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Question : Directions: In the following question, select the missing number of the given series. 4, 6, 8, 10, ?, 14
Option 1: 11
Option 2: 12
Option 3: 14
Option 4: 15
Correct Answer: 12
Solution : Given: 4, 6, 8, 10, ?, 14
Add 2 to the previous number, to obtain the next number in the series – 4 + 2 = 6; 6 + 2 = 8; 8 + 2 = 10, 10 + 2 = 12; 12 + 2
Question : Directions: Dinesh travels from point A, 8 km eastward towards B, turns right and walks 12 km to C, turns again right and walks 4 km to point D, again turns right and travels 8 km to E. From E, he turns left and walks to F, 4 km. Now how far is he from his starting point?
Option 1: 4 km
Option 2: 6 km
Option 3: 8 km
Option 4: 12 km
Correct Answer: 4 km
Solution : Firstly, we will draw the diagram as per the given instructions – Now, we have to find the distance between the starting point and the endpoint.
In the given figure, A is the starting point and F is the finishing point. So, AF is
Question : If $(x+\frac{1}{x})^{2}=3$, then the value of $(x^{3}+\frac{1}{x^{3}})$ is:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: –1
Correct Answer: 0
Solution : Given: $(x+\frac{1}{x})^{2}=3$, Taking square root on both sides, we get $(x+\frac{1}{x})=\sqrt{3}$ Now, Cubing both sides we get $(x+\frac{1}{x})^3=(\sqrt{3})^3$ ⇒ $x^3+\frac{1}{x^3}+3×x×\frac{1}{x}(x+\frac{1}{x})=(3\sqrt{3})$ ⇒ $x^3+\frac{1}{x^3}=3\sqrt{3}–3(x+\frac{1}{x})$ $\because x+\frac{1}{x}=\sqrt{3}$ Thus, $x^3+\frac{1}{x^3}=3\sqrt{3}–3\sqrt{3} = 0$ Hence, the correct answer is 0.
Question : Directions: Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 98 : 7 :: 162 : 9 :: 242 : ?
Option 4: 13
Correct Answer: 11
Solution : Given: 98 : 7 :: 162 : 9 :: 242 : ?
Like, (7)2 × 2 = 49 × 2 = 98 (9)2 × 2 = 81 × 2 = 162 Similarly, (?)2 × 2 = 242 ⇒ (?)2 = 242
Question : A solid cuboid is melted to form several cubes. If the length, breadth and height of a cuboid are 20 cm, 16 cm and 8 cm and the edge of each cube is 4 cm, then the number of cubes is:
Option 1: 50
Option 2: 44
Option 3: 40
Option 4: 48
Correct Answer: 40
Solution : Dimensions of cuboid are 20, 16 and 8 cm. The length of the side of the cube = 4 Volume of cuboid = $l\times b\times h$ Volume of cube = $a^3$ Number of cubes = $\frac{\text{Volume of cuboid}}{\text{Volume of cube}}$ = $\frac{20\times 16\times 8}{4\times4\times4}$ =
Question : In $\triangle ABC, \angle B=90^{\circ}$ and AB : BC = 1 : 2. The value of $\cos A+\tan C$ is:
Option 1: $\frac{5+\sqrt{5}}{2 \sqrt{5}}$
Option 2: $\frac{1+\sqrt{5}}{2 \sqrt{5}}$
Option 3: $\frac{2 \sqrt{5}}{2+\sqrt{5}}$
Option 4: $\frac{2+\sqrt{5}}{2 \sqrt{5}}$
Correct Answer: $\frac{2+\sqrt{5}}{2 \sqrt{5}}$
Solution : In $\triangle ABC, \angle B=90^{\circ}$ AB : BC = 1 : 2 ⇒ $\frac{\text{AB}}{\text{BC}} = \frac{1}{2}$ ⇒ $\frac{\text{AB}}{1} = \frac{\text{BC}}{2}=$ k ⇒ AB = k, BC = 2k Using the Pythagoras theorem, AC$^2$ = BC$^2$ + AB$^2$ = (2k)$^2$ + k$^2$ = 5k$^2$ So,
Question : Directions: Some equations are solved based on a certain system. Find the correct answer for the unsolved equation on that basis. 678 = 366; 567 = 255; 946 = ?
Option 1: 334
Option 2: 499
Option 3: 699
Option 4: 634
Correct Answer: 634
Solution : Given: 678 = 366, 567 = 255, 946 = ?
The numbers on the L.H.S. and R.H.S. of the equation have a difference of 312 in common. Like, 678 = 366→678 – 312 = 366 And, 567 = 255→567 – 312 = 255 Similarly, follow
Question : Comprehension:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
Clean India Mission is one of the most (1) _____ and popular missions to have taken place in India. This mission includes a reward to a state and a city. This encourages every citizen to keep the surroundings clean. This cleanliness campaign was (2) _____ by the Indian government at the national level, (3) _____ all the rural towns and urban cities. Its primary objective is to spread awareness of the importance of cleanliness. Slogans are written on the banners and pictures are painted in a very attractive manner to evoke the feeling of cleanliness. After that, a major objective was to teach citizens to (4) _____ of waste mindfully and to provide basic (5) _____ facilities. For this, wet and dry dustbins are kept by every citizen whether it is home or office. Select the most appropriate option to fill in the blank number 2.
Option 1: governed
Option 2: rehearsed
Option 3: dominated
Option 4: unorganised
Correct Answer: governed
Solution : The correct option will be the second option.
To govern means to legally control a country or its people and be responsible for introducing new laws, organising public services, etc.
Question : M is three times as good a worker as N and together they finish a piece of work in 30 days. In how many days will M alone finish the work?
Option 2: 40
Option 3: 60
Option 4: 45
Solution : Given: M is three times as good as N. Let the efficiency of N and M be $x$ and $3x$ respectively. So, total work $=30×(x+3x)=120x$ units Therefore, the time required by A to finish the work alone = $\frac{120x}{3x}$ = 40 days Hence, the correct
Question : If a certain sum becomes 3 times in 6 years at compound interest, then in how many years, it will become 81 times?
Option 1: 81 years
Option 2: 162 years
Option 3: 27 years
Option 4: 24 years
Correct Answer: 24 years
Solution : By applying the formula: Amount = P[$(1+\frac{r}{100})^n$] where P is principal, $r$ is the rate of interest compounded annually for $n$ years. Let the sum be $x$, then: Amount = $x(1+\frac{r}{100})^6 = 3x$ ⇒ $(1+\frac{r}{100})^6 = \frac{3x}{x}=3$ ⇒ $(1+\frac{r}{100}) =3^\frac{1}{6}$ Now, the sum becomes
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