IIT Ramaiah SAT April 30 2017 Question Paper

IIT Ramaiah SAT April 30 2017 - Question 1

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The digit in the units place of $$2017^{28} + 28^{2017}$$ is

A

2

B

5

C

9

D

8

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IIT Ramaiah SAT April 30 2017 - Question 2

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Two circles having different radii are touching each other. A common tangent $$\overleftrightarrow{PQ}$$ is touching one circle at $$P$$ and the other at $$Q$$. If $$PQ = 12$$ then the product of their radii is equal to

A

36

B

24

C

12

D

$$\frac{8}{3}$$

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IIT Ramaiah SAT April 30 2017 - Question 3

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If $$a$$, $$b$$, $$c$$ and $$d$$ are four real numbers such that $$a^2 + 2b^2 + 13c^2 + 5d^2 - 2ab + 4bc - 12cd - 6d + 9 = 0$$ then $$2a + b + 11c + 2d$$ is equal to

A

0

B

16

C

$$-28$$

D

2017

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IIT Ramaiah SAT April 30 2017 - Question 4

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On a level ground there is a tree and a building. A girl standing in front of the tree started backing until she could see just the top edge of the building from above the tree top. She marked her place and measured it from the tree and it was $$5\text{ m}$$. If tree height is $$2.8\text{ m}$$, her eyes at a height of $$1.6\text{ m}$$ and distance between the tree and the building is $$30\text{ m}$$, height of the building in meters is

A

$$\frac{20}{3}$$

B

28

C

14

D

10

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IIT Ramaiah SAT April 30 2017 - Question 5

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If $$98765^2 = 9754525225$$ then $$98766^2 =$$ __________

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IIT Ramaiah SAT April 30 2017 - Question 6

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Two chords $$AB$$ and $$CD$$ of a circle are intersecting in a point $$P$$. A relation between the lengths of all the line segments $$PA$$, $$PB$$, $$PC$$ and $$PD$$ is __________

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IIT Ramaiah SAT April 30 2017 - Question 7

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The number of real solutions $$(a, b)$$ of the equation $$\frac{a + b}{a} = \frac{b}{a + b}$$ is __________

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IIT Ramaiah SAT April 30 2017 - Question 8

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$$ABC$$ is an equilateral triangle of side $$a$$ units. Midpoint of the side $$BC$$ is $$D$$. $$D$$ is also the midpoint of the side $$PQ$$ of a rectangle $$PQRS$$ having its side $$PQ$$ along $$BC$$. Also $$P$$ is the midpoint of the line segment $$BD$$. If the vertex $$A$$ of the triangle lies on the side $$RS$$ of the rectangle, the area of the rectangle is __________

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IIT Ramaiah SAT April 30 2017 - Question 9

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If $$a$$ and $$b$$ are two positive integers greater than 20172017 and $$b - a > 4034$$ then there exist at least one pair $$a$$, $$b$$ such that the product $$(a - 2017)(b + 2017)$$ is greater than the product $$(a + 2017)(b - 2017)$$

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IIT Ramaiah SAT April 30 2017 - Question 10

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There is a diagram of a triangle $$ABC$$ right angled at $$A$$ and the perpendicular drawn from $$A$$ onto the side $$BC$$ is meeting the side $$BC$$ in $$D$$. There are exactly two similar triangles in the diagram.

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IIT Ramaiah SAT April 30 2017 - Question 11

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There is at least one system of linear equations $$ax + by = c$$, $$dx + ey = f$$, in variable $$x$$, $$y$$, having exactly 2017 solutions.

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IIT Ramaiah SAT April 30 2017 - Question 12

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$$r_1$$, $$r_2$$ are the radii of two circles passing through the centres of one another. If $$3r_1 + r_2 = 15$$ then $$r_1$$ is equal to $$\frac{15}{4}$$

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IIT Ramaiah SAT April 30 2017 - Question 13

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Write $$2ab^3 + a^2c^2 + b^2c^2 - a^2b^2 - 2abc^2 - b^4$$ as a product of linear factors

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IIT Ramaiah SAT April 30 2017 - Question 14

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$$ABCD$$ is a square of area 64 sq. units. $$AEFG$$ is another square of area 25 sq. units such that $$E$$, $$G$$ lie on the line segments $$AB$$, $$AD$$ respectively. If the line segments $$ED$$ and $$FG$$ meet in $$N$$, then find the ratio of the area of the region $$EBCDGNE$$ to the area of the region $$AGNE$$

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IIT Ramaiah SAT April 30 2017 - Question 15

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Two functions $$f$$, $$g$$ are defined on the set of real numbers $$\mathbb{R}$$, such that $$f(x) = |x|$$, $$g(x) = [x]$$, for all $$x \in \mathbb{R}$$. (where $$[x]$$ denotes the greatest integer less than or equal to $$x$$). Draw the graphs of the functions $$fog(x)$$, $$gof(x)$$.

