"Answer these questions and you will become like me."
Posted on 03/13/2006 8:40:36 PM PST by USMMA_83
Fellow Freepers, last week and this week is class 12 exam time in India. There have already been a handful of suicides due to the pressure to pass the final year exam. It's compulsory to pass this exam to get into college in India. Have a look at the sample question papers, and you'll see how far our education is falling behind.
MATHEMATICS CLASS- XII
Matrices
1. Find a, b, c when f(x) = ax2 + bc + c, f(2) = 11 and f(-3) = 6 = f(0) Determine the quadratic function f(x) and find its value when x = 1.
2. Using determinants solve the following system of equations : (i) 2x – 4y = -3 (b) 4x + 3y = 3 4x + 2y = 9 8x – 9y = 1.
3. Solve the following system of equations using Cramer’s rule : (i) x + 2y = 1 (b) 9x + 5y = 10 3x + y = 4 3y – 2x = 8
4. Solve the following system of equations by using Cramer’s rule : (a) x + y + z = 6 (b) 3x + y + z = 10 x – y + z = 2 x + y – z = 0 2x + y – z = 1 5x – 9y = 1
(c) 2x – y + 3z = 9 (d) 3x + y + 2z = 3 x + y + z = 6 x + y – z = -3 x – y + z = 2 x – 2y + z = 4
5. Solve the following system of equations by using Cramer’s rule : (a) x – y + z – 4 = 0 (b) x + y + z = 1 2x + y – 3z = 0 3x + 5y + 6z = 4 x + y + z – 2 = 0 9x + 2y – 36z = 17
6. Solve the following system of equations by using Cramer’s rule : (a) 5t – s + 4u = 5 (b) x + y + z + w = 1 2t + 3s + 5u = 2 x – 2y + 2z + 2w = -6 5t – 3s + 6u = -1 2x + y + 2z – 2w = -5 3x – y + 3z – 3w = -3. 7. Adjoint of a Square Matrix : The adjoint of a square matrix is the transpose of the matrix obtained by replacing each element of A by its co-factor in | A |.
8. Theorem : If A be any n-rowed square matrix : then (Adj. A) A = A(Adj. A) = | A | ln where ln is the n-rowed matrix.
9. For the following matrix A ; prove that A (Adj. A) = 0 1 -1 1 A = 2 3 0 18 2 10
10. Find the adjoint of the matrix 1 0 -1 A = 3 4 5 0 -6 -7
11. Singular Matrix : A square A is called a singular matrix of a non-singular matrix according as | A | or | A | 0, respectively.
12. Theorem: If A, B, be two n-rowed non-singular matrices, then A B is also non-singular and (AB) –1 = b –1 A –1 i.e. the inverse of a product is the product of the inverses taken in the order.
3 8 13. Let A be the matrix Find A –1 and verify that A –1 = 1/13 A – 4/13 I 2 1 where I is 2 2 unit matrix.
3 1 4 0 14. If A = and B = verify that (AB) –1 = B –1 A –1 4 0 2 5
1 2 15. Find the adjoint of the matrix A = and verify A (Adj.A) A = | A | I2 3 -5 a b 16. If A = , find Adj. A. c d
2 -3 17. Given A = , compute A –1 and show that 2A –1 9I – A. -4 7
1 0 0 18. Find Adj. A and A –1, if it exits where A = 3 3 0 5 2 -1
1 -1 1 19. If A = 2 -1 0 , find A2 and show that A2 = A –1 1 0 0
3 -1 2 1 20. If A = -4 0 and B = -1 -2 . Find (A’B) –1 2 1 1 1
1 2 5 21. Compute the inverse of the matrix A = 2 3 1 and verify that A-1 A = 1 -1 1 1
1 2 2 22. Let A = 2 1 2 . Prove that A2 - 4A – 5I = 0, Hence obtain A –1 2 2 1
2 0 -1 23. If A = 5 1 0 Prove that A –1 = A2 – 6A + 11I. 0 1 3
-4 -3 -3 24. If A = 1 0 1 Show that Adj. A = A 4 4 3
1 1 1 24. If A = 1 2 -3 Verify the theorem A (Adj. A) = (Adj. A ) A = | A | I. 2 -2 1
1 -2 3 25. Find A (Adj. A) for the matrix A = 0 2 -1 -4 5 2
26. Compute the inverse of each of the following matrices. 1 2 3 cos -sin 0 (i) 2 3 2 (ii) sin cos 0 3 3 4 0 0
27. Verify that (A B) –1= B –1 A –1 for the matrices A and B
2 1 4 5 Where A = and B = 5 3 3 4
2 0 0 1 28. Where A = and B = Verify that (AB) –1= B –1 A –1 5 3 2 4
2 5 29. If A = , find A-1 and verify that A –1 = -1/7 A + 8/7 I. 1 6
1 1 2 1 2 0 30. If A = 1 9 3 and B = 1 3 -1 , verify that (AB) –1 = B –1 A –1 1 4 2 1 -1 3
4 5 31. If A = then, show that A – 3I = 2[I + 3A –1] 2 1 32. Find the inverse of each of the following matrices and verify : A –1 A = I
2 0 -1 2 3 1 (i) 5 1 0 (ii) 3 4 1 0 1 3 3 7 2
-8 1 4 33. (a) If A = 1/9 4 4 7 Prove that A –1= A’. 1 -8 4
0 -1 2 0 1 (b) Given A = , B –1 1 0 2 -2 0 1 1
From the product C = AB and find C –1. What is the matrix BA? cos x -sin x 0 34. (a) If F(x) = sin x cos x 0 0 0 0
then show that F(x)F(y) = F(x + y), Hence prove that [F(x)] –1 = F(-x).
