[Solved] IIT Ramaiah SAT April 24 2016 Question Paper Paper with Solutions

IIT Ramaiah SAT April 24 2016 - Question 1

If the roots of $$2016x^2 + bx + c = 0$$ are $$\frac{5}{63}$$, $$-\frac{7}{32}$$ then $$b + 6c$$ is equal to

IIT Ramaiah SAT April 24 2016 - Question 2

$$P$$ is a point between the parallel lines $$\overleftrightarrow{AB}$$, $$\overleftrightarrow{CD}$$ such that $$A$$ and $$C$$ lie on the same side of the line perpendicular to the parallel lines and passing through $$P$$. $$\angle PAB = 40^\circ$$ and $$\angle PCD = 60^\circ$$ then $$\angle APC =$$

IIT Ramaiah SAT April 24 2016 - Question 3

Let $$a = \left(\sqrt[3]{2} - 1\right)^{1/3}$$, $$b = \sqrt[3]{\frac{1}{9}} - \sqrt[3]{\frac{2}{9}} + \sqrt[3]{\frac{4}{9}}$$ then

IIT Ramaiah SAT April 24 2016 - Question 4

In a triangle $$ABC$$ right angled at $$A$$, $$AD$$ is the altitude through $$A$$. If $$AD = 2$$ and $$CD = 3$$ then $$AB =$$

IIT Ramaiah SAT April 24 2016 - Question 5

The sum of a two digit number and the number represented with the aid of the same digits but in the reverse order is a perfect square. The number of such two digit numbers is ______

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IIT Ramaiah SAT April 24 2016 - Question 6

In the Cartesian plane let $$O(0, 0)$$, $$P(\cos\theta, \sin\theta)$$, $$Q(-\sin\theta, \cos\theta)$$ be the vertices of a triangle. Two circles drawn with $$OP$$, $$OQ$$ as diameters intersect at $$R$$ then $$OR =$$ _____

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IIT Ramaiah SAT April 24 2016 - Question 7

$$p$$, $$q$$ are positive integers. The number of ordered pairs $$(p, q)$$, such that the LCM of $$p$$ and $$q$$ is 12 is ______

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IIT Ramaiah SAT April 24 2016 - Question 8

If $$r$$ and $$s$$ are positive real numbers such that $$\log(rs) = 10$$ and $$\log\left(\frac{r}{s}\right) = 2$$ then $$3\log(r) + 5\log(s) =$$ ____

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IIT Ramaiah SAT April 24 2016 - Question 9

State True or False. If the solution set of the equation $$\sqrt{x + 3 - 4\sqrt{x - 1}} + \sqrt{x + 8 - 6\sqrt{x - 1}} = 1$$ is $$[a, b]$$ then $$b - a = 5$$

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IIT Ramaiah SAT April 24 2016 - Question 10

State True or False. A class of 32 is counted off once beginning with number 1. Each student who counted an even number stood up. Then the students who were still seated counted off by once again. Each student who counted an even number also stood up. After the second counting was over, the number of students remained seated was 8.

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IIT Ramaiah SAT April 24 2016 - Question 11

State True or False. If $$a$$, $$b$$ are integers such that $$a^2 + b^2 = 29$$ then the maximum value of $$|a - b| = 3$$

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IIT Ramaiah SAT April 24 2016 - Question 12

State True or False. Given a point $$P$$ inside a circle, different from its centre, there is more than one chord through $$P$$ having $$P$$ as mid point.

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IIT Ramaiah SAT April 24 2016 - Question 13

If $$f \colon \mathbb{R} \rightarrow \mathbb{R}$$ is a function defined by $$f(x) = 2|x| + 3$$ for every $$x$$ in $$\mathbb{R}$$ then draw the graph of $$f(f(x))$$.

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IIT Ramaiah SAT April 24 2016 - Question 14

$$E$$ is a point on the side $$AC$$ of a triangle $$ABC$$. $$D$$ and $$F$$ are points on the sides $$BC$$ and $$AB$$ respectively such that the line segments $$DE$$, $$FE$$ are parallel to the sides $$AB$$ and $$BC$$ respectively. If $$\Delta_1$$, $$\Delta_2$$, $$\Delta_3$$ are the areas of the quadrilateral $$BDEF$$, triangle $$AEF$$, triangle $$CDE$$ respectively then evaluate $$\frac{\Delta_1^2}{\Delta_2 \Delta_3}$$.

