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1)Has the rational number 27 2 441 257 .. a terminating or a non-terminating decimal representation? CBSE Mathematics
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2)If α, β are the zeroes of a polynomial, such that α + β = 6 and αβ = 4, then write the polynomial. CBSE Mathematics
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3)If the sum of first p terms of an A.P. is ap 2 + bp , find its common difference. CBSE Mathematics
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4)If P(2, p ) is the mid-point of the line segment joining the points A(6, -5) and B(-2, 11), find the value of p. CBSE Mathematics
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5)If A(1, 2), B( 4, 3) and C( 6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of the fourth vertex D. CBSE Mathematics
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6)A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting a red face card. CBSE Mathematics
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7)Find the value of k for which the following pair of linear equations have infinitely many solutions: CBSE Mathematics
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8)In an A.P., the first term is 2, the last term is 29 and sum of the terms is 155. Find the common difference of the A.P. CBSE Mathematics
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9)If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus. CBSE Mathematics
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10)Find the value of cosec 30° geometrically. CBSE Mathematics
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11)The sum of numerator and denominator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1, the fraction becomes 1/2 . Find the fraction. CBSE Mathematics
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12)In an A.P., fhe sum of first ten terms is –150 and the sum of its next ten terms is –550. Find the A.P. CBSE Mathematics
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13)Construct a triangle ABC in which BC = 8 cm, ∠ B = 45°, AB-AC = 3.5cm. CBSE Mathematics
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14)If R( x, y ) is a point on the line segment joining the points P( a, b ) and Q( b, a ), then prove that x + y = a + b. CBSE Mathematics
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15)Cards bearing numbers 1, 3, 5, _ _ _, 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing CBSE Mathematics
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16)Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46, find the integers. CBSE Mathematics
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17)The difference of squares of two numbers is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers. CBSE Mathematics
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18)Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. CBSE Mathematics
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19)If the areas of two similar triangles are equal, then prove that the triangles are congruent. CBSE Mathematics
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20)From the top of a 7 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of the foot of the tower is 30,°. Find the height of the tower. CBSE Mathematics
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21)If α, β are the zeroes of the polynomial 2y 2 + 7y + 5, write the value of α + β + αβ. CBSE Mathematics
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22)If the sum of the first q terms of an A.P. is 2q + 3q 2 , what is its common difference? CBSE Mathematics
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23)What is the distance between the points A(c, 0) and B(0, - c) ? CBSE Mathematics
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24)In a ∆ ABC, right-angled at C, AC = 6 cm and AB = 12 cm. Find ∠ A. CBSE Mathematics
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25)CBSE Mathematics
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26)The slant height of the frustum of a cone is 5 cm. If the difference between the radii of its two circular ends is 4 cm, write the height of the frustum. CBSE Mathematics
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27)A die is thrown once. What is the probability of getting a number greater than 4 ? CBSE Mathematics
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28)For what value of k, is 3 a zero of the polynomial 2x 2 + x + k ? CBSE Mathematics
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29)Find the value of m for which the pair of linear equations 2x + 3y – 7 = 0 and (m – 1) x + (m + 1) y = (3m – 1) has infinitely many solutions. CBSE Mathematics
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30)Find the common difference of an A.P. whose first term is 4, the last term is 49 and the sum of all its terms is 265. CBSE Mathematics
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31)The sum of the numerator and the denominator of a fraction is 4 more than twice the numerator. If 3 is added to each of the numerator and denominator, their ratio becomes 2: 3. Find the fraction. CBSE Mathematics
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32)In an A.P., the sum of its first ten terms is – 80. and the sum of its next ten terms is – 280. Find the A.P. CBSE Mathematics
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33)In an A.P., the sum of its first ten terms is – 80. and the sum of its next ten terms is – 280. Find the A.P. CBSE Mathematics
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34)Prove the following: CBSE Mathematics
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35)Prove the following: CBSE Mathematics
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36)If the points (p, q); (m, n) and (p – m, q – n) are collinear, show that pn = qm. CBSE Mathematics
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37)The rain-water collected on the roof of a building, of dimensions 22 m x 20 m, is drained into a cylindrical vessel having base diameter 2 m and height 3.5 m. If the vessel is full up to the brim, find the height of rain-water on the roof. CBSE Mathe
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38)A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears CBSE Mathematics
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39)A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages. CBSE Mathematics
