IIT Ramaiah SAT April 23 2011 Question Paper

IIT Ramaiah SAT April 23 2011 - Question 1

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If 2011 is written as the sum of 11 consecutive primes in their ascending order, then the $$6^{\text{th}}$$ prime is

A

167

B

187

C

181

D

211

E

183

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IIT Ramaiah SAT April 23 2011 - Question 2

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In a triangle $$ABC$$, $$D$$ is the mid point of $$BC$$ and $$AD > \frac{BC}{2}$$. Then $$\angle A$$ is

A

$$< 90^\circ$$

B

$$< 120^\circ$$

C

$$< 135^\circ$$

D

$$< 60^\circ$$

E

$$< 45^\circ$$

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IIT Ramaiah SAT April 23 2011 - Question 3

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Let $$l$$ be a fixed line. $$ABCD$$ be a square having a fixed side length, moving such that its vertex $$D$$ is at a fixed point on the line $$l$$ and such that the square is on one side of the line $$l$$. Let $$A'$$, $$C'$$ be the feet of the perpendiculars of $$A$$ and $$C$$ on $$l$$ respectively. Then $$\triangle AA'D$$ and $$\triangle DC'C$$ are congruent if angle $$BDA' =$$

A

$$30^\circ$$

B

$$45^\circ$$

C

$$90^\circ$$

D

$$60^\circ$$

E

none of these

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IIT Ramaiah SAT April 23 2011 - Question 4

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If $$x < y$$ and $$x + y = k$$ then

A

$$x < \frac{k}{2}$$ only when $$k > 0$$

B

$$y > \frac{k}{2}$$ only when $$k > 0$$

C

$$x < \frac{k}{2}$$

D

$$y > \frac{k}{2}$$

E

$$x < \frac{k}{2}$$ when $$k > 0$$ and $$x > \frac{k}{2}$$ when $$k < 0$$

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IIT Ramaiah SAT April 23 2011 - Question 5

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In the sequence obtained by omitting the perfect squares from the sequence of natural numbers, $$2011^{\text{th}}$$ term is ____________

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IIT Ramaiah SAT April 23 2011 - Question 6

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In a plane, given any three non collinear points, the number of parallelograms that can be formed such that the three given points become three consecutive vertices is _______

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IIT Ramaiah SAT April 23 2011 - Question 7

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A certain integer has only two distinct prime factors. The number of its divisors is 6, and the sum of the divisors is 28. The integer is_______

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IIT Ramaiah SAT April 23 2011 - Question 8

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The value of $$2^{\log_6 18} \cdot 3^{\log_6 3}$$ in decimal form is _______

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IIT Ramaiah SAT April 23 2011 - Question 9

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State True or False. $$2011^{64} + 64$$ is a composite number.

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IIT Ramaiah SAT April 23 2011 - Question 10

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State True or False. There exist four distinct points $$A$$, $$B$$, $$C$$, $$D$$ in a plane such that $$\overleftrightarrow{AD} \perp \overleftrightarrow{BC}$$ and $$\overleftrightarrow{BD} \perp \overleftrightarrow{CA}$$.

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IIT Ramaiah SAT April 23 2011 - Question 11

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State True or False. There exist a pair of non negative real numbers $$a$$, $$b$$ such that $$(a - b)\left(a(a + b) - 2b^2\right)$$ is negative.

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IIT Ramaiah SAT April 23 2011 - Question 12

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State True or False. If $$n$$ is a natural number, $$2n + 1$$ and $$3n + 1$$ are squares then $$5n + 3$$ is not a prime.

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IIT Ramaiah SAT April 23 2011 - Question 13

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If $$[x]$$ represents the greatest integer less than or equal to $$x$$ then solve the equation $$x^{2011} - [x]^{2011} = (x - [x])^{2011}$$ in positive real numbers.

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IIT Ramaiah SAT April 23 2011 - Question 14

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Find all possible ordered triads $$(a, b, c)$$ such that $$(n + 3)^2 = a(n + 2)^2 + b(n + 1)^2 + cn^2$$ for every positive integer $$n$$.

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IIT Ramaiah SAT April 23 2011 - Question 15

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State and Prove Alternate Segment Theorem on circles.

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IIT Ramaiah SAT April 23 2011 - Question 16

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Write any two functions $$f \colon \mathbb{R} \rightarrow \mathbb{R}$$ such that $$f(x) = f\left(\frac{x}{2}\right)$$ for every real number $$x$$.

