RRB JE 31st May 2019 Shift-1

For the following questions answer them individually

Express the the following expression in terms of partial fraction :
$$ \frac{X}{(X+1)^2} $$ 

Three 2 V cells are connected in series and used as a battery in a circuit. What is the potential difference at the terminals of the battery?

Which colour among the seven colours of the white light gets most deviated after dispersion of light through a glass prism?

Evaluate: $$ \left(\frac{ sin  47^\circ  } {cos  43^\circ}\right)^2   + \left(\frac{ cos  43^\circ  } {sin  47^\circ}\right)^2 -  4cos^2 45^\circ   $$

Pooja's age 4 years back and Deepa's age after 4 years are equal. The ratio of Pooja's age 4 years hence and Deepa's age 4 years before is 3 : 1. What is the ratio of their present ages?

Vijayan started walking towards south. After walking 15 m, he turned left and walked 15 m. He again turned left and walked 15 m. How far and in which direction is he from his starting point?

Which of the following form a set of homologous series?

If 'sti nro kti' stands for 'clouds pour down', 'nro bsi mit' stands for 'down he goes', and 'bsi nro zpi' stands for 'died down he', which word would mean 'goes'?

Two tables are bought for Rs.2000 by a person. He sells them later, one at a loss of 5%, the other at a gain of 5% thereby incurring a loss of Rs.20. What are the cost prices of the two tables?

A certain sum invested for T years at 10% per annum Simple Interest amounts to Rs.400. The amount gets halved when the interest comes down to 4% per annum, the principal and time being the same. What is the principal and value of T?

The frictional force on an object in a fluid depends on what?

After completing a work together in 2 days, P and Q received Rs.1200 and Rs.400 respectively as wages. In how many days will Q alone complete the work?

In this question, a statement is given followed by two conclusions. Choose the conclusion(s) which best fit(s) logically.
Statement:
Video-libraries are flourishing very much these days.
Conclusions:
I. People in general have got a video craze.
II. It is much cheaper to see as many movies as one likes on videos rather than going to the cinema hall.

A sum of money amounts to Rs.9800 in 5 years and Rs.12005 in 8 years at the same rate of simple interest. What is the rate of interest?

Mohan started from point A and proceeded 7 km straight towards east, then he turned left and proceeded straight for a distance of 10 km. He then turned left again and proceeded straight for a distance of 6 km, and then turned left again and proceeded straight for another 10 km. How far and in which direction is he from the point A?

Two varieties of rice each costing Rs.50 per kg and Rs.60 per kg respectively are mixed in some ratio, and the mixed rice is sold at Rs.70 per kg, so as to get 20% profit. What is the ratio in which the two varieties are mixed?

In this question, two statements are given followed by two conclusions. Choose the conclusion(s) which best fit(s) logically.
Statements:
1) All colours are pants.
2) All pants are brushes.
Conclusions:
I. Some brushes are pants.
II. Some brushes are colours.

Simplify: $$ \frac{sin  \theta - 2 sin ^ 3 \theta}{ 2  cos ^3 \theta  -  cos \theta} $$

The base of a right pyramid is a square of side 24 cm and height of the pyramid is 16 cm. What is its lateral surface area?

Find the area of a parallelogram with base 48 cm and height 32 cm.

P can complete a work in 6 days. Working with the help of Q, the job is completed in 7 days. If P starts the work and P and Q work on alternate days, in how many days can Q alone complete the job?

A circular wire of radius 7cm is bent to form a rectangle whose sides are in the ratio 4 : 7 what is the area of the rectangle so formed?

When the digits of a two-digit number are reversed, the value of the number is increased by 45. The sum of the digits is 11. What is the original number?

Read the following information carefully and answer the question given below.

Eight captains of different volleyball teams—Iran, Germany, Romania, Serbia, Tunisia, China, Brazil and Cuba are sitting around a circular table and are facing the centre, but not necessarily in the same order. Romanian captain sits third to the left of the Tunisian captain. Only two people sit between the Iran captain and Brazil captain. Neither the Iran captain nor Brazil captain is an immediate neighbour of the Romanian captain. The captain of Cuba sits second to the right of the China captain. China captain is not an immediate neighbour of the Romanian captain. The Iran captain sits third to the left of the Romanian captain. Captains of Serbia and Germany are not immediate neighbours. Serbia captain sits third to the left of the China captain.

How many persons are sitting between the captain of China and Romania in clockwise direction?

To row a certain distance upstream and downstreamtakes $$t_1$$ hours and $$t_2$$ hours respectively and speed of stream is 'y' km/h. Find speed
in still water.

Which of the following statements is FALSE?
1. The object is always placed to the left of the spherical mirror.
2. All distances parallel to principal axis are measured from pole of the mirror.
3. All distances measured to the right of the origin are taken as negative.
4. Distances measured perpendicular to and above the principal axis are taken as positive.

In this question, a statement is given followed by four conclusions. Choose the conclusion(s) which best fit(s) logically.

Statement:
In the university examination, most of the candidates take exam in Hindi medium.
Conclusions:

I. Some candidates take exam in Hindi.
II. Most of the candidates appeared for the examination are from Hindi medium.
III. In this examination no candidate writes answers in medium other than Hindi.
IV. All the candidates who appear in this examination write answers in Hindi.

What is the name given to the phenomenon of throwing light in various random directions ?

Read the following information carefully and answer the question given below.
Eight students—S, T, U, V, W, X, Y and Z are sitting around a circle facing the center. S is second to the right of Y who is third to the right of T. V is second to the left of X who sits between Y and S. U is not a neighbour of T or W.
Who is to the immediate left of U?

When copper oxide is heated with hydrogen, copper metal and water are formed. What happens to the copper oxide in this reaction?

After spending 30% of his salary, a man had Rs.2100 left. From the remaining amount, he spent 15% on minor repairs. What are his savings?

Find the value of $$ tan^2 60^\circ - 2 tan^2 45^\circ - cot^2 30^\circ + 2 sin^2 30^\circ + 3/4 cosec^2 45^\circ $$

In a two-digit number, the digit in the unit's place is four times the digit in ten's place and sum of the digits is equal to 10. Find the number.

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