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IIT Ramaiah SAT April 24 2016 - Question 15

Find the number of integral solutions of $$5x^2 - 7y^2 = 9$$.

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IIT Ramaiah SAT April 24 2016 - Question 16

In a plane $$AB$$ is a fixed line segment of length 8. $$P$$ is a varying point in the same plane such that $$\overline{AB}$$ subtends a right angle at $$P$$ and the length of the perpendicular from $$P$$ on to $$\overline{AB}$$ is 3. Find the number of such points $$P$$.

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IIT Ramaiah SAT April 24 2016 - Question 17

A car travels from A to B covering half the distance at $$v_1$$ and the remaining half of the distance at $$v_2$$. This car then returns from B to A at $$v_3$$. If the time taken for the return journey from B to A is half of the time taken to go from A to B, find the relation between $$v_1$$, $$v_2$$ and $$v_3$$.

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IIT Ramaiah SAT April 24 2016 - Question 18

Equal volumes of two liquids A and B whose densities are in the ratio $$1 \colon 2$$ are mixed to form a homogenous mixture. When a solid body C is dropped in to this mixture, it floats with half of its volume submerged. If the ratio of the volumes liquids A and B is changed to $$2 \colon 1$$, find the fraction of the submerged volume of C.

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IIT Ramaiah SAT April 24 2016 - Question 19

A ray of light is incident on the left face of a transparent slab A and is refracted in to it. Find the refractive index of the slab A. The ray emerging from the right face of the slab A is incident on top face of slab B and emerges through the bottom face of B. Find the angle between emergent ray from bottom face of B and the incident ray on the left face of A. ($$\sin 53^\circ = \frac{4}{5}$$ and $$\sin 37^\circ = \frac{3}{5}$$)
[image]

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IIT Ramaiah SAT April 24 2016 - Question 20

Resistances $$R_1$$ and $$R_2$$ are in the ratio $$1 \colon 2$$. Equivalent resistance between A and B is $$8\,\Omega$$. Find $$R_1$$ and $$R_2$$. If $$R_1$$ is now doubled and a potential difference of $$20\text{ V}$$ is applied between A and B find the current flowing from A to B
[image]

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IIT Ramaiah SAT April 24 2016 - Question 21

A linear object AB of length $$5\text{ cm}$$ is placed along the principal axis of a convex mirror of radius of curvature $$20\text{ cm}$$. If A and B are 5 and $$10\text{ cm}$$ from the pole of the mirror, find the length of the image (in cm).

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IIT Ramaiah SAT April 24 2016 - Question 22

On fission of $$\text{U}^{235}$$ nucleus $$200\text{ MeV}$$ of energy is released. Assume $$50\%$$ efficiency and find the number of $$\text{U}^{235}$$ nuclei undergoing fission in 1 hour in a nuclear power plant of $$200\text{ MW}$$. Also find the mass converted in to energy in this time. ($$1\text{ eV} = 1.6 \times 10^{-19}\text{ J}$$, velocity of light $$c = 3 \times 10^8\text{ m/s}$$)

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IIT Ramaiah SAT April 24 2016 - Question 23

A block of mass $$4\text{ kg}$$ is moving a long a smooth curved path (below, left) in a vertical plane. Its kinetic energy at A is $$600\text{ J}$$. Find least and largest velocities of the block as it moves along the path. (Assume $$g = 10\text{ m/s}^2$$. Figure is not to scale)
[image]

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IIT Ramaiah SAT April 24 2016 - Question 24

In the circuit shown (above, right) current through $$2R$$ is $$3\text{ A}$$. Find the current (in A) through $$R$$ if a $$24\text{ V}$$ cell replaces the $$60\text{ V}$$ cell.
[image]

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IIT Ramaiah SAT April 24 2016 - Question 25

A vertical wire carries current upward. A positively charged particle located east of the wire has a velocity directed a) upward b) westward. In each of the cases find the direction of the force on the wire.

