Your Answer : (Not Answered)

Correct Answer : B

The lowest percentage is for Arts, 1992.

Compare the four candidates offered:

• Arts 1992: \(\frac{20}{3160} \approx 0.63\%\).
• Arts 1993: \(\frac{24}{3200} = 0.75\%\).
• Others 1994: \(\frac{47}{4440} \approx 1.06\%\).
• Science 1995: \(\frac{120}{7000} \approx 1.71\%\).

Arts in 1992 had a big jump in applications (from 2000 to 3160) while selections actually fell, from 22 to 20, which is why its rate is the lowest in the whole table.

Your Answer : (Not Answered)

Correct Answer : C

The area of S is 32.

S₁ is the rectangle \(-1 \le x \le 3\), \(-5 \le y \le 1\), with area 4 × 6 = 24.

S₂ is bounded by \(y \ge 1\), \(x \le 3\) and \(y \le x + 2\): a triangle with corners (-1, 1), (3, 1) and (3, 5), with area \(\tfrac{1}{2} \times 4 \times 4 = 8\).

The two regions meet only along the segment y = 1, which has no area, so the union has area 24 + 8 = 32. 26 and 28 undercount the triangle, and 34 counts something twice.

Your Answer : (Not Answered)

Correct Answer : B

\[ \bar{x} = \frac{\sum wx}{\sum w} = \frac{10(2) + 20(3)}{2 + 3} \]

\[ = \frac{80}{5} = 16 \]

The plain average would be 15; the heavier weight on 20 pulls it up.

Your Answer : (Not Answered)

Correct Answer : B

The elements of set A are 1, 2, and the set {3, 4}.

Option A is false because 3 is not an element of A; it's an element of the element {3, 4}.

Option B is true because 1 and 2 are elements of A, so the set containing them, {1, 2}, is a subset of A.

Option C is false because {3, 4} is an element of A, not a subset. For it to be a subset, 3 and 4 would have to be elements of A themselves.

Option D is false for the same reason as A.

Your Answer : (Not Answered)

Correct Answer : C

In each suit, there are 9 cards that are not face cards and ace.

Hence, there will be a total of 18 cards in a deck which are black and are not face cards and ace.

We know that, Probability of an event E, P (E) =number of favourable outcomes/total number of outcomes

Required probability is 18/52 = 9/26.

Your Answer : (Not Answered)

Correct Answer : A

There are ten animals in all. "At least one cow" is easiest through the complement.

\[ \text{total} = {}^{10}C_{4} = 210 \]

\[ \text{no cow} = {}^{4}C_{4} = 1 \]

\[ 210 - 1 = 209 \]

With only four buffalos there is exactly one all-buffalo selection, which is what makes the complement so small.

Your Answer : (Not Answered)

Correct Answer : C

A cuboid has three pairs of identical faces.

\[ \text{TSA} = 2(lb + bh + hl) \]

\[ = 2(16 \times 14 + 14 \times 7 + 7 \times 16) \]

\[ = 2(224 + 98 + 112) = 2 \times 434 = 868 \text{ m}^{2} \]

The volume, a different quantity, would be \( 16 \times 14 \times 7 = 1568 \) m³.

Your Answer : (Not Answered)

Correct Answer : A

Volume needs the perpendicular height, not the slant height, so find it by Pythagoras first.

\[ h = \sqrt{l^{2} - r^{2}} = \sqrt{5^{2} - 4^{2}} = \sqrt{9} = 3 \text{ cm} \]

\[ V = \frac{1}{3}\pi r^{2} h = \frac{1}{3}\pi (4)^{2}(3) = \frac{1}{3}\pi (16)(3) = 16\pi \text{ cm}^{3} \]

Using the slant height of 5 in place of \( h \) would give \( \tfrac{80}{3}\pi \) - the standard slip in every cone question that supplies \( l \) rather than \( h \).

Your Answer : (Not Answered)

Correct Answer : D

Let \( x \) litres of the Rs. 40 oil be mixed with 240 litres of the Rs. 60 oil.

\[ \frac{40x + 60(240)}{x + 240} = 52 \]

\[ 40x + 14{,}400 = 52x + 12{,}480 \]

\[ 1920 = 12x \quad\Longrightarrow\quad x = 160 \text{ litres} \]

Alligation confirms it: \( \tfrac{x}{240} = \tfrac{60-52}{52-40} = \tfrac{8}{12} = \tfrac{2}{3} \), and \( \tfrac{2}{3} \times 240 = 160 \).