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40)In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then prove that the angle opposite the first side is a right angle. CBSE Mathematics
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41)In an isosceles triangle PQR, PQ = QR and PR 2 = 2 PQ 2 . Prove that ∠ Q is a right angle CBSE Mathematics
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42)A man on the deck of a ship, 12 m above water level, observes that the angle of elevation of the top of a cliff is 60° and the angle of depression of the b ase of the cliff is 30°. Find the distance of the cliff from the ship and the height of the
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43)The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud from the surface of the lake CBSE Mathematics
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44)The surface area of a solid metallic sphere is 616 cm 2 . It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed. CBSE Mathematics
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45)The difference be tween the outer and inner curved surface areas of a hollow right circular cylinder, 14 cm long, is 88 cm^2 . If the volume of metal used in making the cylinder is 176 cm^3 , find the outer and inner diameters of the cyli
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46)Find the 9 th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185. CBSE Mathematics
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47)Cards marked with number 3, 4, 5, ...., 50 are placed in a box and mixed thoroughly. A card is drawn at random form the box. Find the probability that the selected card bears a perfect square number. CBSE Mathematics
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48)Cards marked with number 3, 4, 5, ...., 50 are placed in a box and mixed thoroughly. A card is drawn at random form the box. Find the probability that the selected card bears a perfect square number. CBSE Mathematics
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49)The x-coordinate of a point P is twice its y-coordi nate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P. CBSE Mathematics
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50)How many terms of the A.P. 65, 60, 55, .... be take n so that their sum is zero? CBSE Mathematics
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51)A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular rin g of width 3 m to form an embankment. Find the height of the embankment. CBSE Mathematics
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52)If the sum of first 7 terms of an A.P. is 49 and t hat of its first 17 terms is 289, find the sum of first n terms of the A.P. CBSE Mathematics
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53)The angles of depression of the top and bottom of a 50 m high building from the top of a tower are 45° and 60° respectively. Find the height of the tower and the horizontal distance between the tower and the building. CBSE Mathematics
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54)A box consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Ramesh, a shopkeeper will buy only those s hirts which are good but Kewal another shopkeeper will not buy shirts with major d efects. A shirt is taken o
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55)A toy is in the form of a cone of base radius 3.5 c m mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15 .5 cm, find the total surface area of the toy. CBSE Mathematics
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56)A passenger, while boarding the plane, slipped form the stairs and got hurt. The pilot took the passenger in the emergency clinic at the a irport for treatment. Due to this, the plane got delayed by half an hour. To reach the des tination 1500 km
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57)A bird is sitting on the top of a 80 m high tree. F rom a point on the ground, the angle of elevation of the bird is 45°. The bird flies away h orizontally in such a way that it remained at a constant height from the ground. Afte r
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58)Prove that the area of a triangle with vertices (t, t −2), (t + 2, t + 2) and (t + 3, t) is independent of t. CBSE Mathematics
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59)The sum of three numbers in A.P. is 12 and sum of t heir cubes is 288. Find the numbers. CBSE Mathematics
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60)Prove that the lengths of tangents drawn from an ex ternal point to a circle are equal. CBSE Mathematics
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61)The time taken by a person to cover 150 km was 2(1/2) hours more than the time taken in the return journey. If he returned at a speed of 10 km/hour more than the speed while going, find the speed per hour in each direction. CBSE Mathematics
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62)For what value of k will k + 9, 2k – 1 and 2k + 7 a re the consecutive terms of an A.P.? CBSE Mathematics
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63)A ladder, leaning against a wall, makes an angle of 60° with the horitonzal. If the foot of the ladder is 2.5 m amay from the wall, find the le ngth of the ladder. CBSE Mathematics
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64)A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither red card nor a quee n. CBSE Mathematics
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65)Let P and Q be the points of trisection of the line segment joining the points A(2, –2) and B(–7, 4) such that P is nearer to A. Find the coord inates of P and Q. CBSE Mathematics
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66)Prove that the points (3, 0), (6, 4) and (−1, 3) ar e the vertices of a right angled isosceles triangle. CBSE Mathematics
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67)The 4 th term of an A.P. is zero. Prove that the 25 th term of the A.P. is three times its 11 th term. CBSE Mathematics
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68)If the point P(x, y) is equidistant from the points A(a + b, b − a) and B(a − b, a + b). Prove that bx = ay. CBSE Mathematics
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69)A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. CBSE Mathematics
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70)A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 32/9 cm. Find the diameter.