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IIT Ramaiah SAT April 23 2011 - Question 17

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Two bodies of equal volume connected by a string are floating with one of them completely submerged and the other with half of its volume outside the liquid as in the figure (Below, Left). Find the densities of the materials of the bodies if the densities are in the ratio $$1 \colon 3$$. If the volume of the floating body is doubled, find the fraction of the floating body that now lies submerged in the liquid. (Density of liquid $$= 800\text{ kg m}^{-3}$$)
[image]

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IIT Ramaiah SAT April 23 2011 - Question 18

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An insect crawls along the sides of a regular hexagon (Above, Right) with a uniform speed $$v$$ in the anticlockwise sense. Find the magnitude of its average velocity in moving from (i) A to C and (ii) A to D and (iii) A to E
[image]

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IIT Ramaiah SAT April 23 2011 - Question 19

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Two parallel rays of light separated by $$d$$ (Below, Left) are incident at the boundary of air and a medium of refractive index $$\sqrt{2}$$ at $$45^\circ$$. Find the angle of deviation of each ray and the distance between these rays in the medium
[image]

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IIT Ramaiah SAT April 23 2011 - Question 20

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A wire of resistance $$R$$ is bent in the form of a circle and is connected to a $$220\text{ V}$$ source as shown (Above, Right). If the energy provided by the source in $$42\text{ s}$$ is same as the energy required to raise the temperature of 11 kg of water through $$44^\circ\text{C}$$, find the value of $$R$$ (in ohm).
[image]

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IIT Ramaiah SAT April 23 2011 - Question 21

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Resistances of $$2\,\Omega$$ and $$3\,\Omega$$ are connected in series between terminals A and B, and a potential difference of $$20\text{ V}$$ is applied between the terminals. An unknown resistance is connected in parallel to the $$3\,\Omega$$ resistance and the current in this unknown resistance is $$\frac{5}{12}$$ times the current that was flowing from A to B before it was connected. Find the unknown resistance (in ohm).

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IIT Ramaiah SAT April 23 2011 - Question 22

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A long conductor carries a current northward. A moving positively charged particle is located vertically below the conductor. Find the force acting on it if its velocity is directed (i) downward (ii) westward

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IIT Ramaiah SAT April 23 2011 - Question 23

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Rate at which energy is incident on $$1\text{ m}^2$$ area facing the sun is 1400 W. The average area of the roof top of a moderate home is $$150\text{ m}^2$$. Since the angle of incidence of the energy from sun on the roof top varies during the day, the average rate for a 12 hour duration is half of the maximum rate of incidence at the noon time. Find the energy received in 12 hour duration by the roof of the building. Assuming yield of 200 MeV per reaction in the fission of uranium nucleus, find the number of reactions that produce the same amount of energy as provided by the sun to the roof in the 12 hour duration.

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IIT Ramaiah SAT April 23 2011 - Question 24

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A stream of particles each of mass 1 g moving horizontally with a velocity of $$5\text{ m/s}$$ strike a vertical wall. The particles stick to the wall after hitting the wall. Number of particles per $$\text{m}^3$$ of the stream is 10000.<br>Find the number of particles striking a square area of side 50 cm of the wall in one second.

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IIT Ramaiah SAT April 23 2011 - Question 25

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A stream of particles each of mass 1 g moving horizontally with a velocity of $$5\text{ m/s}$$ strike a vertical wall. The particles stick to the wall after hitting the wall. Number of particles per $$\text{m}^3$$ of the stream is 10000.<br>Find the number of particles of the stream that cross a vertical section of area $$0.4\text{ m}^2$$ in two seconds

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IIT Ramaiah SAT April 23 2011 - Question 26

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A stream of particles each of mass 1 g moving horizontally with a velocity of $$5\text{ m/s}$$ strike a vertical wall. The particles stick to the wall after hitting the wall. Number of particles per $$\text{m}^3$$ of the stream is 10000.<br>The change in momentum (in $$\text{kg m s}^{-1}$$) of the particles that strike an area $$2\text{ m}^2$$ of the wall in four seconds.

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IIT Ramaiah SAT April 23 2011 - Question 27

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Ferrous sulphate is treated with potassium permanganate in the presence of suphuric acid. Potassium sulphate, manganese sulphate, ferric sulphate are the products of the reaction. The number of moles of sulphuric acid required for 1 mole of $$\text{KMnO}_4$$ ____.

