IIT Ramaiah SAT 2010 Question Paper

IIT Ramaiah SAT 2010 - Question 1

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Let $$l_1$$, $$l_2$$ be any two parallel lines and $$B$$, $$C$$ be any two points on $$l_1$$ and $$A_1, A_2, \ldots, A_{2010}$$ be points on $$l_2$$. If $$\Delta_i$$ denotes the area of the triangle $$A_i BC$$ and if $$\sum_{i=1}^{2010} \Delta_i = 2010$$, Then the area of $$\triangle A_{2010}BC$$ is

A

1

B

$$\frac{1}{2}$$

C

2

D

2010

E

1005

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IIT Ramaiah SAT 2010 - Question 2

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Let $$\{a_n\}$$ be a sequence of integers such that $$a_1 = 1$$, $$a_{m+n} = a_m + a_n + mn$$ for all positive integers $$m$$ and $$n$$. Then $$a_{12}$$ is

A

6

B

70

C

78

D

76

E

72

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IIT Ramaiah SAT 2010 - Question 3

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In a triangle $$ABC$$, $$a$$, $$b$$, $$c$$ denote the lengths of the sides $$BC$$, $$CA$$, $$AB$$. If $$D$$ is the midpoint of the side $$BC$$ and $$AD$$ is perpendicular to $$AC$$, then

A

$$3b^2 = a^2 - c^2$$

B

$$3a^2 = b^2 - 3c^2$$

C

$$b^2 = a^2 - c^2$$

D

$$a^2 + b^2 = 5c^2$$

E

none of these

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IIT Ramaiah SAT 2010 - Question 4

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If $$k$$ is an integer then which of the following is true?

A

An integer of the form $$4k + 1$$ can always be put in the form $$2k - 1$$

B

An integer of the form $$4k + 3$$ can always be put in the form $$2k + 1$$

C

An integer of the form $$2k - 1$$ can always be put in the form $$4k + 1$$

D

An integer of the form $$2k - 1$$ can always be put in the form $$4k + 3$$

E

An integer of the form $$2k + 1$$ can always be put in the form $$4k + 3$$

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IIT Ramaiah SAT 2010 - Question 5

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The number of elements in $$\{(a, b, c) \mid a = b, (a - c)^2 = 0, a + b + c = 0, a, b, c \text{ are real numbers}\}$$ is

A

0

B

1

C

6

D

3

E

infinitely many

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IIT Ramaiah SAT 2010 - Question 6

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The no. of solutions of the equation $$xy(x + y) = 2010$$, where $$x$$ and $$y$$ denote positive prime numbers, is______

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IIT Ramaiah SAT 2010 - Question 7

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The number of elements in the set $$\{n \in \mathbb{N} \mid n^3 - 8n^2 + 20n - 13 \text{ is a prime number}\}$$ is ________

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IIT Ramaiah SAT 2010 - Question 8

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The solution set of the equation $$\sqrt{x^2 - 4x + 4} + (x - 2) = 0$$ is _______

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IIT Ramaiah SAT 2010 - Question 9

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State True or False. Given any two diameters of a circle the convex quadrilateral formed by joining the extremities of the diameters is always a rectangle.

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IIT Ramaiah SAT 2010 - Question 10

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If $$P = 3^{2010} + 3^{-2010}$$, $$Q = 3^{2010} - 3^{-2010}$$ then $$P^2 - Q^2 =$$ ________

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IIT Ramaiah SAT 2010 - Question 11

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Solve the equation $$\log_{2010}(2009x) = \log_{2009}(2010x)$$.

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IIT Ramaiah SAT 2010 - Question 12

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In a quadrilateral $$ABCD$$, $$AB = 3$$, $$BC = 4$$, $$CD = 5$$, $$\angle ABC = \angle BCD = 120^\circ$$. Find the area of the quadrilateral.

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IIT Ramaiah SAT 2010 - Question 13

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I was trying to solve $$\frac{4}{x - 2} > 5$$. While writing the question I mistakenly wrote a digit other than 5 and solved the inequality and got $$2 < x < 4$$. What digit did I write possibly?

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IIT Ramaiah SAT 2010 - Question 14

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In a right angled triangle what is the relation between the square of the altitude on to the hypotenuse and the product of the segments of the hypotenuse?

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IIT Ramaiah SAT 2010 - Question 15

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Is it possible to find two functions $$f$$ and $$g$$ such that the domain of $$f$$ is not finite, the domain of $$g$$ is finite, $$gof$$ is defined? Justify your answer.

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IIT Ramaiah SAT 2010 - Question 16

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If the last digits (unit places) of the products $$1 \cdot 2$$, $$2 \cdot 3$$, $$3 \cdot 4$$, $$\ldots$$, $$n(n + 1)$$ are added, the result is 2010. How many products are used?