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IIT Ramaiah SAT April 24 2016 - Question 26

One end of a cylindrical conducting rod is maintained at $$T_1$$ and the other end at $$T_2$$. The amount of heat transferred from hotter end to colder end in 2 minutes is $$200\text{ J}$$. If the radius and the length of the rod were doubled and same temperature difference were to be maintained between the ends, find the amount of heat (in J) transferred through this rod in 5 minutes. Given that heat transferred by a conducting rod is given by $$Q = \frac{KA(T_1 - T_2)t}{L}$$ where $$Q$$ is the amount of heat transferred in time $$t$$ by a conductor of length $$L$$ and cross section $$A$$ when its ends are maintained at $$T_1$$ and $$T_2$$. $$K$$ is the coefficient of thermal conductivity which is a property of the material of the conductor. (Ignore heat losses from the curved surfaces of the conductor)

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IIT Ramaiah SAT April 24 2016 - Question 27

Ground state electronic configuration of chromium is against to

IIT Ramaiah SAT April 24 2016 - Question 28

Which of the following pairs of ions have the same electronic configuration

IIT Ramaiah SAT April 24 2016 - Question 29

The correct set of quantum numbers for the valence electron of sodium (Z = 11) is

IIT Ramaiah SAT April 24 2016 - Question 30

The first I.P values of three elements are 1314, 1680, 2080 $$\text{kJ mol}^{-1}$$. The correct sequence of elements is

IIT Ramaiah SAT April 24 2016 - Question 31

Which pair of species has same percentage of carbon

IIT Ramaiah SAT April 24 2016 - Question 32

For the reaction, the equilibrium constant values are given $$A \rightleftharpoons B$$, $$K_1 = 2$$; $$B \rightleftharpoons C$$, $$K_2 = 4$$; $$C \rightleftharpoons D$$, $$K_3 = 3$$. The equilibrium constant for the reaction $$A \rightleftharpoons D$$ is

IIT Ramaiah SAT April 24 2016 - Question 33

The addition of HCl will not suppress the ionization of

IIT Ramaiah SAT April 24 2016 - Question 34

When a mixture of 10 moles of $$\text{SO}_2$$ and 16 moles of $$\text{O}_2$$ were passed over a catalyst, 8 moles of $$\text{SO}_3$$ were formed at equilibrium. The number of moles of $$\text{SO}_2$$ and $$\text{O}_2$$ remaining unreacted were

IIT Ramaiah SAT April 24 2016 - Question 35

Which of the following compound(s) liberate gas on reaction with water?

IIT Ramaiah SAT April 24 2016 - Question 36

For which of the following cases does the reaction go to nearly completion

IIT Ramaiah SAT April 24 2016 - Question 37

Arrange in the increasing order of first I.Ps for Li, Be, B, C, N, O ___________

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IIT Ramaiah SAT April 24 2016 - Question 38

To demonstrate volcanic eruption in science exhibitions ammonium dichromate is used ($$(\text{NH}_4)_2\text{Cr}_2\text{O}_7$$). Show balanced decomposition reaction of $$(\text{NH}_4)_2\text{Cr}_2\text{O}_7$$ ________

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IIT Ramaiah SAT April 24 2016 - Question 39

Give the hybridization and no. of lone pairs over the central atom (Molecule - Hybridization - No. of lone pairs) i) $$\text{XeF}_4$$ ________ _________ ii) $$\text{ICl}_3$$ ________ _________ iii) $$\text{NH}_3$$ ________ _________

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IIT Ramaiah SAT April 24 2016 - Question 40

The main oxides of Li, Na and K are formed when they are burnt in excess of air i) Li - ___________ ii) Na - ___________ iii) K - ___________

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IIT Ramaiah SAT April 24 2016 - Question 41

$$\text{CH}_3\text{CH}_2\text{Br} + \text{CH}_3\text{CH(CH}_3)\text{CH}_2\text{Br} \xrightarrow[\text{dry ether}]{\text{Na}}$$ Products In the above wurtz reaction, maximum no. of carbon atoms in one of the products is ____

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IIT Ramaiah SAT April 24 2016 - Question 42

0.1 M HCl is diluted from 1 lit to 10 lit. The pOH of the resulting solution is _____

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IIT Ramaiah SAT April 24 2016 - Question 43

In a reaction $$A + B \rightarrow C + D$$, $$5\text{ mol L}^{-1}$$ of 'A' is allowed to react with $$3\text{ mol L}^{-1}$$ of 'B'. After 10 min the concentration of A was found to be $$4\text{ mol L}^{-1}$$. Rate of reaction with respect to 'A' (in $$\text{mol L}^{-1}\text{ min}^{-1}$$) is _______