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71)A sphere of diameter 12 cm, is dropped in a right c ircular cylindrical vessel, partly filled with water. If the sphere is completely submerged i n water, the water level in the cylindrical vessel rises by 359 cm. Find the diamet er o
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72)A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the an gle of depression of the base of hill as 30°. Find the distance of the hill from the ship and the heig
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73)Three different coins are tossed together. Find the probability of getting CBSE Mathematics
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74)Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively offered to the state government to provide place and the canvas for 1500 tents to be fixed by the government and decided to share the whole expenditure equally.
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75)Prove that the lengths of the tangents drawn from a n external point to a circle are equal. CBSE Mathematics
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76)Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60° to each other. CBSE Mathematics
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77)The angle of elevation of the top Q of a vertical t ower PQ from a point X on the ground is 60°. From a point Y, 40 m vertically above X, the a ngle of elevation of the top Q of tower is 45°. Find the height of the tower PQ and the distan ce PX.
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78)The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses proce eding the house numbered X is equal to sum of the numbers of houses following X. CBSE Mathematics
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79)A number x is selected at random from the numbers 1 , 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16. CBSE Mathematics
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80)A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot . Find the speed of the stream. CBSE Mathematics
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81)For what value of k will the consecutive terms 2k + 1, 3k + 3 and 5k − 1 form an A.P. ? CBSE Mathematics
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82)20 tickets, on which numbers 1 to 20 are written, a re mixed thoroughly and then a ticket is drawn at random out of them. Find the probabilit y that the number on the drawn ticket is a multiple of 3 or 7. CBSE Mathematics
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83)A two digit number is four times the sum of the dig its. It is also equal to 3 times the product of digits. Find the number. CBSE Mathematics
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84)Find the ratio in which the point ( −3, k) divides the line -segment joining the points ( −5, −4) and (−2, 3). Also 6ind the value of k. CBSE Mathematics
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85)Prove that the points (2, −2), (−2, 1) and (5, 2) a re the vertices of a right angled triangle. Also find the area of this triangle. CBSE Mathematics
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86)If the ratio of sum of the first m and n terms of a n AP is m 2 : n 2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1). CBSE Mathematics
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87)If the point C (–1, 2) divides internally the line- segment joining the points A (2, 5) and B (x, y) in the ratio 3 : `4, find the value of x 2 + y 2 . CBSE Mathematics
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88)A cylindrical tub, whose diameter is 12 cm and hei ght 15 cm is full of ice-cream. The whole ice-cream is to be divided into 10 children i n equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conic
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89)Two men on either side of a 75 m high building and in line with base of building observe the angles of elevation of the top of the building as 30° and 60°. Find the distance between the two men. CBSE Mathematics
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90)A game consist of tossing a one-rupee coin 3 times and noting the outcome each time. Ramesh will win the game if all the tosses show the same result, (i.e. either all thee heads or all three tails) and loses the game otherwise. Find the probabili
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91)A pole has to be erected at a point on the boundary of a circular park of diameter 13 m in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? I
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92)Prove that the lengths of tangents drawn from an external point to a circle are equal. CBSE Mathematics
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93)Solve for x and y: CBSE Mathematics
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94)If the HCF of the polynomials p(x) = (x + 1) (x^2 + ax + 4) and q(x) = (x + 4) (x^2 + bx +2) is h(x) = x^2 + 5x + 4, find the values of a and b.
