India Class 12 Exams...can you pass this?

CBSE India ^ | March-14-2006 | me

[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

[ccmay]

A decision is made by the age of 14 or 15 whether you are going on a college track or into a trade school, so when you compare the average scores, you are comparing apples to oranges.

Also, keep in mind that tests like this are designed to be graded on a curve. Even in a country of a billion people, all of them obsessed with education, there is only a relative handful who will get anything remotely like a perfect score on this test.

I must admit, I am startled at the degree of physics and other science knowledge required. Can it be true that even those Indians headed for careers in government service or law or art are required to take this?

-ccm

[MarkL]

It's really amazing how your skills deteriorate when you don't use them. I think that I would have scored pretty well in 1987, just 19 years ago... But then I was also a CS/EE major, and using those tools on a regular basis. Could I have done this in highschool? No way, but then I was a highschool dropout, only managed basic math & algebra, though I did go back and (barely) graduated on time. But highschool did not prepare me for college. Not really the school's fault. I was an awful student.

Mark

[Fishing-guy]

Welcome them over and turn them into citizens.
The mind is a terrible thing to waste.

[ccmay]

Where are the questions about how to fit a condom over a cucumber?

Right after the questions on advanced anal fisting.

-ccm

[CarrotAndStick]

Can it be true that even those Indians headed for careers in government service or law or art are required to take this?

Nope. See #40.

[Bogey78O]

I could have probably passed in 12th grade. Don't need to know the stuff now.

[CarrotAndStick]

All that matters is that they are hugely profitable. Thats all the smarts needed, IMHO.

[Denver Ditdat]

However the science section surprised me regarding the electrical section, more akin to a freshman first semester EE course at your local college.

That was all part of the first year course when I took electronics in high school circa 75-76. In my third year, our final exam was to take a field trip to the FCC field office in Detroit and take the Second Class Radiotelephone exam.

My electronics teacher was a huge influence on my life, and a couple years ago when I was visiting my old hometown I tried to look him up to drop in and say thanks. Unfortunately, he had long since moved on. So had the school district, dropping electronics from the curriculum sometime on the late 80s.

Too bad. That was one class where the theoretical concepts from math and science came to life. I learned to troubleshoot TVs and stereos there, and to rob parts from those beyond hope and build something new. (There were plenty of free-for-the-asking junker tube TVs with generic parts available back then. Trying to cobble together an 80m ham CW transmitter from a modern junk TV would be an exercise in futility).

Times sure have changed.

[Do not dub me shapka broham]

I got a C+ in the only physics class I took in college.

Don't even ask me what my math scores were.

Too embarrassing.

[Old_Mil]

Well, for those of you who are making excuses for the public school system, take a look at the 8th grade final for the Salina, Kansas schools from 1895 taken from the original document on file at the Smoky Valley Genealogical Society and Library in Salina, Kansas and reprinted by the Salina Journal.

Grammar (Time, one hour)
1. Give nine rules for the use of Capital Letters.
2. Name the Parts of Speech and define those that have no modifications.
3. Define Verse, Stanza and Paragraph.
4. What are the Principal Parts of a verb? Give Principal Parts of do, lie, lay and run.
5. Define Case, Illustrate each Case.
6. What is Punctuation? Give rules for principal marks of Punctuation.
7-10. Write a composition of about 150 words and show therein that you understand the practical use of the rules of grammar.

Arithmetic (Time, 1.25 hours)
1. Name and define the Fundamental Rules of Arithmetic.
2. A wagon box is 2 ft. deep, 10 feet long, and 3 ft. wide. How many bushels of wheat will it hold?
3. If a load of wheat weighs 3942 lbs., what is it worth at 50cts. per bu, deducting 1050 lbs. for tare?
4. District No. 33 has a valuation of $35,000. What is the necessary levy to carry on a school seven months at $50 per month, and have $104 for incidentals?
5. Find cost of 6720 lbs. coal at $6.00 per ton.
6. Find the interest of $512.60 for 8 months and 18 days at 7 percent.
7. What is the cost of 40 boards 12 inches wide and 16 ft. long at $.20 per inch?
8. Find bank discount on $300 for 90 days (no grace) at 10 percent.
9. What is the cost of a square farm at $15 per acre, the distance around which is 640 rods?
10.Write a Bank Check, a Promissory Note, and a Receipt.

