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  MEAN AND STANDARD DEVIATION   x ᵢ fᵢ fᵢxᵢ xᵢ² fᵢxᵢ² 3 1 3 9 9 4 1 4 16 16 5 2 10 25 50 6 3 18 36 108 7 6 42 49 294 8 3 24 64 192 9 2 18 81 162 10 1 10 100 100 11 1 11 121 121 Total 20 140 1052 Mean = Σfᵢxᵢ / Σfᵢ = 140 / 20 = 7 Standard deviation 𝞂 = (1/N)√[NΣfᵢxᵢ²  - (Σfᵢxᵢ)²]    = (1/20) √[20(1052) - (140)²]    = (0.05) √(21040 - 19600)    = (0.05) √1440    = (0.05)(37.947) = 1.897 = 1.9

  CLASS 12 MATH REVISION   INVERSE TRIGONOMETRY RELATIONS AND FUNCTIONS CONTINUITY AND DIFFERENTIABILITY 1. Let A = {1,2,3}, B = {4,5,6,7} and let f ={(1,4), (2,5), (3,6)}  be a function from A to B.  Show that  f is one-one. 2. Let A and B be sets.  Show that f: AxB → BxA such that f(a,b) = (b,a) is bijective function. 3. State whether the function f: R →  R defined by f(x) = 3 - 4x is one-one, onto or bijective.  4. Check injectivity and surjectivity of f: N → N given by f(x) = x³. 5. Check whether the relation R defined in the set {1,2,3,4,5,6} as R={(a, b): b = a+1} is reflexive, symmetric or transitive. 6. Check whether the relation R in R defined by R = { (a,b) : a ≤ b³} is reflexive, symmetric or transitive. 7.   Find the principal value of: 1. sin⁻¹ (-1/2) 2. cos⁻¹ (√3/2) 3. cot⁻¹ (-1/√3) 4. cosec⁻¹ (-√2) 5. sec⁻¹ (2/√3) 6. tan⁻¹(-1) 8. Find the value of the following: 1. tan⁻¹(1)  +  cos⁻¹ (-1/2)  +  sin⁻¹ (-...

 CLASS 12  PHYSICS MAGNETISM 1. Define magnet and magnetism. 2. What are artificial magnets?  Name their common shapes. 3. Define 1. Magnetic field                 2. Uniform magnetic field                 3. Magnetic poles                 4. Magnetic axis 4. State the properties of magnets. 5. State Coulomb's law of magnetic force.   6. Define unit magnetic pole. 7. What is the source of magnetic field or magnetism? 8. Repulsion is the surer test of magnetism.  Comment. 9. What is the origin of the word magnetism? 10.  Define 1. Magnetic equator                    2. Magnetic length                    3. Magnetic dipole                    4. Magnetic dipole moment 11. What are magnetic ...

  CLASS 11  LAWS OF MOTION ASSIGNMENT 6 1. Define force.  State the various effects produced by force. 2. State Aristotle's law of motion. 3. State Galileo's law of inertia. 4. What is inertia? 5. Write the different types of inertia and give one example of each. 6. Define momentum.  Is it a scalar or vector quantity? 7. State Newton's laws of motion. 8. State and explain Newton's first law of motion. 9. Give a qualitative definition of force. 10.  Why is Newton's first law of motion also called as law of inertia? 11. Give one example from daily life that illustrates Newton's first law of motion based on (i) inertia of rest (ii) inertia of motion (iii) inertia of direction. 12. Explain how Newton's second law of motion gives a quantitative definition of force. 13. Define inertial mass of a body. 14. Is any external force required to keep a body in uniform motion? 15. Write the dimensions of force.  Is force a scalar or vector quantity? 16. Is it correct to ...

  CLASS 7 REVISION 2  LINES AND ANGLES AND SIMPLE EQUATIONS     2. Find the supplement of the following:      (i) 105°    (ii) 138°   (iii) 126°   3.   Find in the blanks:    x 2 7 9 15 19 30 x+12 23-x   4. Find the value of x in each of the following: (i) x + 2 = 10 (ii) x - 14 = 38 (iii) 2x + 4 = 20 (iv) (x/5) + 3 = 33 (v) 3x - 12  = 72 (vi) (4x/5) - 23 = 17 (vii) 4x - 9 = -19 (viii) 5x + 21 = -49 (ix) (2x/3) + 4/5 = 11/5 (x) (x/7) - 1/8 = 1/6 (xi) x/12 = 36/24 (xii) 6x = 72/15 5. Find the value of the unknown angle in the following triangles: ( All angles are in degrees)          36 48 x       2. 97 z 67       3. 45 65 y       4. 90 x 30       5. z 32 78       6. x 33 77       7. 25 y 105 6. Write equations for the following statements: (i) The sum of numbers x and 12 is...