Let the angle be \(\theta\),

\(p . q = |p||q| \cos \theta\)

\((3i - j).(3i + 4j) = 9 - 4 = 5\)

\(|3i - j| = \sqrt{3^{2} + (-1)^{2}} = \sqrt{10}\)

\(|3i + 4j| = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5\)

\(5 = (\sqrt{10})(5) \cos \theta \implies \cos \theta = \frac{\sqrt{10}}{10} = 0.3162\)

\(\theta = \cos^{-1} 0.3162 = 71.567° \approxeq 71.6°\)

(b)

(i) Resolving the forces along the x and y axes, we obtain

Resultant (R) = (10i + 20j) N.

Magnitude = \(\sqrt{10^{2} + 20^{2}} = \sqrt{500}\)

= \(10\sqrt{5} \approxeq 22.4 N\)

(ii) Direction : \(\tan \theta = \frac{20}{10} = 2\)

\(\theta = \tan^{-1} 2 = 63.4°\).

Correct Answer: C. specialization

Correct Answer: B) The same product of the same quality is sold for different prices to different buyers

Explanation

This question is asking about price discrimination. Price discrimination is when a company charges different prices for the same product to different groups of customers. The question is asking which of the options is an example of price discrimination.

Option A suggests that the same product of the same quality is sold for different prices to the same buyer. This is not an example of price discrimination, because the buyer is still paying the same price for the same product.

Option B is the correct answer. It suggests that the same product of the same quality is sold for different prices to different buyers. This is an example of price discrimination because the company is charging different prices to different groups of customers.

Option C suggests that different products are sold for the same price to the same buyers. This is not an example of price discrimination because the buyers are still paying the same price for different products.

Option D suggests that different products are sold for the same price to different buyers. This is also not an example of price discrimination because the buyers are still paying the same price for the same product.

In summary, the correct answer to this question is option B, which states that price discrimination exists when the same product of the same quality is sold for different prices to different buyers.

Correct Answer: D. Both I and II are sufficient

Correct Answer: C. lure Jesus Christ from His mission

Explanation

(a) Range = \(\frac{U^2 sin 2\theta}{g}\)

for first attempy, Range = \(\frac{8^2 \sin 60}{10} = \frac{64 x\times 0.8660}{10}\)

= 5.5424m

for second attemt; Range = \(\frac{8^2 \sin 90}{10} = \frac{64 \times 1}{10}\)

= 6.4m

gain 6.40 - 5.54 = 0.8576m

(b)(i) Hooke's law states that provided the limit of proportionality is not exceeded, the force is proportional to the extension in an elastic material.

(ii) Description: Suspend the spiral spring from a rigid support with a pointer attached at the free end. Suspend a stretching weight from the free end, and note the position of the pointer. Suspend a known mass, note the new position and determine the extension. Repeat the experiment using various known masses. Repeat the above procedure while unloading and determine mean extension. Plot a graph of load against mean extension. A straight line graph through the origin verifies Hooke's law.

Precautions: (i) Loading beyond elastic limit should be avoided

(ii) Pointer to be rigidly attached to the free end and made perpendicular to the spring.

(iii) Avoid parallax error while taking readings.

(c) mg = Ke, m = total mass If m = mass of scale pan then;

(m + 40)g = 1.8k-----------(i)

(m + 60) = 2.05k --------- (ii)

Dividing (i) by (ii) \(\frac{m + 40}{m + 60} = \frac{1.8}{2.05}\)

2.05(m + 40) = 1.8 (m + 60)

M = \(\frac{26}{0.25}\) = 104gm