Your Answer : (Not Answered)

Correct Answer : C

As printed, the smallest number is 0.33.

Leading zeros do not change the value of a whole number: 007 is 7 and 002 is 2. So the four numbers are 7, 0.80, 0.33 and 2, and the only ones below 1 are the two decimals. Of these, 0.33 is less than 0.80.

The trap is reading 007 and 002 as decimals; neither has a decimal point, so both are larger than 0.80.

Your Answer : (Not Answered)

Correct Answer : B

The ratio is 1 : 1.

In case M, four circles fill the 1 cm square in a 2 by 2 grid, so each has diameter 1/2 cm and radius 1/4 cm. In case N, nine circles fill it in a 3 by 3 grid, so each has radius 1/6 cm. The shaded areas are:

\[ \begin{aligned} M: \; 4 \times \pi \left(\tfrac{1}{4}\right)^{2} &= \tfrac{\pi}{4} \\ N: \; 9 \times \pi \left(\tfrac{1}{6}\right)^{2} &= \tfrac{\pi}{4} \end{aligned} \]

Both unshaded areas are therefore \(1 - \pi/4\) square cm, and the ratio is 1 : 1.

In general, \(n^{2}\) touching circles in an \(n\) by \(n\) grid always cover \(\pi/4\) of the square, whatever \(n\) is. The ratios 2 : 3 and 3 : 2 come from comparing the numbers of circles, 4 and 9, or their rows, instead of their areas.

Your Answer : (Not Answered)

Correct Answer : A

Let C be the set of people who like cheese and A be the set of people who like apples.

n(C) = 63, n(A) = 76. We are looking for n(C ∩ A) = x.

The value of x (the intersection) must be less than or equal to the smaller of the two individual percentages. So, x ≤ 63.

We also know n(C ∪ A) = n(C) + n(A) - n(C ∩ A). The maximum value for the union is 100% (everyone). So, \(100 \ge 63 + 76 - x \Rightarrow 100 \ge 139 - x \Rightarrow x \ge 39\).

Combining the two inequalities, we get 39 ≤ x ≤ 63.

Your Answer : (Not Answered)

Correct Answer : A

An integral curve is a curve whose tangent at every point matches the direction the differential equation prescribes there - that is, a particular solution drawn in the plane.

The family of all such curves fills the direction field, and an initial condition picks out one of them.

Your Answer : (Not Answered)

Correct Answer : B

In these problems the two runners are compared by the distances they cover in the same time, so their speeds are in the ratio of those distances.

\[ A\,100 : B\,80, \qquad A\,100 : C\,72 \]

\[ B : C = 80 : 72 \]

In a game of 100, when B scores 100:

\[ C = 100 \times \frac{72}{80} = 90 \]

\[ \text{B can give C} = 100 - 90 = 10 \text{ points} \]

Your Answer : (Not Answered)

Correct Answer : A

For cones of equal height the volume \( \tfrac{1}{3}\pi r^{2}h \) varies as \( r^{2} \), so the height cancels from the ratio.

\[ \frac{V_{1}}{V_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{3^{2}}{5^{2}} = \frac{9}{25} \]

The ratio is \( 9 : 25 \). Carrying the radii through unsquared would give \( 3 : 5 \), which is the shape of the second distractor.

Your Answer : (Not Answered)

Correct Answer : C

\[ \text{SI} = \frac{P \times R \times T}{100} \]

The rate changes with the period, so add the three slabs. Beyond five years leaves \( 9 - 5 = 4 \) years at 14%.

\[ P\left(\frac{6 \times 2}{100} + \frac{9 \times 3}{100} + \frac{14 \times 4}{100}\right) = 11400 \]

\[ P(0.12 + 0.27 + 0.56) = 0.95P = 11400 \]

\[ P = \text{Rs. } 12{,}000 \]

The final slab runs for four years, not nine - "beyond five years" means the remainder of the nine.

