IIT Ramaiah SAT April 29 2012 Question Paper

IIT Ramaiah SAT April 29 2012 - Question 1

Report

$$x^2 - 507x + 2012 < 0$$ if $$x \in$$

A

$$(4, 503)$$

B

$$\mathbb{R} - (4, 503)$$

C

$$(1, 2012)$$

D

$$(10, 201)$$

View Solution

IIT Ramaiah SAT April 29 2012 - Question 2

Report

A circle of radius 14 units is inscribed in a square. And a square is inscribed in the circle such that its sides are parallel to the first square then the area bounded between the two squares is equal to

A

49

B

98

C

196

D

392

View Solution

IIT Ramaiah SAT April 29 2012 - Question 3

Report

If $$P$$ and $$Q$$ are two subsets of a set $$S$$ then $$(P - Q) \cup (Q - P)$$ is equal to

A

$$(P' \cap Q) \cup (P \cap Q')$$

B

$$(P \cup Q) - (P \cap Q)$$

C

$$(P \cup Q) \cap (P \cap Q)'$$

D

$$(P' \cup Q') \cap (P \cup Q)$$

View Solution

IIT Ramaiah SAT April 29 2012 - Question 4

Report

Let $$P(x) = \sum_{r=0}^{7} a_r x^r$$, where $$a_7 = 1$$ and $$P(k) = k$$ for $$k = 1, 2, 3, \ldots, 7$$ then $$P(8) =$$

A

5040

B

5048

C

5050

D

none of these

View Solution

IIT Ramaiah SAT April 29 2012 - Question 5

Report

Area of the region bounded by $$|x| + |y| = 2012$$ is ____________

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 6

Report

If $$f(n) = n(n + 1)$$ for all natural numbers $$n$$, then the set of values of $$n$$ such that $$f(n + 4) = 4f(n) + 4$$ is ____

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 7

Report

Consider a right angled triangle $$ABC$$ with right angle at $$A$$. The radius of its incircle is $$r$$. Radius of the circle drawn touching the line segments $$AB$$, $$AC$$ and the incircle of triangle $$ABC$$ is __________

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 8

Report

$$A$$ and $$B$$ are two different numbers selected from the first forty natural numbers. The largest value that $$\frac{A \cdot B}{A - B}$$ can have is __________

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 9

Report

State True or False. $$2^{2^{2011}} + 1$$ divides $$2^{2^{2012}} - 1$$

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 10

Report

State True or False. If $$x$$ and $$y$$ are perfect squares and $$y = x + 1$$ then number of such ordered pairs $$(x, y)$$ is more than 1

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 11

Report

State True or False. $$\log_2 13$$ is irrational.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 12

Report

State True or False. The number of four digit numbers which are perfect squares and in which the first two digits are equal to each other and the last two digits are equal to each other is 2

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 13

Report

If one root of the polynomial equation $$Ax^3 + Bx^2 + Cx + D = 0$$, $$A \ne 0$$, is the arithmetic mean of the other two, find a simplest relation between $$A$$, $$B$$, $$C$$ and $$D$$.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 14

Report

Let $$f \colon A \rightarrow B$$ be a function defined as $$f(x) = (x^2 - 4x + 4)^{1/2}$$ where $$A$$ and $$B$$ are subsets of $$\mathbb{R}$$. Then find the largest possible subset $$A$$ of $$\mathbb{R}^+$$ such that $$f$$ is bijective and find the corresponding $$B$$.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 15

Report

In a triangle $$ABC$$, if $$AD$$ is the median through $$A$$ intersecting the side $$BC$$ in $$D$$ then show that $$AB^2 + AC^2 = 2(AD^2 + BD^2)$$.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 16

Report

Find all possible positive integers $$n$$ such that $$n^4 - 4n^3 + 22n^2 - 36n + 18$$ is a perfect square.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 17

Report

Narrow square paths ABCD and abcd have sides of $$200\text{ m}$$ and $$100\text{ m}$$. Two persons P and Q are initially located at a and A respectively. They both start walking in a clockwise sense with speeds of $$2\text{ m/s}$$ simultaneously.<br>When are they farthest from each other? (Give the first such time, in seconds after the start.)
[image]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 18

Report

Narrow square paths ABCD and abcd have sides of $$200\text{ m}$$ and $$100\text{ m}$$. Two persons P and Q are initially located at a and A respectively. They both start walking in a clockwise sense.<br>Starting from the same initial positions P and Q walk at $$1\text{ m/s}$$ and $$2\text{ m/s}$$ respectively, find the shortest distance (in m) between them.
[image]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 19

Report

Narrow square paths ABCD and abcd have sides of $$200\text{ m}$$ and $$100\text{ m}$$. Two persons P and Q are initially located at a and A respectively.<br>With same initial positions as earlier and the speeds of $$1\text{ m/s}$$ and $$2\text{ m/s}$$, if Q were to move anticlockwise along the path, find the largest distance (in m) between them.
[image]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 20

Report

A thin long rod A revolves at 300 rpm about a vertical axis. Another rod B is held vertically with it's lower end just above the horizontal plane swept by rod A during it's rotation. Find the maximum length (in m) of rod B, if it should fall without being hit by the rotating rod after B is released from rest. (Assume $$g = 10\text{ m/s}^2$$)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 21

Report

Using 3 identical wires each having resistance $$30\,\Omega$$, letter 'B' is formed. Ends of the straight wire are connected to a cell of potential difference $$220\text{ V}$$. (i) Find the effective resistance of the circuit (ii) find the rate at which energy is delivered by the cell?