Your Answer : (Not Answered)

Correct Answer : A

The key treats this inference as definitely true.

The paragraph calls for innovative and sustainable waste minimization techniques and complains of obsolete technology and poor opportunities for recycling, which together point to waste handling that needs modernizing. The key takes the statement as following directly.

The paragraph speaks of small pesticide units and not of India's waste management as a whole, so a stricter reading would call the inference only probably true. The key does not.

Your Answer : (Not Answered)

Correct Answer : C

The opinion of the author of this statement is not clear from his words. It is sure that he is either favourable or against such an action of the Prime Minister. Hence, either (I) or (II) but not both, is an assumption.

Your Answer : (Not Answered)

Correct Answer : E

Correct answer: P, N, A, L

Filling the blanks gives P < N < A > L, from which A > N > P and therefore A > P. The expression asked for is one making A < P definitely false, and establishing the opposite relation is what does that - leaving the two unrelated would make it undetermined rather than false.

Your Answer : (Not Answered)

Correct Answer : D

The statement that is not true is that dried yellow beans of the khejri are stored and used for cooking round the year.

What Rajasthan dries and stores for cooking is sangri, the green, unripe pods of the khejri (Prosopis cineraria), which are cooked as a vegetable through the year, famously in ker-sangri. Yellow beans are not the stored food.

The other statements are accepted. The ripe, dried pods, called khokha, have a sweetish pulp and are eaten, especially by children. Khejri is the most dominant tree of the arid west, and it was declared the state tree of Rajasthan in 1983, the year the option gives as 1982-83.

Your Answer : (Not Answered)

Correct Answer : C

The Battle of Plassey (23 June 1757) was fought between Siraj ud-Daulah, the Nawab of Bengal, and Robert Clive of the East India Company. Clive had won over Mir Jafar, the Nawab's commander, who stood aside with a large part of the army, and this made the Company's victory easy. Mir Jafar was therefore not an opponent of Clive in the battle, which rules out the second option. Shuja-ud-Daulah, the Nawab of Awadh, and Hector Munro, the Company commander, belong to the Battle of Buxar (1764), so the first and fourth options mix the two battles.

Your Answer : (Not Answered)

Correct Answer : A

Movements in response to light are shown by flowering plants.

Phototropism bends the shoot towards light; the sunflower head tracking the sun and the leaves of the prayer plant folding at dusk are other examples. Such movements need the differential growth or turgor changes that the higher plants possess.

Your Answer : (Not Answered)

Correct Answer : B

Sulphuric acid is used in refining crude petroleum, in the treating stages that remove sulphur compounds, unsaturated hydrocarbons and gums from the distilled fractions.

The separation of the crude into fractions is done by distillation; the acid treatment is what cleans those fractions up afterwards.

Your Answer : (Not Answered)

Correct Answer : A

M. Fathima Beevi was the first woman judge of the Supreme Court.

She was appointed in 1989, thirty-nine years after the Court was established, and later served as Governor of Tamil Nadu. Anna Chandy was the first woman High Court judge, in 1959.

Your Answer : (Not Answered)

Correct Answer : B

The National Science Centre is at Delhi.

Opened in 1992 near Pragati Maidan, it is a museum of the National Council of Science Museums, with galleries on the human body, prehistoric life and India's heritage in science.

Your Answer : (Not Answered)

Correct Answer : A

He ruled Magadha.

Bimbisara of the Haryanka line ruled from about 544 to 492 BCE, annexed Anga, and built the strength of Magadha by marriage alliances with Kosala, Vaishali and Madra. He was a contemporary and patron of both the Buddha and Mahavira.

Your Answer : (Not Answered)

Correct Answer : B

The divergence contracts the operator with the field and returns a scalar rate of outflow per unit volume. The curl and the gradient both return vectors, and the curl of a gradient is a vector too, albeit the zero vector. Keeping track of which operations change the rank is what stops ill-formed identities being written