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IIT Ramaiah SAT April 30 2017 - Question 16

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A year is called a prime year if that year number is a prime number. For example, 2017 is a prime year. Assume that a person born in 2017 graduates, turns 21 years in the same year. What is the sum of all the prime years starting from the year of his birth to the year of his graduation?

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IIT Ramaiah SAT April 30 2017 - Question 17

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A body A floats with $$50\%$$ of volume submerged in a liquid B and $$75\%$$ of its volume submerged in a liquid C. What is the ratio of the densities of A, B and C? What fraction of the body A will be seen above the surface of a homogenous mixture of equal volumes of the liquids B and C?

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IIT Ramaiah SAT April 30 2017 - Question 18

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A particle is moving along a straight line with constant acceleration. If the distance travelled by the body in $$n^{\text{th}}$$ and $$(n + 1)^{\text{th}}$$ seconds is $$100\text{ m}$$, find it's velocity (in $$\text{m/s}$$) at the end of $$n^{\text{th}}$$ second.

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IIT Ramaiah SAT April 30 2017 - Question 19

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Two particles A and B are moving around a circular path of radius $$35\text{ m}$$ at $$2.2\text{ m/s}$$ and $$4.4\text{ m/s}$$ respectively and are located as shown (Figure A, below) at a certain moment. Find the time elapsed before they meet. Also find the angle covered by A in this duration.
[image]

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IIT Ramaiah SAT April 30 2017 - Question 20

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A block of $$100\text{ g}$$ of ice at $$0^\circ\text{C}$$ is added to some water at $$40^\circ\text{C}$$ contained in a vessel of negligible water equivalent. What should be the least amount of water for entire block to melt? If the amount of water (at $$40^\circ\text{C}$$) is twice the required amount to just melt the block, what is the final temperature of the mixture?

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IIT Ramaiah SAT April 30 2017 - Question 21

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A bright object is fixed at a distance of $$100\text{ cm}$$ from a wall. A convex lens placed between the object and the wall at position A forms a sharp image of the object magnified 4 times on the wall. Find the focal length of the lens. The lens is moved to a new position B to obtain sharp image again. Find the distance between positions A and B.

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IIT Ramaiah SAT April 30 2017 - Question 22

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A ray of light incident at the boundary of two media travels along the path shown (figure B, below). Find the angle (in degrees) in the denser medium if the angle in the rarer medium is doubled.
[image]

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IIT Ramaiah SAT April 30 2017 - Question 23

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A uniform wire of resistance $$6\,\Omega$$ is bent to form a regular hexagon. Find the least and largest resistance possible between any two corners of the hexagon.

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IIT Ramaiah SAT April 30 2017 - Question 24

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Find the equivalent resistance between A and B. (Figure C, above)<br>Some current enters the terminal A and leaves through B. This current splits at various junctions and flows through different resistances. If the current in the $$2\,\Omega$$ resistance is $$1\text{ A}$$, find the potential difference between A to B.
[image]

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IIT Ramaiah SAT April 30 2017 - Question 25

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A long horizontal conductor carries a current eastward. A moving positively charged particle is located vertically above the conductor at a given moment. Find the direction of the force acting on it if its velocity is directed (i) downward (ii) westward (iii) northward

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IIT Ramaiah SAT April 30 2017 - Question 26

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A 1000 MW thermal power plant burns $$10^6\text{ kg}$$ of coal in one hour. How many kg of coal is burnt to produce the energy required to provide electrical energy to a $$2000\text{ W}$$ water heater for 2 hours a day in a month (Assume 30 days to a month).

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IIT Ramaiah SAT April 30 2017 - Question 27

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Consider the following ionization enthalpies of two elements 'A' and 'B' 

Which of the following statements is/are correct?