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 22

Report

A cube of side 10 cm is made of a material of density $$\frac{d}{2}$$. It is floating in a large vessel containing two immiscible liquids whose densities are $$d$$ and $$\frac{3d}{2}$$ (i) Find the depth of immersion of the cube in the denser liquid (ii) Two opposite faces of the cube are pulled apart such that they are 12 cm apart and the resulting cuboid floats vertically in the same vessel, find its depth of immersion in the denser liquid?
[image]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 23

Report

A ray of light is incident as shown on the face AB an isosceles right angled prism ABC. Find the angle of deviation of the ray emerging through face BC. Ray partially reflected at the face BC emerges through AC. Find the deviation of this ray too. Refractive index of the material of the prism is $$\sqrt{2}$$.
[image]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 24

Report

If 2 g of ice at $$0^\circ\text{C}$$ is added to 2 g of water at $$60^\circ\text{C}$$, Find the temperature of resultant mixture? What are the resulting contents?

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 25

Report

In a nuclear fission reaction $$0.01\%$$ of the mass of the nucleus undergoing fission is converted in to energy. Find the energy (E) released in the fission of 20 g of fission material, if the energy released per reaction is $$200\text{ MeV}$$. A square meter of the earth's surface receives 1400 J every second from the sun. Find the area which receives the same energy E from the sun in one second. (Assume normal incidence)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 26

Report

Two rods A and B of lengths 100 m each are joined end to end. Velocity of sound in A is $$800\text{ m/s}$$. Young's modulus ($$Y$$) and density ($$d$$) of B are two and eight times of their respective values of A. Find the time taken (in s) by sound to travel between the free ends of the rods. (Velocity of sound in the rod is $$v = \sqrt{\frac{Y}{d}}$$)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 27

Report

Identify the mixed anhydride

A

NO

B

$$\text{N}_2\text{O}_3$$

C

$$\text{NO}_2$$

D

$$\text{N}_2\text{O}_4$$

View Solution

IIT Ramaiah SAT April 29 2012 - Question 28

Report

Aluminium sulphate is treated with excess of caustic soda and ammonium hydroxide separately

A

first white precipitate and then clear solution is resulted by both substances

B

first white precipitate and then clear solution is remitted by caustic soda only

C

first white precipitate and then clear solution is resulted by ammonium hydroxide only

D

first white precipitate and then remains as white precipitate

View Solution

IIT Ramaiah SAT April 29 2012 - Question 29

Report

Which statement describes a chemical property?

A

$$\text{CO}_2$$ gas is passed through aqueous solution to prepare aerated drink

B

ethyl alcohol is added to aqueous solution to prepare liquor

C

magnesium ribbon burns in air to give dazzling UV light

D

acid rain occurs during lightening in atmosphere

View Solution

IIT Ramaiah SAT April 29 2012 - Question 30

Report

Equal volumes of 0.5 M HCl, 0.25 M NaOH and 2.75 M NaCl are mixed. The molarity of the $$\text{Cl}^-$$ ion and NaCl respectively

A

1.0 M & 1.0 M

B

1.0 M & 2.0 M

C

1.0 M & 0.5 M

D

2.0 M & 1.0 M

View Solution

IIT Ramaiah SAT April 29 2012 - Question 31

Report

In halogens, which of the following increases from iodine to fluorine?

A

bond length

B

electronegativity

C

ionization energy

D

oxidising power

View Solution

IIT Ramaiah SAT April 29 2012 - Question 32

Report

Silver coating is formed on the walls of the test tube when silver nitrate is added to the organic compound in the presence of ammonia solution. The functional group present is ___________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 33

Report

Atoms of elements in a group in the periodic table have similar chemical properties. This similarity is most closely related to ______________ electron.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 34

Report

A gaseous component X is mixed with gaseous component Y form ideal gaseous solution. Similarly a liquid component A is mixed with another liquid component B form ideal liquid solution. The similarity in both systems _________________________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 35

Report

The main function cryolite in the extraction of aluminum metal from alumina is ___________

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 36

Report

Though nitrogen acts as an inert gas, it is not used as an inert atmosphere in the extraction of magnesium metal. Coal gas is used as inert atmosphere in the extraction. This is because ___________

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 37

Report

Name the compound. The salt which on thermal decomposition leaves a coloured residue, liberated a reddish brown gas and a colourless gas. The residue reacts with caustic soda to give sodium plumbite.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 38

Report

Name the compound. The element X (Z = 85) combines with element Y (Z = 38). The formula of the binary compound.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 39

Report

Name the compound. The product formed at the cathode during electrolysis of aqueous potassium chloride solution.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 40

Report

Name the compound. Quick-lime is fused with coke. An unsaturated hydrocarbon is resulted on adding cold water to the resulting compound.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 41

Report

Name the compound. The reduced product is obtained when ammonia is passed over the heated copper oxide.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 42

Report

Calculate the equilibrium constant, $$K$$ for the reaction $$\text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^-$$ at $$25^\circ\text{C}$$ temperature. Given that density of water is 1 gm/cc at $$25^\circ\text{C}$$.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 43

Report

The colourless vapours of a colourless liquid are pungent and bring tears in eyes on exposure. The yellowish green flame is resulted on burning vapours in $$\text{O}_2$$. In the presence of platinum catalyst the same reacts to give colourless gas which turns to reddish brown on explosive to air<br>(a) write balanced equations (b) calculate the volume of oxygen used separately for these reaction when 300 cc of vapour burn in $$\text{O}_2$$ at STP.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 44

Report

pOH of a base in the range of

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 45

Report

Give the balanced equation. An oxidizing agent which reacts with concentrated hydrochloric acid on heating, liberating chlorine gas and forming two metallic chlorides one of which is chromium chloride.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

IIT Ramaiah SAT April 29 2012 - Question 46

Report

Give the balanced equation. A colourless compound decomposes on treatment with dilute HCl with evolution of $$\text{SO}_2$$ and precipitation of sulphur.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution