Correct Answer: AP = MP

Solution : The correct option is AP = MP.

The point where MP intersects AP is also where AP is at its greatest. When MP drops below AP, AP ceases to increase and instead begins to decrease. Consequently, it is true to say that AP is at its highest when MP and AP are both equal.

Correct Answer: 90°

Solution : Given: The ratio of the three sides of the triangle is 5 : 13 : 12.
The ratio of the three sides of the triangle forms Pythagoras triplets.
Let the sides of the triangle be $x$.
According to the question,
$(5x)^2+(12x)^2$
= $25x^2+144x^2$
= $169x^2$
= $(13x)^2$
So, the ratio of the three sides of the triangle forms Pythagoras triplets.
Therefore, the triangle is a right-angled triangle.
Thus, the largest angle of the triangle = 90°.
Hence, the correct answer is 90°.

Correct Answer: RSPQ

Solution : The correct choice is the second option: RSPQ.

Explanation: The sentences are logically arranged to provide a coherent paragraph. It begins with an introduction of Jason (R) to set the context, followed by a description of his personality (S). Then, it introduces the fact that Jason is well aware of the role he and his people play in keeping Shivsagar Lake beautiful and ecologically thriving (P). Finally, it concludes with the challenge he faces due to the urban idea of conservation, which often seeks to keep traditional dwellers out (Q).

Correct Answer: WVTS

Solution : Given:
EDBA, KJHG, QPNM, ?

First part → EDBA → E – 1 = D; D – 2 = B; B – 1 = A

Second part → KJHG → K – 1 = J; J – 2 = H; H – 1 = G
A (fourth letter of the first part) + 10 = K (first letter of the second part)

Third part → QPNM → Q – 1 = P; P – 2 = N; N – 1 = M
G (fourth letter of the second part) + 10 = Q (first letter of the third part)

Fourth part → WVTS → W – 1 = V; V – 2 = T; T – 1 = S
M (fourth letter of the third part) + 10 = W (first letter of the fourth part)

Therefore, the series becomes → EDBA, KJHG, QPNM, WVTS

Hence, first option is correct.

Correct Answer: (i), (ii) and (iii)

Solution : The incorrect statements are (i), (ii) and (iii).

India 2020: A Vision for the New Millennium was written by former President A. P. J. Abdul Kalam. The author of "The Great Indian Novel" is Shashi Tharoor. It is a satirical novel that was published in 1989. My country, my life book, was written by Lal Krishna Advani, an Indian politician who was also the deputy PM of India from 2000 to 2004.

Correct Answer: Kerala

Solution : The correct option is Kerala.

The first-of-a-kind state-level bird atlas is in Kerala. It covers several species found in Kerala. It has details of the rare species and the common species found in Kerala. Kerala is also known as "God's Own Country." It is also famous for its spices, beaches, and wildlife sanctuaries.

Correct Answer: The resistance of a wire depends on the length and cross-section of the wire.

Solution : The correct answer is The resistance of a wire depends on the length and cross-section of the wire.

The resistance of a conductor is determined by the following characteristics.

• the length of the conductor
• the cross-sectional area of the conductor
• the character or resistance of the substance.

Correct Answer: 0

Solution : Given: $x^2+\frac{1}{x^2}=2$
We know that the algebraic identity is $(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-2$
Substitute the value of $x^2+\frac{1}{x^2}=2$ in the above expression, we get,
$(x-\frac{1}{x})^2=2-2$
⇒ $(x-\frac{1}{x})^2=0$
⇒ $(x-\frac{1}{x})=0$
Hence, the correct answer is 0.

Correct Answer: (142, 83, 69)

Solution : Given:
(168, 35, 143); (182, 65, 127)

In the given sets, subtract the third number from the first number and then add 10.
(168, 35, 143)→168 – 143 = 25; 25 + 10 = 35
(182, 65, 127)→182 – 127 = 55; 55 + 10 = 65
Let's check the options –
First option: (142, 83, 69)→142 – 69 = 73; 73 + 10 = 83
Second option: (253, 99, 154)→253 – 154 = 99; 99 + 10 = 109 ≠ 99
Third option: (203, 89, 117)→203 – 117 = 86; 86 + 10 = 96 ≠ 89
Fourth option: (159, 62, 87)→159 – 87 = 72; 72 + 10 = 82 ≠ 62

So, only the first option follows the same pattern as followed by the given set of numbers. Hence, the first option is correct.

Correct Answer: (3)

Solution : The error lies in the third part of the sentence. 

The comparative degree "better" is employed to compare two things. In this particular sentence, it compares the climates of two places. When comparing one thing to another, it's appropriate to use "that of" for singular comparison after the comparative degree of the adjective in the sentence.

So, the correct sentence should be: "The climate of Mumbai is better than that of Hyderabad."