Mathematics Question Paper For Class 10th CBSE Board (India), Essays (high school) of Mathematics

Download Mathematics Question Paper For Class 10th CBSE Board (India) and more Essays (high school) Mathematics in PDF only on Docsity! Class - 10th Mathematics – Standard Max. Marks: 80 Duration: 3 hrs SECTION – A There are 10 MCQ. Each question carries 1 mark. 1. If the sum of zeroes of the quadratic polynomial 3x2- kx+6 is 3 ,then find the value of k. (a)3 (b)4 (c) 5 (d)9 2. If ∆ABC ≈ ∆PQR , perimeter of ∆ABC = 32 cm , perimeter of ∆PQR = 48 cm and PR = 6 cm . then find the length of AC. (a)2 cm (b) 4cm (c)6cm (d)8cm 3. If tan θ + cot θ = 5, find the value of tan 2 θ + cot 2 θ. (a)21 (b) 23 (c)25 (d)27 4. If 1 is a root of the equations ay 2 + ay + 3 = 0 and y 2 + y + = 0, then find the value of ab. (a)3 (b)4 (c)5 (d)6 5. If the area of a circle is equal to sum of the areas of two circles of diameter 10cm and 24 cm , calculate the diameter of the larger circle. (a)25cm (b) 26cm (c)27cm (d)28cm 6. The circumference of a circle is 22cm. calculate the area of its quadrant. (a) 77/4 (b) 77/ 2 (c)77/8 (d)77/6 7. A solid right cone is cut into two parts at the middle of its height by a plane parallel to its base. Find the ratio of the volume of the smaller cone to the whole cone. (a)1:8 (b)1:6 (c) 1:7 (d)1:16 8. Find the distance of the point (-3,4) from the x-axis (a)3 (b)5 (c)6 (d)4 9. The decimal of the rational number 43/2453 will terminate after how many places of decimals. (a)215/104 (b)315/104 (c)415/104 (d)515/104 10. If ax + by = a2 – b2 and bx + ay = 0 , find the value of (x+y). (a) x+y = a – b (c) x – y = a – b (b) x + y = a+b (d) x – y = a + b (11–15). Fill in the blanks. Each question carries 1 mark. 25. Show that 5 + 3√2 is an irrational number. 26. Solve graphically the following system of linear equations: 3x – y = 2; x + 2y = 10. Also, find the coordinates of the points where the lines meet the axis of y. Section - C (27-34). each question carries 3 marks. 27. In fig. AB ║DE and BD ║ EF. Prove that DC 2 = CF × AC 28. In triangle PQR, PS is perpendicular to QR and PS2 = QS.RS. Show that the triangle is angle triangle. 29. Prove that identity: √ (1+sinθ)/ (1-sinθ) + √ (1-sinθ)/ (1+sinθ) = 2secθ. Or If secθ – tanθ = x, show that secθ + tanθ = 1/x and hence find the value of cosθ and sinθ. 30. Find the value of k, if the point P (2, 4) is equidistance from the point A (5, k) and B (k, 7). 31. All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is (1) a black face card. (2) a red card 32. Solve the following quadratic equation for x: X 2 – 4ax – b 2 + 4a 2 = 0 33. Draw a triangle ABC with BC = 7cm, √B = 45° and √C = 60°. Then construct another triangle, whose sides are 3/5 times the corresponding sides of ∆ABC. Or A circle is inscribed in a triangle PQR with PQ = 10cm, QR = 8cm, and PR = 12cm. find the length of QM, RN and PL. 34. In fig. O is the centre of the circle with AC = 24cm, AB = 7cm, and √BOD = 90°. Find the area of the shaded region. Section - D (34-40) each question carry 4 marks. 35. The distribution below gives the weight of 30 student of a class. Find the mean and the median weight of the students. weight 40- 45 45- 50 50- 55 55- 60 60- 65 65- 70 70- 75 No. of std. 2 3 8 6 6 3 2 36. Places A and B ae 160 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 8 hrs, but if they travel towards each other, they meet in 2 hrs. what are the speeds of the two cars? Or A man sold a chair and a table together for 760rs thereby making a profit of 25% on chair and 10% on table. By selling them together for 767.50 rs he