10th CBSE Maths Chapter: Quadratic Equation Solved Question and Self Evaluation Question
More Download Paper Click on link Self Evaluation Question Quadratic Equation Solved Question and Self Evaluation Question part-1 Download File Quadratic Equation Solved Question and Self Evaluation Question part-2 Download File Assignment Class X Quadratic Equations 1. Find the value of k for kx2 + 2x - 1 = 0, so that it has two equal roots 2. Find the value of k for k x2 - 2√ 5 x + 4 = 0, so that it has two equal roots. 3. If the roots of the equation (b - c) x2 + (c - c) x + (a - b) = 0 are equal, accordingly prove that 2b = a + c. 4. Find the discriminant of the quadratic equation 3x2– 4 √3 x + 4 = 0, and hence find the nature of its roots. 5. Find the value of k for 2 x2 + k x + 3 = 0, so that it has two equal roots. 6. Find the value of k for k x (x – 2) + 6 = 0, so that it has two equal roots. 7. Find the value of k for which the equation x2 + 5kx + 16 = 0 has no real roots. 8 Find the discriminant of the quadratic equation 2x2– 6x + 3 = 0, and hence find the nature of its roots. 9. Find the value of k for k2 x2 – 2 (2 k - 1) x + 4 = 0, so that it has two equal roots. 10. Find the value of k for (k + 1) x2 – 2 ( k - 1) x + 1= 0, so that it has two equal roots.
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Q. 1. If a1, a2, a3, a4, a5,…… are the n terms of an A.P. Derive the formula for its nth term.
Q. 2. If a1, a2, a3, a4, a4,…… are the n terms of an A.P. Derive the formula for the sum of its n terms. Q. 3. If nth term of an A.P. is given by an = 5n – 3. Find the sum of its 50 terms. Q. 4. Sum of n terms of a sequence is given by Sn = 2n2 – 2n. If it is an A.P. then find its 20th term. Q. 5. Find the sum of the following series: 10 + 14 + 18 + 22 + …………104 Q. 6. If the sum of first 13 terms of an A.P. is 91 and sum of its first 30 terms is 465. Find the sum of its 50 terms. Q. 7. The sum of three numbers which are in A.P. is 9 and sum of their squares is 35. Find the numbers. Q. 8. Divide 32 into 4 parts such that they are in AP and the ratio of the product of first term and fourth terms = product of second and third terms is equal to 7/15. Q. 9. If the pth,qth,rth terms of an AP are a,b,c then prove a(q – r) + b(r-p) = c (q – p) Q. 10. If pth term of an A.P be 1/q and the qth term be 1/p, show that the sum of pq terms is Q. 11. The sum of n terms of an A.P. is given by Sn = 5n2 + 3n, find the nth term of A.P. Q. 12. How many terms of the A.P. -6, -11/2, -5, ………are needed to give the sum -25? Explain the double answer. Q. 13. Find the 30th and 60th terms of the following sequence: (1) 13, 18, 23, 28, 33,………. (2) -10, -7, -4, -1…………….. Q. 14. Find the sum of the following series: (1.) 3+8+13+18+23 …………………….248 (2). -10, -15, -20, -25,………….-105 Q.15 If Sn, the sum of first n terms of an A.P is given by Sn = 3n2 – 4n, then find its nth term (6n – 7) 10th Arithmetic progression (6 Posts) Q. 20.Find three numbers in an A.P. whose sum is 15 and product 80
Q. 21 How many terms of A.P. 22, 20, 18, . . . . . . . . should be taken so that their sum is zero? Q. 22 Find the sum of odd positive integers less than 199. Q. 23 How many two digits numbers between 3 and 102 are divisible by 6? Q. 24 If 7 times the 7thterm is equal to 11 times the 11th term of an A.P. Find its 18th term. Q. 25 Which term of A.P. 13, 21, 29, . . . . . . will be 48 less than its 19th term? Q. 26 Find the A.P. whose 3rd term is –13 and 6th term is +2. Q. 27 Find the A.P., whose 5th term is 23 and 9th term is 43. Q. 28 The angles of a triangle are in A.P. If the smallest angle is one fifth the sum of other two angles. Find the angles. Q. 29 Aditi saved Rs. 500 in the first month of a year and then increased her monthly savings by Rs. 50. If in the nth month, her monthly savings become Rs 1000. Find the value of 'n'. Q. 30 The sum of first n terms of an A.P. is 2n2 + n . Find nth term and common deference of the A.P. Q. 31 The sum of 3rd and 7th terms of an A.P. is 14 and the sum of 5th and 9th terms is 34. Find the first term and common difference of the A.P. Q. 32. Find the sum of the first 30 terms of an A.P., whose nth term is 2–3n. If mth and nth terms of an A.P. are 1/n and1/m respectively, then find the sum of mn terms Q. 33 If mth , nth and rth terms of an A.P. are x, y and z respectively, then prove that :- m( y – z) + n(z – x) + r (x – y) = 0 Q. 34. If the roots of the equation a(b – c) x2 + b(c – a) x + c (a – b) = 0 are equal, then show that 1/a , 1/b , 1/c are in A.P. Q. 35. If the sum of m terms of an A.P. is n and the sum of n terms is m, then show that sum of (m +n) terms is – ( m + n). Download documents Visit Arithmetic Progressions Example 1 :There are 4 red balls and 3 green balls in a bag. One ball is taken out at random.What is the probability of getting a red ball ?