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95) Solve for x: 12abx^2 — (9a^2 — 8b^2) x - 6ab = 0 CBSE Mathematics
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96)A two-digit number is such that the product of its digits is 35. When 18 is added to the number, the digits interchange their places. Find the numbe r. CBSE Mathematics
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97) The 6th term of an Arithmetic Progression (AP) is —10 and the term is —26. Determine the 15 th term of the AP. CBSE Mathematics
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98) Find the sum of all the two digit natural numbers when are divisible by 4. CBSE Mathematics
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99) A household article is available for Rs. 2,500 cas h or Rs. 520 cash down payment followed by four equal monthly instalments. If the rate of inte rest charged under the instalment plan is 25% per annum, find the amount of each instalment. CBSE Ma
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100) A man borrows Rs. 36,410 from a finance company an d has to repay it in three equal annual instalments. Find the amount of each instalment if the rate of interest is 10% per annum compounded annually. CBSE Mathematics
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101)Draw the graphs of the equations: 4x – y – 8 = O and 2x - 3y + 6 = O CBSE Mathematics
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102) A train travels a distance of 300 km at a uniform speed. If the speed of the train is increased by 5km an hour, the journey would have taken two hours less. Find the original speed of the train. CBSE Mathematics
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103) The radius of the base and the height of a solid right circular cylinder are in the ratio 2 : 3 and its volume is 1617 Cu. cm. Find the total surface area of the cylinder. CBSE Mathematics
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104) The radius of the base and the height of a solid r ight circular cylinder are in the ratio 2 : 3 and its volume is 1617 Cu. cm. Find the total surface a rea of the cylinder. CBSE Mathematics
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105) Find the value of p for which the point (p,-1), (2, 1) and (5, -1) are collinear. CBSE Mathematics
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106)A box contains 20 balls bearing numbers 1, 2, 3, 4, ..., 20. A ball is drawn at random from the box. What is the probability that the number on the ball is CBSE Mathematics
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107) The rain water from a roof 22 m x 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. lithe vessel is just full, find the rainfall in cm. CBSE Mathematics
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108)A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the bucket if the cost of metal sheet used is Rs. 15 per 100 cm2. CBSE
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109) The angles of depression of the top and the bottom of a building 50 metres high as observed from the top of a tower are 30 0 and 60 0 respectively. Find the height of the tower and also the horizontal distance between the building and the tower.
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110) Annual income from salary of Mrs. Usha, who is a s enior citizen, is Rs. 3,85,000. She donates Rs. 10,000 to Prime Minister’s Relief Fund (100% ex emption) and Rs. 10,000 to a Charitable Society (50% exemption). She contributes Rs. 70,000 towar
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111)Using Euclid’s Division Lemma .Find H.C.F. of 56,96404. CBSE Mathematics
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112)Find the zeros of the polynomial 4x^2 -9 CBSE Mathematics
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113)Find out whether the following pair of Linear equations are consistent or inconsistent: 3x+2y = 5 , 2x - 3y = 7. CBSE Mathematics
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114)Find the sum of first 30 natural numbers. CBSE Mathematics
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115)Cards each marked with numbers 4,5,6,...,.20 are placed in a box and mixed thoroughly . One card is drawn at random . Find the probability of getting an even prime number. CBSE Mathematics
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116)Evaluate sec 70 o sin 20 o – cos 20 o cosec 70 o . CBSE Mathematics
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117)The length of minute hand of a clock is 14 cm .Find the area swept by the minute hand in 5 minutes. CBSE Mathematics
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118)Give the relationship between mean , median and mode. CBSE Mathematics
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119)Prove that the length of the tangents drawn from an external point to a circle is equal. CBSE Mathematics
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120)Find the value of p which will make the product of 2p - 5 and p - 4 equal in value to p + 8. Mathematics CBSE class 10 2013
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121)Which term of the AP 21, 18,15, ... is zero? Mathematics CBSE class 10 2013
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122)Find a relation between x and y such that the point (x,y) is equidistant from the point (7,1) and (3,5) Mathematics CBSE class 10 2013
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123)If the circumference of a circle exceeds the diameter by pi units, then find the diameter of the circle. Mathematics CBSE class 10
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124)Which term of the sequence 25,22,19, ... is the first negative term? Mathematics CBSE class 10
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125)The incircle of an isosceles triangle ABC, with ABC with AB = AC touches the sides AB. Bc, and CA at D E and F respectively. Prove that E bisects BC. Mathematics CBSE class 10
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126)Find the probability of getting 53 Mondays in a leap year. Mathematics CBSE class 10
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127)A solid cube is cut into eight cubes of equal volumes. Find the ratio of the total surface area of the given cube and that of one small cube. Mathematics CBSE class 10
