Mathematics Question for revision There will be 10 questions and timing will be 1 hour. 1. The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of the first sixteen terms of the AP. 2. Find the sum of the first 22 terms of an AP in which d = 7 and 22nd term is 149. 3. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference. 4. How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78? 5. The sum of 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP. 6. How many multiples of 4 lie between 10 and 250? 7. If the 3rd and the 9th terms of an AP are 4 and -8, respectively, then which term of this AP is zero. 8. Check whether – 150 is a term of the AP: 11, 8, 5, 2 . . . 9. Which term of the AP: 21, 18, 15, . . . is – 81? Also, is any term 0? Give reason for yo...

Mathematics Question for revision There will be 10 questions and timing will be 1 hour. 1. On comparing the ratios a1/a2 , b1/b2 , c1/c2 find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident: (i) 5x – 4y + 8 = 0 7x + 6y – 9 = 0 (ii) 9x + 3y + 12 = 0 18x + 6y + 24 = 0 (iii) 6x – 3y + 10 = 0 2x – y + 9 = 0 2. Solve the following pair of linear equations by the substitution method : (i) x + y = 14 x – y = 4 (ii) s – t = 3 (s/3) + (t/2) = 6 (iii) 3x – y = 3 9x – 3y = 9 (iv) 0.2x + 0.3y = 1.3 0.4x + 0.5y = 2.3 (v) √2x + √3y = 0 √3x - √8y = 0 (vi) (3x/2) – (5y/3) = -2 (x/3) + (y/2) = (13/6) 3. The coach of a cricket team buys 7 bats and 6 balls for Rs.3800. Later, she buys 3 bats and 5 balls for Rs.1750. Find the cost of each bat and each ball. 4. A fraction becomes 9/11 , if 2 is added to both the numerator and the denominator. I...

Mathematics Question for revision There will be 10 questions and timing will be 1 hour. 1. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Find the Length of PQ. 2. In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to 3. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°, What is the value of ∠ POA ? 4. Prove that the tangents drawn at the ends of a diameter of a circle are parallel. 5. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre. 6. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. 7. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of ...

Mathematics Question for revision There will be 10 questions and timing will be 1 hour. 1. Find the roots of the following quadratic equations by factorisation: i) 100x 2 – 20x + 1 = 0 ii) 2x 2 + x – 6 = 0 iii) 2x 2 – x +1/8 = 0 2. Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (i) 2x 2 – 7x +3 = 0 (ii) 2x 2 + x – 4 = 0 (iii) 4x 2 + 4√3x + 3 = 0 3. Find the roots of the following equations: (i) x-1/x = 3, x ≠ 0 (ii) 1/x+4 – 1/x-7 = 11/30, x ≠ -4, 7 4. Prove the quadratic formula for finding the roots using the completing the square method 5. Find the nature of the roots of the following quadratic equations. If the real roots exist, find them. i) 2x 2 – 3x + 5 = 0 (ii) 3x 2 – 4√3x + 4 = 0 (iii) 2x 2 – 6x + 3 = 0 6. Find the values of k for each of the following quadratic equations so that they have two equal roots. (i) 2x 2 + kx + 3 = 0 (ii) kx (x – 2) + 6 = 0...

Statistics - Mathematics Question Paper There will be 9 question and 1 hr time 1. Consider the following distribution of daily wages of 50 workers of a factory. Daily wages (in Rs.) 500-520 520-540 540-560 560-580 580-600 Number of workers 12 14 8 6 10 Find the mean daily wages of the workers of the factory by using an appropriate method. 2. The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f. Daily Pocket Allowance(in c) 11-13 13-15 15-17 17-19 19-21 21-23 23-25 Number of children 7 6 9 13 f 5 4 3. The following data gives the information on the observed lifetimes (in hours) of 225 electrical components: Lifetime (in hours) 0-20 20-40 40-60 60-80 80-100 100-120 Frequency 10 35 52 61 38 29 Determine...

Mathematics Question for revision There will be 15 questions and timing will be 1.5 hour. 1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically. 2. On comparing the ratios a1/a2 , b1/b2 , c1/c2 find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident: (i) 5x – 4y + 8 = 0 7x + 6y – 9 = 0 (ii) 9x + 3y + 12 = 0 18x + 6y + 24 = 0 (iii) 6x – 3y + 10 = 0 2x – y + 9 = 0 3. Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73. 4. If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero. 5. Which term of the A.P. 3, 15, 27, 39,.. will be 132 more than its 54th term? 6. Determine if the points (1, 5), (2, 3) and (-2, -11) are c...

Probability and Application of Trigonometry Question There will be 15 questions and timing will be 1.5 hour. 1. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red ? (ii) not red? 2. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) the queen of diamonds 3. 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one. 4. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divis...