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IIT Ramaiah SAT April 23 2011 - Question 28

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Amongst the following the total number of compounds whose aqueous solution turns red litmus paper blue is ___.<br>KCN, $$\text{K}_2\text{SO}_4$$, NaCl, $$\text{Zn(NO}_3)_2$$, $$\text{FeCl}_3$$, $$\text{K}_2\text{CO}_3$$, $$\text{NH}_4\text{NO}_3$$, LiCN

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IIT Ramaiah SAT April 23 2011 - Question 29

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The value of $$n$$ in the molecular formula $$\text{Be}_n\text{Al}_2\text{Si}_6\text{O}_{18}$$ is ___

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IIT Ramaiah SAT April 23 2011 - Question 30

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Total number of diprotic acids among the following is ___<br>$$\text{H}_3\text{PO}_4$$, $$\text{H}_2\text{SO}_4$$, $$\text{H}_3\text{PO}_3$$, $$\text{H}_2\text{CO}_3$$, $$\text{H}_2\text{S}_2\text{O}_7$$, $$\text{H}_3\text{BO}_3$$, $$\text{H}_3\text{PO}_2$$, $$\text{H}_2\text{CrO}_4$$, $$\text{H}_2\text{SO}_3$$

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IIT Ramaiah SAT April 23 2011 - Question 31

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Among the following the number of elements showing only one non-zero oxidation state ___<br>O, Cl, F, N, P, Sn, Tl, Na, Ti

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IIT Ramaiah SAT April 23 2011 - Question 32

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Iron (II) sulphide is heated in air to form compound A, and an oxide of sulphur. The oxide of sulphur is dissolved in water to give an acid. The basicity of this acid is ___.

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IIT Ramaiah SAT April 23 2011 - Question 33

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A current of 10 A flows for 2 hours through an electrolytic cell containing a molten salt of metal X and results in the deposition of 0.25 moles of metal X at cathode. The oxidation state X in the electrolysed salt is ____ .

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IIT Ramaiah SAT April 23 2011 - Question 34

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Ar and He are both gases at room temperature. The average velocity of He atom is $$x$$ times of average molecular velocity Ar atoms at this temperature. The numerical value of $$x$$ is ___. (atomic wt of Ar = 36, He = 4)

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IIT Ramaiah SAT April 23 2011 - Question 35

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Among $$\text{BF}_3$$, $$\text{NF}_3$$, $$\text{PH}_3$$, $$\text{IF}_3$$, $$\text{IF}_5$$ and $$\text{SF}_4$$ the number of species having the same number of loan pair of electrons on central atom is ____

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IIT Ramaiah SAT April 23 2011 - Question 36

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On heating 1.763 g of hydrated $$\text{BaCl}_2$$ to dryness 1.505 g of anhydrous salt remained. Number of moles of $$\text{H}_2\text{O}$$ present in the mole of hydrated $$\text{BaCl}_2$$ is ____ (mol. wt. of anhydrous $$\text{BaCl}_2$$ is 208)

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IIT Ramaiah SAT April 23 2011 - Question 37

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Dry air contains at one atmosphere pressure contains $$78\%$$ nitrogen $$21\%$$ oxygen and $$1\%$$ other gases. The partial pressure of other gases is $$a \times 10^{-2}$$ atm where $$a$$ is ___.

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IIT Ramaiah SAT April 23 2011 - Question 38

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The bond energy of an O-H bond is $$109\text{ kcal mol}^{-1}$$. When $$5 \times 10^{-3}$$ mole of water is formed, the energy released in k.cal is ____.

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IIT Ramaiah SAT April 23 2011 - Question 39

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On decomposition of $$\text{NH}_4\text{HS}$$ the following equation is established $$\text{NH}_4\text{HS}(s) \rightleftharpoons \text{NH}_3(g) + \text{H}_2\text{S}(g)$$. If the total pressure is $$p$$ atmospheres then the equilibrium constant $$K_p$$ will be equal to $$\frac{p^2}{x}\text{ atm}^2$$ where $$x$$ is ___

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IIT Ramaiah SAT April 23 2011 - Question 40

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10 ml of pure ethyl alcohol of density 0.785 g/ml was diluted with water to a final value of 100 ml. The density of resulting solution was 0.9866 g/ml. Percentage by weight of ethyl alcohol is ___.

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IIT Ramaiah SAT April 23 2011 - Question 41

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Match the following<br>Column I - A) 0.55 mole, B) 0.10 mole, C) 0.20 mole, D) 0.50 mole<br>Column II - p) 4.48 lit of $$\text{SO}_2$$ at NTP, q) 100 ml of $$\text{H}_2\text{O}$$, r) 22 g of $$\text{CO}_2$$, s) 2.24 lit. $$\text{NH}_3$$, t) 0.1 g atom of Iron

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