U.S. History (Time, 45 minutes)
1. Give the epochs into which U.S. History is divided.
2. Give an account of the discovery of America by Columbus.
3. Relate the causes and results of the Revolutionary War.
4. Show the territorial growth of the United States.
5. Tell what you can of the history of Kansas.
6. Describe three of the most prominent battles of the Rebellion.
7. Who were the following: Morse, Whitney, Fulton, Bell, Lincoln, Penn, and Howe?
8. Name events connected with the following dates: 1607, 1620, 1800, 1849, and 1865?

Orthography (Time, one hour)
1. What is meant by the following: Alphabet, phonetic orthography, etymology, syllabication?
2. What are elementary sounds? How classified?
3. What are the following, and give examples of each:
Trigraph, subvocals, diphthong, cognate letters, linguals?
4. Give four substitutes for caret 'u'.
5. Give two rules for spelling words with final 'e'. Name two exceptions under each rule.
6. Give two uses of silent letters in spelling. Illustrate each.
7. Define the following prefixes and use in connection with a word: Bi, dis, mis, pre, semi, post, non, inter, mono, super.
8. Mark diacritically and divide into syllables the following, and name the sign that indicates the sound: Card, ball, mercy, sir, odd, cell, rise, blood, fare, last.
9. Use the following correctly in sentences, Cite, site, sight, fane, fain, feign, vane, vain, vein, raze, raise, rays.
10.Write 10 words frequently mispronounced and indicate pronunciation by use of diacritical marks and by syllabication.

Geography (Time, one hour)
1. What is climate? Upon what does climate depend?
2. How do you account for the extremes of climate in Kansas?
3. Of what use are rivers? Of what use is the ocean?
4. Describe the mountains of N.A.
5. Name and describe the following: Monrovia, Odessa, Denver, Manitoba, Hecla, Yukon, St. Helena, Juan Fermandez, Aspinwall and Orinoco.
6. Name and locate the principal trade centers of the U.S.
7. Name all the republics of Europe and give capital of each.
8. Why is the Atlantic Coast colder than the Pacific in the same latitude?
9. Describe the process by which the water of the ocean returns to the sources of rivers.
10.Describe the movements of the earth. Give inclination of the earth.

I daresay most of our college students would fail this, let alone our 8th graders.

[pop-gun]

A stupid public is the delight of our enemies.

[latina4dubya]

I don't think we're too far behind...

you may want to think again... tell me where i'd find a high school exit exam in the US that is even close to this exam in difficulty... i'm not saying that there are no government-schooled students who could pass it with flying colors... just that it's surely not the norm... most would not earn a high school diploma...

[Denver Ditdat]

The majority of us would fail the rules for the use of the apostrophe in the English language. I think the apostrophe should be renamed the "tack", since its obvious modern use is to keep the S from falling off the end of words.

[Myrddin]

The math was covered in about 2 weeks when I was in high school. A two day refresher would be fine before sitting for that part of the exam. The electricity and optics are subsets of the freshman physics classes I took in college. Again, it would be a two day refresh on a couple 10 week classes before sitting for the exam. When you don't use stuff like this everyday, it helps to review. I could answer about half of the questions cold. As noted by others, the kids sitting for this exam have been learning it fresh over the last year or two. It should be cause of much concern.

[Myrddin]

It should be not a cause of much concern.

[Republican Party Reptile]

darn it! just can't figure out them Cramer's rules ...

[INDIAN_REPUBLICAN]

You could not leave India to get to America unless you get a perfect score on this god forsakenly hard test.

[INDIAN_REPUBLICAN]

At least India's exam is in English.

[INDIAN_REPUBLICAN]

Keep dreaming - you couldn't pass that test if you tried - in fact, you couldnt pass it even if you worked on it for 24 hours - by this time tomorrow, post your answers.

Ready, get set, go!

[Myrddin]

CMM is good for giving management visibility, but doesn't do a lot to guarantee what is happening "under the hood" of a software app.

Agreed. Show my cyclomatic complexities by function. Halstead volumes are helpful too. For object-oriented software, fan-in/fan-out per class. Instrument the code and run a coverage analyzer to expose just how much code is actually being run. Execute with a memory checker e.g. BoundsChecker or Purify to expose sloppy handling of memory. Run a good quality Lint e.g. Flexilint over C code to look for abysmal coding screwups. Get a ratio of lines of code vs comments. See if the comments are actually correct. Use a code profiler to examine call paths. A good analysis tool can spot calling hierarchies. An excellent one doesn't fall apart when indirect recursion magically shows up.