A

both A and B belong to group-2, where 'A' comes below 'B'

B

both A and B belong to group-2, where 'B' comes below 'A'

C

both A and B belong to group-1, where 'B' comes below 'A'

D

both A and B belong to group-1 where 'A' comes below 'B'

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IIT Ramaiah SAT April 30 2017 - Question 28

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Which electron is associated with least energy

A

$$n = 3$$, $$l = 2$$, $$m = -2$$, $$s = +\frac{1}{2}$$

B

$$n = 4$$, $$l = 0$$, $$m = 0$$, $$s = +\frac{1}{2}$$

C

$$n = 4$$, $$l = 1$$, $$m = 1$$, $$s = +\frac{1}{2}$$

D

$$n = 5$$, $$l = 0$$, $$m = 0$$, $$s = +\frac{1}{2}$$

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IIT Ramaiah SAT April 30 2017 - Question 29

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The periodic table consists of 18 groups. An isotope of copper on bombardment with protons undergoes a nuclear reaction yielding element 'x' as shown below. To which group, the element X-belongs in the period table<br>$${}^{63}_{29}\text{Cu} + {}^{1}_{1}\text{H} \rightarrow 6\,{}^{1}_{0}n + \alpha + 2\,{}^{1}_{1}\text{H} + X$$

A

$$10^{\text{th}}$$ group

B

$$18^{\text{th}}$$ group

C

$$8^{\text{th}}$$ group

D

$$11^{\text{th}}$$ group

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IIT Ramaiah SAT April 30 2017 - Question 30

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Which of the following pairs carry same no. of electrons, but electronic configuration is not same

A

$$\text{Cr}^+$$, $$\text{Mn}^{2+}$$

B

$$\text{Fe}^{3+}$$, $$\text{Mn}^{2+}$$

C

$$\text{Co}^{3+}$$, $$\text{Ni}^{4+}$$

D

$$\text{Cu}^+$$, Ni

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IIT Ramaiah SAT April 30 2017 - Question 31

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The correct order of anions present for the following $$\text{CaC}_2$$, $$\text{Al}_4\text{C}_3$$, $$\text{Mg}_2\text{C}_3$$

A

$$\text{C}^{4-}$$, $$\text{C}_2^{2-}$$, $$\text{C}_3^-$$

B

$$\text{C}_2^{2-}$$, $$\text{C}_3^{4-}$$, $$\text{C}_3^{2-}$$

C

$$\text{C}_2^{2-}$$, $$\text{C}^{4-}$$, $$\text{C}_3^{4-}$$

D

$$\text{C}^{4-}$$, $$\text{C}_2^{2-}$$, $$\text{C}_3^{4-}$$

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IIT Ramaiah SAT April 30 2017 - Question 32

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$$80\%$$ of a first order chemical reaction completed in 100 sec, what time it will take for the completion of $$99.2\%$$

A

200 sec

B

400 sec

C

300 sec

D

150 sec

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IIT Ramaiah SAT April 30 2017 - Question 33

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A metal M reacts with nitrogen gas to afford $$\text{M}_3\text{N}$$. $$\text{M}_3\text{N}$$ on heating at high temperature gives back M and on reaction with water produces gas B. Gas B reacts with aqueous solution of $$\text{CuSO}_4$$ to form a deep blue compound. M and B respectively

A

Li and $$\text{NH}_3$$

B

Al and $$\text{N}_2$$

C

Ba and $$\text{N}_2$$

D

Na and $$\text{NH}_3$$

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IIT Ramaiah SAT April 30 2017 - Question 34

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Match the fuel gases with main component present in them<br>List-I (fuel gases) - A) LPG, B) Natural gas, C) Coal gas, D) Producer gas<br>List-II (main component gas) - p) $$\text{N}_2$$, q) n-butane, r) $$\text{CH}_4$$, s) $$\text{H}_2$$

A

A $$\rightarrow$$ r, B $$\rightarrow$$ q, C $$\rightarrow$$ p, D $$\rightarrow$$ s

B

A $$\rightarrow$$ s, B $$\rightarrow$$ r, C $$\rightarrow$$ p, D $$\rightarrow$$ q

C

A $$\rightarrow$$ q, B $$\rightarrow$$ r, C $$\rightarrow$$ s, D $$\rightarrow$$ p

D

A $$\rightarrow$$ p, B $$\rightarrow$$ q, C $$\rightarrow$$ r, D $$\rightarrow$$ s

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IIT Ramaiah SAT April 30 2017 - Question 35