Total no.of balls = 4+3 = 7 Favourable balls = 4 (as there are 4 red balls ) Required Probability = Total no. of fav. balls /Total no. of balls = 4/7 Example 2.What is the probability of not getting a red ball ? Total no.of balls = 4+3 = 7 Favourable balls = 3 (as there are 3 balls other than red balls ) Required Probability = Total no. of fav. balls /Total no. of balls = 3/7 Example 3 :There are 4 red balls , 5 blue balls and 3 green balls in a bag. One ball is taken out at random.What is the probability of getting a red ball ? Total no.of balls = 4+5+3 = 12 Favourable balls = 4 (as there are 4 red balls ) Required Probability = Total no. of fav. balls /Total no. of balls = 4/12=1/3 Example 4. What is the probability of not getting a red ball ? Total no.of balls = 4+5+3 = 12Favourable balls = 8 (as there are 8 balls other than red balls )Required Probability = Total no. of fav. balls /Total no. of balls = 8/12 =2/3 Example 5. What is the probability of not getting a red or a green ball ? Total no.of balls = 4+5+3 = 12 Favourable balls = 9 (as there are 4 red balls and 5 green balls ) Required Probability = Total no. of fav. balls /Total no. of balls = 9/12 =3/4 For more solved questions Visit: http://jsuniltutorial.weebly.com/probability.html Practice Test paper 1. Two dice are thrown once. What is the probability of getting a doublet? 2. A jar contains 54 marbles of colour blue, green and white. The probability of selecting a blue marble at random from the jar is 1/3 and the probability of selecting a green marble at random is 4/9. How many white marbles do the jar contains? 3. In a leap year, find the probability that there are 53 Sundays in the year. 4. A letter is chosen at random from the word MISSISSIPPI. Find the probability of getting (i) a vowel ( ii) a consonant. 5. A bag contains 4 whit balls, 6 red balls and 7 black balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is i) not a black ball ii) neither white nor black iii) red or white. 6. A box has cards numbered from 20 to 100. Cards are mixed thoroughly and a card is drawn from the box at random. Find the probability that the number on the card drawn from the box is i) an odd number ii) a perfect square number and iii) a number divisible by 7. AREAS RELATED TO CIRCLES CLASS X
1. The radius of the circle is 3 m. What is the circumference of another circle, whose area is 49 times that of the first? 2. Two circles touch externally. The sum of their areas is 130 p sq. cm and the distance between their centres is 14 cm. Find the radii of the circles. 3. A wire when bent in the form of an equilateral triangle encloses an area of 121 √3 cm2 . If the same wire is bent in the form of a circle, find the area of the circle. 4. The area enclosed between the two concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle. 5. A wheel of diameter 42 cm, makes 240 revolutions per minute. Find :(i) the total distance covered by the wheel in one minute. (ii) the speed of the wheel in km/hr. 6. An arc of length 20pcm subtends an angle of 144° at the centre of the circle. Find radius of circle. 7. The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector. 8. In the given figure, the length of the minor arc is 7/24 of the circumference of the circle. Find : (i) <AOB(ii) If it is given that the circumference of the circle is 132 cm, find the length of the minor arc AB and the radius of the circle. File downloaded from http://jsuniltutorial.weebly.com Read more » |
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