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ECAT and MCAT Preparation: Post your doubts here!

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its b ryt??thoough i solved it orally.....i said ....for max value cos x and cos (sqrt(2)x) shud be 1 which only occurs when x is o.....
 

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its d ryt...?
how to solve second one.......
 

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its d ryt...?
how to solve second one.......
The answer to the first one is D i think. The answer to the second one is -1/2
First use the formula cosP - cosQ= -2[sin(P+Q)/2][sin(P-Q)/2]
Now the move the 2 the denominator of 1/x making it 1/(x/2).
move this 1/(x/2) to the denominator of sin(x/2) making it sin(x/2)/(x/2)
Apply limit which would make this sin term =1 (theorem)
And you'll get -sin [(pie/6) + (x/2)] applying limit on which, you'll get -1/2.
 
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Some questions:

Q42:
The numerical value of N/n (where N is the number of molecules ina given sample of gas and n is the number of moles of the gas) is
A. 8.314
B. 6.02 * 10^23
C. 1.62 * 10^-24
D. 1.66 * 10^-19

Correct : C

Q50:
4 g of copper was dissolved in conc. nitric acid. The copper nitrate so obtained on strong heating gave 5 g of its oxide. The equivalent weight of copper is
A. 23
B. 32
C. 12
D. 20

Correct : B

Q57:
What is the concentration of nitrate ions if equal volumes of 0.1M AgNO3 and 0.1M NaCl are mixed together?
A. 0.1M
B. 0.2M
C. 0.05M
D. 0.25M

Correct : C

Q58:
A solution of 10mL of M/10 FeSO4 was titrated with KMnO4 solution in acidic medium, the amount of KMnO4 used will be
A. 5 mL of 0.1M
B. 10mL of 0.1M
C. 10mL of 0.5M
D. 10mL of 0.02M

Correct : D
Mine : C
 
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A charged particle moves through a magnetic field perpendicular to its direction. Then
(1) the momentum changes but the kinetic energy is constant
(2) both momentum and kinetic energy of the particle are not constant
(3) both, momentum and kinetic energy of the particle are constant
(4) kinetic energy changes but the momentum is constant
 
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A charged particle moves through a magnetic field perpendicular to its direction. Then
(1) the momentum changes but the kinetic energy is constant
(2) both momentum and kinetic energy of the particle are not constant
(3) both, momentum and kinetic energy of the particle are constant
(4) kinetic energy changes but the momentum is constant
A is believe as direction of velocity changes but magnitude is same!
 
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In the momentum question. As momentum is a vector quantity which depends on velocity and mass of the particle. So as the particle enters the magnetic field, it starts to move in a circular path. If a charge is moving in a circular path, then its centripetal force becomes equal to the magnetic force. If you put them them equal and solve the equation, the relation formed will be (R = mv/qB⊥).
Velocity is always varying in a circle so momentum's magnitude will be constant but its direction will be varying. Finally momentum will not be constant but K.E will be constant.
 
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A ladder 5 m in length is resting against vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of 1.5 m/sec. The length of the highest point of the ladder when the foot of the ladder is 4.0 m away from the wall decreases at the rate of

(A) 2 m/sec (B) 3 m/sec

(C) 2.5 m/sec (D) 1.5 m/sec
 

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hassam, in the matrix question, i think the determinant should be splitted up and then the determinant could be found easily. I am not 100 percent sure.
 
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