5 0 4 1 3 3 (b) Given A = 2 3 2 , B –1 = 1 4 3 compute (AB) -1 1 2 1 1 3 4
cos sin 35. If A = , verify that (i) (A –1) –1 = A (ii) (A’) –1 = (A –1)’ sin cos
PHYSICS Class XII
EMI, AC and OPTICS
Q.1> Define mutual inductance. Write its SI unit and give 2 factors on which it depends.
Q.2> Two coherent sources whose intensity ratio is 81:1 produce interference fringes. Find the ratio of intensity of maxima to that of minima
Q.3> A concave mirror and a concave lens are held in water. What changes, if any, do you expect in their focal lengths.
Q.4> You are given two convex lenses of focal length 80mm and 800mm. Which one will you use as an objective and which one as an eyepiece in an astronomical telescope. Draw the ray diagram for image formation and write the formula for magnification.
Q.5> With the help of a labeled diagram, explain the construction and working of an AC generator
Q.6> An LCR circuit has L = 4H, C = 0.1mF and R = 40ohm connected across a variable frequency 220V supply. Calculate a.> Resonance frequency b.> Impedance of circuit and amplitude of current at resonance c.> Rms potential drop across L, C and R at resonance d.> Phase difference b/w Current and Voltage at resonance
Q.7> A choke coil and a bulb are connected in series to a DC source. How does the brightness of the bulb change when an iron core is inserted into the choke.
Q.8> Define Self inductance. Give its SI unit and state 2 factors on which it depends
Q.9> The two slits in YDSE are separated by 0.03mm and the screen is kept 1.5m away. The 4th bright fringe is at a distance of 1cm from the central maxima. Calculate the wavelength of light used.
Q.10> Explain why white light is dispersed while passing through a prism.
Q.11> With the help of a ray diagram, illustrate the formation of image in a compound microscope. Derive the expression for magnifying power. How can the magnifying power be increased.
Q.12> Explain, with the help of a labeled diagram, the principle, construction and working of a step up transformer. Why is its core laminated?
Q.13> A 25μF capacitor, 0.1H inductor and 25ohm Resistor are connected across an AC source given by E = 310sin( 314t ). Find (a) Frequency of AC (b) Reactance of the circuit (c) Impedance (d) RMS current
Q.14> If a rate of change of current of 2A/s induces an emf of 10mV in a solenoid then find its inductance
Q.15> Give 3 differences b/w the fringes obtained in single slit experiment and YDSE
Q.16> A ray of light travelling from a denser to a rarer medium undergoes total internal reflection. Derive the expression for critical angle in terms of speed of light in the two media.
Q.17> The radius of curvature of each face of a biconvex lens of refractive index 1.5 is 30cm. Calculate the focal length in air and in water.
Q.18> A capacitor C, Resistor R and a 40mH inductor are connected across 60Hz AC. Calculate the capacitance if current is in phase with the voltage
Q.19> Prove that an ideal Inductor or Capacitor does not dissipate power in an AC circuit
Q.20> How can one distinguish b/w polarized and unpolarized light?
Q.21> A resistor R is connect across AC supply Eosinωt. Show that the power dissipated in Eo2/2R
Q.22> What is the difference b/w resistance, reactance and impedance?
Q.23> An astronomical telescope consist of 2 thin lenses 36cm apart and has a magnifying power of 8. Calculate the focal length of the lenses.
Q.24> Why is diffraction of sound waves easier to observe than that of light waves. What major changes would you expect in the diffraction experiment if white light is used instead of monochromatic light?
