RULEMATH | MATH ONLINE/DIRECT CLASS | MATH WEBSITE | SCIENCE CLASS 10, PHYSICS CLASS 11 AND 12

  PROBABILITY MEAN OR EXPECTATION 1. Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice.  Find the mean or expectation of X. 2. Find the mean of X where X denotes the number obtained on a throw of an unbiased die. 3. A coin is biased so that head is 3 times as likely to occur as tail.  If the coin is tossed twice, find the mean of X where X denotes the number of tails. 4. Find the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces, and 5 on one face.

CLASS 8 EXPONENTS AND POWERS  ALGEBRAIC EXPRESSIONS AND IDENTITIES REVISION   1. Evaluate: (i) 6 -2  (ii) (-2) -3 (iii) (3/4) -2    2.  Simplify and express the result in power notation with positive exponent:   (i) -(3) 4 ×(5/3) 4   (ii) (3 -7 ÷3 -10 )×3 -5      3. Find the value of :   (i) (1/2) -2 +(1/3) -2 +(1/4) -2   (ii) {(-2/3) -2 } 2  4. Evaluate (i) (8 -1 ×5 3 )/2 -4 (ii) (5 -1 ×2 -2 )×6 -1 5. Find the value of  m  for which 5 m  ÷ 5 -3  = 5 5 6 . Express the following numbers in standard form. (i) 0.000000000012085 (ii) 0.00000000008467   (Iii) 31860000000 7. Express the following numbers in usual form.   (i) 7×10 -8  (ii) 1.0001×10 9 (iii)  6.7×10 12 (iv) 3.5472×10 6 8. In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack? 9 .     Identify the terms, their coef...

  CLASS 8 OCTOBER REVISION RATIONAL NUMBERS SQUARES AND SQUARE ROOTS 1. Using appropriate properties find. (i) -2/3 × 4/7 + 5/2 –  4/7 × 1/6 2. Multiply 18/11 by the reciprocal of - 9/55 3 . Represent  -3/7, -5/7 and -9/7  on the number line. 4. Find the ratio nal numbers between -2/5 and  1/4. 5. What will be the unit digit of the squares of the following numbers? i. 679 ii. 2723   6 . Find ten rational numbers between 2/7 and 3/5.   7. Without adding, find the sum.  1 + 3 + 5 + 7 + 9 8. Express 49 as the sum of 7 odd numbers.  0 9. How many numbers lie between squares of the following numbers? i. 12 and 13 10. Find the square of the following numbers.  (i)  32  (ii) 78 11. Find the square roots of 100 and 169 by the method of repeated subtraction .   12. Write a Pythagorean triplet whose one member is  6. 13. find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also f...

  CLASS 9 NUMBER SYSTEMS POLYNOMIALS 1 . Find six rational numbers between 3 and 4. 2. Show how  √5  can be represented on the number line. 3. Write the following in decimal form and say what kind of decimal expansion each has : (i) 36/100 (II) 2/11   4. Given that 1/7 = 0.142857, can you predict what the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are, without actually doing the long division? If so, how? 5. Express the following in the form p/q, where p and q are integers and q not equal to zero. (i) 0.6666..... (ii)  0.4\overline{7} 0 . 4 7 6. Write three numbers whose decimal expansions are non-terminating non-recurring.   7. Find three different irrational numbers between the rational numbers 5/7 and 9/11. 8. Visualise 3.765 on the number line, using successive magnification. 9. Simplify:    (3+√3)(2+ √2) 10. Represent (√9.3) on the number line.   11. Rationalize the denominators of the following: ( i) 1/(√5+√2) (ii) 1/(...