IIT Jee Preparation
1. If C is a skew - symmetric matrix of order n and X is n x 1 column matrix , then X'CX is a :
(a) scalar matrix
(b) unit matrix
(c) null matrix
(d) none of these
Answer : (c)
2. If A^2 = A , then (I + A)^4 is equal to :
(a) I + A
(b) I + 4A
(c) I + 14A
(d) I + 15A
Answer : (d)
3. In a triangle ABC , if sinA sinB sinC = p , cos A cosB cosC = q , then tanA , tanB , tanC are the roots of the equation :
(a) qx^3 + px^2 - ( 1 + q ) x + p = 0
(b) qx^3 - px^2 + ( 1 + q )x - p = 0
(c) qx^3 - ( 1 + p ) x^2 + qx - p = 0
(d) qx^3 - ( 1 + p ) x^2 + ( 1 + q )x - p = 0
Answer : (b)
4. In a triangle ABC , r^2 + r1^2 + r2^2 + r3^2 + a^2 + b^2 + c^2 is equal to :
(a) 4R^2
(b) 8R^2
(c) 12R^2
(d) 16R^2
Answer : (d)
5. A + 4HIO4 ----> 3HCOOH + HCHO + CHO - COOH
Glucose derivative 'A' is / are :
(a) gluconic acid
(b) glucaric acid
(c) glucitol
(d) glucouronic acid
Answer : (a)
6. Which of the following is true about the complex [ ptCl2(NH3)(OH2)] ?
(a) It exhibits geometrical isomerism
(b) It is paramagnetic complex
(c) It's geometry is not square planer
(d) Platinum is sp3 hybridized
Answer : (a)
7. An ideal gas expands in such a manner that it pressure and volume can be related by equation PV^2 = constant . During this process , the gas is
(a) heated
(b) cooled
(c) neither heated not cooled
(d) first heated and then cooled
Answer : (b)
8. If pressure of a gas contained in a closed vessel is increased by 0.4% when heated by 1°C , the initial temperature must be
(a) 250 K
(b) 250°
(c) 2500 K
(d) 25°C
Answer : (a)
9. Ethylene glycol is used as an antifreeze in a cold climate . Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at - 6°C will be :
(a) 204.30 g
(b) 400.00 g
(c) 304.60 g
(d) 804.32 g
Answer : (d)
10. If an aqueous solution of glucose is allowed to freeze , then crystals of which will be separated out first ?
(a) glucose
(b) water
(c) both of these
(d) none of these
Answer : (b)
11. A beaker is completely filled with water at 4°C . It will overflow if
(a) Heated above 4°C
(b) Cooled below 4°C
(c) Both heated and cooled above and below 4°C respectively
(d) None of these
Answer : (c)
12. A solid cube and a solid sphere of the same material have equal surface area . Both are at the same temperature 120°C . Then
(a) both the cube and the sphere cool down at the same rate
(b) The cube cools down faster than the sphere
(c) The sphere cools down faster than the cube
(d) Whichever is having more mass will cool down faster
Answer : (b)
13. A particle executing SHM of amplitude 'a' has a displacement a/2 at t = T/4 and a negative velocity . The epoch of the particle is
(a) π/3
(b) 2π/3
(c) π
(d) 5π/3
Answer : (a)
14. The area of the region bounded by the parabola y = x^2 + 1 and the straight line x + y = 3 is given by
(a) 45/7
(b) 25/4
(c) π/18
(d) 9/2
Answer : (d)
15. An increase in intensity level of 1dB implies an increase in density of
(a) 1%
(b) 3.01%
(c) 26%
(d) 0.1%
Answer : (c)
16. The molarity of 900 g of water 💦 is
(a) 50 M
(b) 55.5 M
(c) 5 M
(d) cannot be calculated
Answer : (b)
17. In comparision to a 0.01 M solution of glucose , the depression in freezing point of a 0.01 M MgCl2 solution is ....
(a) the same
(b) about twice
(c) about three times
(d) about six times
Answer : (c)
18. The displacement of a particle is given by x = 3 sin (5πt) + 4 cos(5πt) . The amplitude of particle is
(a) 3
(b) 4
(c) 5
(d) 7
Answer : (c)
19. The equation of the common tangent to the curves y^2 = 8x and xy = -1 is
(a) 3y = 9x + 2
(b) y = 2x + 1
(c) 2y = x + 8
(d) y = x + 2
Answer : (d)
20. Four moles of hydrogen , 2 moles of helium and 1 mole of water vapour form an ideal gas mixture . What is the molar specific heat at constant pressure of mixture ?
(a) 16/7 R
(b) 7 R / 16
(c) R
(d) 23/7 R
Answer :(d)
21. The amount of solute ( molar mass 60 g/mol ) that must be added to 180 g of water so that the vapour pressure of water is lowered by 10% is
(a) 30 g
(b) 60 g
(c) 120 g
(d) 12 g
Answer : (b)
22. A simple pendulum oscillates slightly above a large horizontal metal plate . The bob is given a charge . The time period
(a) has no effect , whatever be nature of charge
(b) always decreases , whatever be nature of charge
(c) always increases , whatever be nature of charge
(d) a increase or decrease depending upon the nature of charge
Answer : (b)
23. Which of the following compounds will not undergo azo coupling reaction with benzene diazonium chloride ?
(a) Aniline
(b) Phenol
(c) Anisole
(d) Nitrobenzene
Answer : (d)
24. If f(x) and | f(x) | are both differentiable , then f(x) is
(a) left continuous at x = 0
(b) right continuous at x= 0
(c) not continuous at x= 0
(d) continuous everywhere
Answer : (d)
25. Of the following 0.10 m aqueous solutions , which one will exhibit the largest freezing point depression ?
(a) KCl
(b) C6H12O6
(c) Al2(SO4)3
(d) K2SO4
Answer : (c)
26. The area bounded by the curve y^2 = 9x and the lines x = 1 , x = 4 and y = 0 in the first quadrant is
(a) 7
(b) 14
(c) 14/3
(d) 28
Answer : (b)
27. The intensity level of two sounds are 100 dB and 50 dB . What is the ratio of their intensities ?
(a) 10^1
(b) 10^3
(c) 10^5
(d) 10^10
Answer : (c)
28. At room temperature , the rms speed of the molecules of a certain diatomic gas is found to be 1930 m/s . The gas is
(a) H2
(b) F2
(c) O2
(d) Cl2
Answer : (a)
29. The KE and PE of a particle executing SHM with amplitude A will be equal when its displacement is
(a) A√2
(b) A/2
(c) A/√2
(d) A√(2/3)
Answer : (a)
30. The degree and order of the differential equation of the family of all parabola whose axis is x axis are respectively
(a) 3,2
(b) 2,3
(c) 2,1
(d) 1,2
Answer : (d)
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