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IIT Ramaiah SAT 2010 - Question 17

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Show that four divides any perfect square or leaves a remainder 1. Also show that nine divides cube of any integer or leaves 1 or 8 as remainder.

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IIT Ramaiah SAT 2010 - Question 18

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Let $$AB$$ be a line segment of length 26. Let $$C$$ and $$D$$ be located on the line segment $$AB$$ such that $$AC = 1$$ and $$AD = 8$$. Let $$E$$ and $$F$$ be the points on one of the semi circles with diameter $$AB$$ for which $$EC$$ and $$FD$$ are perpendicular to $$AB$$. Find the length of the line segment $$EF$$.

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IIT Ramaiah SAT 2010 - Question 19

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In each of the following cases give an example of a system of two linear equations in two variables $$x$$ and $$y$$.<br>i) A system having exactly one solution<br>ii) A system having no solution<br>iii) A system having infinitely many solutions

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IIT Ramaiah SAT 2010 - Question 20

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Using Mathematical Induction Prove that $$3^{2n} + 7$$ is divisible by 8, $$\forall n \in \mathbb{N}$$.

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IIT Ramaiah SAT 2010 - Question 21

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A body dropped from a very large height, experiences resistance to its motion due to air and has a varying acceleration which decreases to zero in time $$t$$. Assume the displacement in this time and the velocity acquired at the end of this time are same as that due uniform acceleration of $$cg$$ ($$c$$ is a constant less than 1). The body then travels with a uniform speed acquired at the end of time $$t$$. Find the displacement of the body in time $$2t$$.

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IIT Ramaiah SAT 2010 - Question 22

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A bright point object is kept at some distance from a lens of focal length 20 cm. If the object distance is changed $$\frac{5}{6}$$ times, the distance of the screen from the lens has to be changed by $$\frac{5}{3}$$ times to obtain a clear image on the screen. Find the distance (in cm) through which the screen has been moved.

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IIT Ramaiah SAT 2010 - Question 23

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ABCD is a square of side 400 m. E and F are points 200 and 300 m away from corner D. Two persons starting from E and F and moving away from D, meet at B. Where would they meet if they were to travel towards D. (Give the distance of the meeting point from D, in m.)
[image]

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IIT Ramaiah SAT 2010 - Question 24

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In the circuit shown PD across $$R$$ is $$V$$. Find the PD across the resistance $$2R$$
[image]

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IIT Ramaiah SAT 2010 - Question 25

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Two liquids of densities $$2\text{ g cm}^{-3}$$ and $$4\text{ g cm}^{-3}$$ of equal volumes form a homogenous mixture. A solid object made of materials of density $$1\text{ g cm}^{-3}$$ and $$5\text{ g cm}^{-3}$$ mixed homogenously is just found to just float in this mixture. What is ratio by volumes/masses of the materials of the solid object?

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IIT Ramaiah SAT 2010 - Question 26

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A man is standing to the south of a vertical conductor carrying current facing the conductor. Direction of the magnetic field at a position in between him and the wire is from his left to right. What would be magnetic field direction behind him if he moved to a position (i) east of the conductor (ii) to the north of the conductor. Assume he always faces the conductor and current direction in the wire remains constant. (Express these directions as east or west etc.)

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IIT Ramaiah SAT 2010 - Question 27

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Average energy required by an adult to sustain himself is 1500 kilocalories per day. A medium sized banana is about 100 g and provides about 100 kilocalories. How many kg of bananas are required per day to sustain a population of 1000 million? If some how the biological processes were to be sustained by nuclear reactions, how many kg of mass must disappear to provide this energy?

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IIT Ramaiah SAT 2010 - Question 28

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A ray of light is incident at $$45^\circ$$ on to a transparent slab of thickness 10 cm made of a material of refractive index $$\sqrt{2}$$. Find the lateral displacement (in cm) of the ray as it emerges from the slab.

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IIT Ramaiah SAT 2010 - Question 29

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Length of a wire of resistance $$R$$ and resistivity $$\rho$$ is doubled by stretching it. What will be its new resistance and resistivity?

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IIT Ramaiah SAT 2010 - Question 30

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A solid object made of material of density $$0.79\text{ g cm}^{-3}$$ of negligible coefficient of cubical expansion is floating in a liquid of density $$0.8\text{ g cm}^{-3}$$ at $$20^\circ\text{C}$$. When the temperature is raised to $$220^\circ\text{C}$$, the solid object starts sinking in the liquid. Find the coefficient of cubical expansion (per degree Celsius) of the liquid.

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IIT Ramaiah SAT 2010 - Question 31

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Velocity time graph of a body is as shown. Find it's displacement (in m) in 10 s.
[image]

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IIT Ramaiah SAT 2010 - Question 32

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Sound wave of wavelength 0.5 m in air passes in to water. What is its wavelength in water? Also find the frequencies of the wave in air and water (Velocity of sound in air and water are 350 m/s and 1400 m/s respectively)

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IIT Ramaiah SAT 2010 - Question 33

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A 1000 MW thermal power plant burns $$10^6$$ kg of coal in one hour. How many kg of coal is burnt to produce the power required to light up a 100 W lamp for 8 hours.

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IIT Ramaiah SAT 2010 - Question 34

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What is the action of heat on following salts? Explain with balanced equations.<br>a) $$\text{FeSO}_4 \xrightarrow{\Delta}$$ b) $$\text{AgNO}_3 \xrightarrow{\Delta}$$

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IIT Ramaiah SAT 2010 - Question 35

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Sugar forms clear solution but soap forms cloudy solutions. Why?

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IIT Ramaiah SAT 2010 - Question 36

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What is the composition of baking powder? Explain how it bakes the bread to make it spongy? (with chemical equations)

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IIT Ramaiah SAT 2010 - Question 37

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When iron is exposed to atmosphere surface of the metal becomes brown but silver under similar conditions becomes black. Explain with equations?

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IIT Ramaiah SAT 2010 - Question 38

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$$\text{BH}_3$$ acts as a Lewis acid whereas $$\text{NH}_3$$ acts as Lewis base. Explain with proper structures?

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IIT Ramaiah SAT 2010 - Question 39

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Write the cathodic and anodic reactions when aqueous solution of $$\text{KNO}_3$$ is electrolysed by using Pt electrodes.

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IIT Ramaiah SAT 2010 - Question 40

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What is electrolyte? What is the basic requirement for a substance to act as electrolyte?

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IIT Ramaiah SAT 2010 - Question 41

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In the given salt cation is called as basic radical and anion is called as acid radical. Why?

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IIT Ramaiah SAT 2010 - Question 42

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Why hydrogen peroxide acts as oxidising as well as reducing agent?

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IIT Ramaiah SAT 2010 - Question 43

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Hardness of IA-group elements gradually decreases down the group. Why?

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IIT Ramaiah SAT 2010 - Question 44

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What way thermochemical equations are more informative than skeletal and balanced chemical equations?

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IIT Ramaiah SAT 2010 - Question 45

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What are the simplest tests that are used for identification of purity of the chemical sample?

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IIT Ramaiah SAT 2010 - Question 46

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Total hardness of water cannot be removed by simple heating. Why?

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IIT Ramaiah SAT 2010 - Question 47

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$$\text{CO}_2$$ and $$\text{SiO}_2$$ are the oxides of elements of same group but $$\text{CO}_2$$ is a gas but $$\text{SiO}_2$$ is solid. Why?

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IIT Ramaiah SAT 2010 - Question 48

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All exothermic reactions are not spontaneous reactions. Why?

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IIT Ramaiah SAT 2010 - Question 49

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What are the internal factors that decide the physical state of the substance?

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IIT Ramaiah SAT 2010 - Question 50

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Aqueous solution of $$\text{CuSO}_4$$ cannot be stored in Zn container but aqueous solution of $$\text{ZnSO}_4$$ can be stored in Cu vessel. Why?

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IIT Ramaiah SAT 2010 - Question 51

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Match each of the chemical species in Column I with its property / properties given in corresponding Column II and Column III. No partial marking.<br>Column I - a) $$\text{BeH}_2$$, b) $$\text{CH}_2\text{BrCl}$$, c) $$\text{PF}_6^-$$, d) $$\text{BF}_3$$<br>Column II - 1. $$sp^3d^2$$, 2. $$sp^3$$, 3. $$sp^2$$, 4. $$sp$$<br>Column III - (i) trigonal planar, (ii) octahedral, (iii) distorted tetrahedron, (iv) linear

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IIT Ramaiah SAT 2010 - Question 52

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Ethanol (density = 0.7893 g/ml) and water (density = 0.9931 g/ml) at $$25^\circ\text{C}$$ are mixed in the volume ratio $$1 \colon 2$$ to get solution of density 0.9571 g/ml. Calculate (i) the fractional change in volume and (ii) the molality of the final solution.

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IIT Ramaiah SAT 2010 - Question 53

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Indicate whether the following reaction is exothermic or endothermic by properly computing the given data<br>$$\text{M}_g + 2\text{X}_g \rightarrow \text{M}^{2+}_g + 2\text{X}^-_g$$; $$\text{IE}_1$$ of $$\text{M}_g = 737.7\text{ kJ mol}^{-1}$$; $$\text{IE}_2$$ of $$\text{M}_g = 1451\text{ kJ mol}^{-1}$$; $$\text{EA}_1$$ of $$\text{X}_g = -328\text{ kJ mol}^{-1}$$

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