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Match the List-I with List-II<br>List-I (type of velocity) - A) Root mean square velocity, B) Average velocity, C) Most probable velocity, D) Velocity possessed by maximum fraction of molecules<br>List-II (equation) - p) $$\sqrt{\frac{3p}{d}}$$, q) $$\sqrt{\frac{3RT}{m}}$$, r) $$\sqrt{\frac{8P}{\pi d}}$$, s) $$\sqrt{\frac{2RT}{m}}$$

A

A $$\rightarrow$$ r, B $$\rightarrow$$ p, q, C $$\rightarrow$$ s, D $$\rightarrow$$ s

B

A $$\rightarrow$$ s, B $$\rightarrow$$ s, C $$\rightarrow$$ p, q, D $$\rightarrow$$ r

C

A $$\rightarrow$$ s, B $$\rightarrow$$ r, C $$\rightarrow$$ s, D $$\rightarrow$$ p, q

D

A $$\rightarrow$$ p, q, B $$\rightarrow$$ r, C $$\rightarrow$$ s, D $$\rightarrow$$ s

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IIT Ramaiah SAT April 30 2017 - Question 36

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The molality and mole fraction of the solute in an aqueous solution containing 6 gm of urea per 500 gm of water (mol. wt. of urea = 60)

A

0.1 M, 0.001

B

0.2 M, 0.00359

C

0.3 M, 0.2

D

0.01, 0.0012

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IIT Ramaiah SAT April 30 2017 - Question 37

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Complete the decomposition reaction of<br>(i) $$\text{LiNO}_3 \xrightarrow{\Delta}$$ __________ (ii) $$\text{NaNO}_3 \xrightarrow{\Delta}$$ __________

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IIT Ramaiah SAT April 30 2017 - Question 38

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Give the hybridization and no. of lone pairs over the central atom (Molecule - Hybridisation - No. of lone pairs)<br>$$\text{XeO}_2\text{F}_2$$ __________ __________<br>$$\text{ICl}_2^-$$ __________ __________<br>$$\text{CO}_2$$ __________ __________

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IIT Ramaiah SAT April 30 2017 - Question 39

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Give the nature of oxides i.e. acidic, basic neutral (or) amphoteric (Oxide - nature of oxide)<br>CO __________<br>$$\text{Al}_2\text{O}_3$$ __________<br>$$\text{SiO}_2$$ __________

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IIT Ramaiah SAT April 30 2017 - Question 40

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Write structural formula of all the isomeric alcohols having the molecular formula $$\text{C}_4\text{H}_{10}\text{O}$$<br>(i) __________<br>(ii) __________<br>(iii) __________<br>(iv) __________

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IIT Ramaiah SAT April 30 2017 - Question 41

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Complete the reactions<br>(i) $$\text{CaO} + \text{C} \xrightarrow{\Delta} \text{A} + \text{B}$$<br>(ii) $$\text{A} + \text{N}_2 \xrightarrow[\text{furnace}]{\text{electric}} \text{D} + \text{graphite}$$<br>(iii) $$\text{D} + \text{H}_2\text{O} \rightarrow \text{E} + \text{NH}_3$$<br>Identify the compound A __________, B __________, D __________, E __________

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IIT Ramaiah SAT April 30 2017 - Question 42

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The concentration of $$\text{H}^+$$ ions in 0.10 M solution of a weak acid is $$1 \times 10^{-5}\text{ mol L}^{-1}$$. Calculate the dissociation constant of the acid __________ [Note - [HA] can be taken as 0.1 M as $$1 \times 10^{-5}$$ is very small]

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IIT Ramaiah SAT April 30 2017 - Question 43

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If one mole of electrons per sec are passing through a point across metallic wire, calculate the charge in coloumbs passing in one sec. __________

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IIT Ramaiah SAT April 30 2017 - Question 44

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Out of the given metals Zn, Mg, Al, Be which will give $$\text{H}_2$$ gas on reaction with NaOH solution __________

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IIT Ramaiah SAT April 30 2017 - Question 45

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Exactly 2 gm of NaOH is dissolved in water to makeup 1 litre of solution. The pH of the solution found to be higher than 7. The HCl gas is then bubbled through this solution at the rate of 1 gm/min. After how many minutes will the pH become 7? __________

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IIT Ramaiah SAT April 30 2017 - Question 46

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The two elements A and B form the compounds $$\text{A}_2\text{B}_3$$ and $$\text{AB}_2$$. If 0.5 mole of $$\text{A}_2\text{B}_3$$ weighs 15.9 grams and 0.15 mole of $$\text{AB}_2$$ weighs 9.3 gm. Find the atomic weights of A and B __________

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