Q.25> Give reasons for the following observations on the MOON (a) Sun rise and sun set are abrupt (b) Sky appears dark (c) Rainbow is never formed
Q.26> An LR circuit is connected across 12V, 50Hz AC supply. The current drawn if 0.5A at an angle of π/3 with the voltage. Calculate the value of L and R.
Q.27> Find the ratio of velocities of red and blue light in air.
Q.28> When a capacitor is connected in series to a LR circuit the current increases. Explain
Q.29> State Lenz law and show that it obeys energy conservation.
Q.30> When an AC of 200V is applied across a device X, a current of 0.5A flows through the circuit and is in phase with the applied voltage. When the same source is applied across another device Y, the same current flows through the circuit but it leads the applied voltage by π/2. Name the devices X and Y (b) Calculate the current if the same source is applied across a combination of X and Y
Q.31> Derive the expression for the fringe width in YDSE
Q.32> Verify Snell’s law of refraction using Huygen’s wave theory
Q.33> A double convex lens made of glass (1.5) has both radii of curvature 20cm. An object 2cm high is placed at 10cm from the lens. Find the position, nature and size of the image.
Q.34> Draw the variation of the following with frequency of AC (a) Reactance of inductor (b) Reactance of capacitor (c) Resistance (d) Inductance
Q.35> An LR circuit draws a power of 560W from a 210V, 60Hz AC source. The power factor of the circuit Is 0.8, Find the value of L and R
Q.36> The image of an object formed by a lens on a screen is not in sharp focus. Suggest a suitable method to get the correct focus without disturbing the object, screen or lens
Q.37> Derive an expression for the width of the central maxima for diffraction of light at a single slit.
Q.38> Find the ratio of current flowing if an inductor is put across 200V,50Hz and 200V,100Hz AC supply. R P
Q.39> An inductor L and a resistor R are connected in parallel to A battery. The resistance of R is same as that of the inductor. Two L Q Identical bulbs are connected in each arm. When the switch is closed Which of the 2 bulbs lights up earlier. Justify.
Q.40> What are coherent sources of light? Why no interference is observed when the 2 sources are placed infinitely close to each other
The answer is simple. Score zero, leave India and go to college in the US. You can be a complete idiot and go to Harvard. Look at a Ted Kennedy.
Okay, so I know who to outsourse to.
I would like to see China's. Bet it is tough also.
Yeah.....they may know all that stuff, but they don't know how to use it to make $100K a year.....
I'm sure I did those math problems in 9th gradee, I didn't take physics though, so I can't say I know any of that, I'm in 12th grade now, and other than the physics, I'd say I could pass that without a large amount of trouble, I don't think we're too far behind... but I also do go to a private school, don't knwo if that makes a difference
Are they allowed to use a calculator? :-)
All your call centers are belonging to us.
whoops (reply to my last comment) just saw some trig/calc lookalikes... that would have been 11th grade, definately didn't do that stuff in 9th
Looks like a pain in the ass, but all stuff I've seen and done before... I bet I could at least pass the thing.
So...why do they live in mud huts?
Good point... it's useless if they could not even get those stinking "holy cows" and their sh$@t out of the streets...
The math section isn't that different than what my kids are taking now in H.S (9th and 11th grade).
However the science section surprised me regarding the electrical section, more akin to a freshman first semester EE course at your local college.
However please note that the state requirements test where I live is waaaaaay watered down from this......
That`s like here in New York city, at NYU. A lot of Asian families overseas lay out everything to send their kid to this bastion of liberal puss, and the kid commits suicide when they don`t learn anything and fail exams because the Professors are too busy talking about the evils of Bush in every lecture. Do a search in Google, "suicide NYU".. Just about every year there is another one.
It is a bit of a silly question- we are seeing the test cold, and I bet the majority of posters have been out of school 10+ years. However, if we had the time that Indian students have to study for the exam, I think many American students would be able to pass it.
I could have passed the Math portion when I was in prep school in 1966. Today? Not a chance.
Yes, private schoold does make a difference. I can guarantee you my public school classmates couldn't have passed that. I was a senior year exchange student in US from souther europe. I'd have no problems passing this end of my sophomore year, actually - but senior year high school in rural midwest - I can guarantee you noone would get 50%.
"Answer these questions and you will become like me."
Boy, they really do love Cramer's Rule and matrices, don't they? :-P
No, I couldn't answer those questions now but I'll bet I could if I'd spent the past year or more studying it. I do remember doing much of that math in high school and I did take physics but don't remember one bit of it. :-P
Cheers!
That's all well and good, but do the students feel good about themselves?
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