Your Answer : (Not Answered)

Correct Answer : B

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]

\[ 45 \text{ km/hr} = 12.5 \text{ m/s} \]

Crossing a pole covers only the train's own length:

\[ L = 12.5 \times 12 = 150 \text{ m} \]

Crossing a bridge covers the train plus the bridge:

\[ t = \frac{150 + 600}{12.5} = \frac{750}{12.5} = 60 \text{ seconds} \]

Your Answer : (Not Answered)

Correct Answer : E

The shopkeeper tells the customer the merits and demerits of various products, thus making it easy for him to choose. So, I is implicit. Since the shopkeeper stresses on buying B because it is based on international technology, so II is also implicit.

Your Answer : (Not Answered)

Correct Answer : C

Correct answer: 2,4,1,3

The words run in order of widening administrative units: Village → Town → District → State.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: 55

The gaps are 11, 11, 11, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is eleven times its position: position 1 gives 11 and position 4 gives 44. The next position is 5, which gives 55. As a check, the same rule applied to the earlier positions reproduces 11, 22, 33, 44 exactly, so it accounts for every term shown and not merely the last. A linear rule in the position number produces a constant difference, so the two descriptions are the same thing seen differently.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: 20 km.

The northward and southward legs cancel - 20 km north and then 20 km south - while the sideways moves come to \( 40 \) west and \( 20 \) east. He finishes 20 km from where he began.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: Sister-in-law

C is A’s child and C is D’s sister, so D is A’s child too - and since D is B’s son, B is the children’s mother and therefore A’s wife. E is A’s brother, so B is E’s sister-in-law.

Your Answer : (Not Answered)

Correct Answer : A

The temple was built by Maharaja Dhanya Manikya.

The Tripura Sundari (Tripureshwari) temple at Udaipur, the old capital of the Manikya kings, was built by Maharaja Dhanya Manikya in 1501. It stands on a small hillock shaped like the back of a tortoise and is counted among the 51 Shakti Peethas, which is why the place is known as Matabari.

Dharma Manikya, Gobinda Manikya and Dev Manikya were other rulers of the same Manikya dynasty, but the building of the Tripureshwari temple is credited to Dhanya Manikya.

Your Answer : (Not Answered)

Correct Answer : B

The battle is the Battle of Ghaghra, fought in May 1529.

After defeating Ibrahim Lodi at Panipat (1526) and Rana Sanga at Khanwa (1527), Babur faced the Afghan chiefs of the east, who had rallied behind Mahmud Lodi, Ibrahim's brother, along with the ruler of Bengal. Babur defeated them on the Ghaghra river near its junction with the Ganga in Bihar, his last major battle.

The battles of Tarain (1191 and 1192) were fought between Prithviraj Chauhan and Muhammad Ghori. Haldighati (1576) was between Maharana Pratap and Akbar's army. No Battle of Ajmer involves Babur and Mahmud Lodi.

Your Answer : (Not Answered)

Correct Answer : A

The answer is reddish brown, green, colourless, orange.

The first three entries settle it. Turmeric is yellow and turns reddish brown in a base (A). China rose turns dark pink (magenta) in an acid and green in a base (B). Phenolphthalein is colourless in an acid and pink in a base (C). Only the first option has all three.

The table's methyl orange row is not accurate as printed: methyl orange is red in acid and yellow in base. But no other option fits A, B and C, so the first option is the answer. The others give turmeric as yellow in base or phenolphthalein as orange or pink in acid, which are wrong.

Your Answer : (Not Answered)

Correct Answer : A

The Essential Commodities Act was enacted in 1955.

It empowers government to control the production, supply, distribution and price of commodities declared essential, and is the statute behind stock limits and the public distribution system.

Your Answer : (Not Answered)

Correct Answer : D

RAM is primary storage.

Primary storage is the memory the processor can address directly and read in nanoseconds. It is volatile, losing its contents when power is removed, which is why work must be saved to secondary storage.

Your Answer : (Not Answered)

Correct Answer : D

All of these are electronic payment systems: credit cards, digital wallets and electronic cheques.

Card payment is much the largest by value; digital wallets store credentials for quick payment; and electronic cheques carry an instruction to debit an account, with a digital signature in place of a written one.

Your Answer : (Not Answered)

Correct Answer : D

The Golden Temple is in India.

Harmandir Sahib stands at Amritsar in Punjab, founded by Guru Ram Das and completed by Guru Arjan, who installed the Adi Granth in it in 1604.