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128)If x = -1/2, is solution of the quadratic equation 3x^2 + 2kx - 3 = 0, find the value of k. Mathematics CBSE class 10 2015
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129)The tops of two towers of height x and y, standing on level ground, subtend angles of 30 degree and 60 degree respectively at the centre of the line joining their feet, then find x:y. Mathematics CBSE class 10 2015
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130)A letter of a English alphabet is chosen at random, Determine the probability that the chosen letter is a consonant. Mathematics CBSE class 10 2015
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131)From a point T outside a circle of centre O, tangents TP and TQ are drawn to the circle. Prove that OT is the right bisector of line segment PQ. Mathematics CBSE class 10 2015
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132)Find the mid term of the AP 6,13,20,....,216. Mathematics CBSE class 10 2015
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133)If A(5,2), B(2,-2) and C (-2,t) are the vertices of a right angled triangle with angle B = 90 degree, then find the value of t. Mathematics CBSE class 10 2015
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134)Find the ratio in which the point P(3/4, 5/12) divides the line segment joining the points A(1/2, 3/2) and B(2,-5). Mathematics CBSE class 10 2015
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135)Find the area of the triangle ABC with A(1,-4) and mid points of sides through A being (2,-1) and (0,-1). Mathematics CBSE class 10 2015
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136)Find the non - zero value of k, for which the quadratic equation kx^2 + 1 - 2(k-1)x + x^2 = 0 has equal roots. Hence find the roots of the equations. Mathematics CBSE class 10 2015
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137)The angle of elevation of the top of a building from thee foot of the tower is 30 degree and the elevation of the top of the tower from the foot of the building is 30 degree and the elevation of the top of the tower from the foot of the building is 4
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138)Two different dice are rolled together. Find the probability of getting: Mathematics CBSE class 10 2015
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139)If Sn, denotes the sum of first n terms of an AP prove that S12 = 3(S8 - S4). Mathematics CBSE class 10 2015
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140)A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 (5/6) cm^3. Find the height of the toy. ALso find the cost of painting the h
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141)The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator then the sum of the new fraction and original fraction is 29/20. Find the original fraction. Mathematics CBSE class 10 2015
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142)What value is generated in the below situation? Mathematics CBSE class 10 2015
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143)Prove that tangent at any point of a circle is perpendicular to the radius through the point of contact. Mathematics CBSE class 10 2015
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144)Construct a triangle ABC with BC = 7 cm, angle B = 60 degree and Ab = 6 cm. Construct another triangle whose sides are 3/4 times the corresponding sides of triangle ABC. Mathematics CBSE class 10 2015
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145)If the length of the flag staff is 5 m find the height of the tower. Mathematics CBSE class 10 2015
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146)Find the probability that the number on the drawn card is Mathematics CBSE class 10 2015
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147)If A (-4,8), B(-3,-4), C(0,-5) and D(5,6) are the vertices of a quadrilateral ABCD find its area. Mathematics CBSE class 10 2015
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148)A well of diameter 4 m is dug 14 m deep. The earth taken out is spread evenly all around the well to form a 40 cm high embankment. Find the width of the embankment. Mathematics CBSE class 10 2015
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149)Find the internal diameter of the pipe, from the given below details Mathematics CBSE class 10 2015
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150)Except for the middle term of the AP 213,205,197,...37. Mathematics CBSE class 10 2015
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151)If the sum of the first n terms of an AP is 1/2(3n^2 + 7n), then find its n th term. Hence write 20th term? Mathematics CBSE class 10 2015
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152)Three distinct coins are tossed together. Find the probability of getting Mathematics CBSE class 10 2015
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153)Find that value of p for which the quadratic equation Mathematics CBSE class 10 2015
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154)Find how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool. Mathematics CBSE class 10 2015
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155)Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then construct triangle whose sides are 3/4 times the corresponding sides of the isosceles triangle. Mathematics CBSE class 10 2015
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156)If P(-5,-3),Q(-4,-6),R(2,-3) and S(1,2) are the vertices of a quadrilateral PQRS, find its area. Mathematics CBSE class 10 2015
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157)All the red face cards are removed from a pack of playing cards......Find the probability that the drawn card is Mathematics CBSE class 10 2015
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158)Find the area of the triangle PQR with Q(3,2) and the midpoints of the sides through Q being (2,-1) and (1,2). Mathematics CBSE class 10 2015
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159)If Sn denotes the sum of first n terms of an AP, prove that S30 = 3[S20 - S10]. Mathematics CBSE class 10 2015
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160)A 21 m deep well with diameter 6 m is dug and the earth from digging is evenly spread to form a platform 27 m x 11 m. Find the height of the platform. Mathematics CBSE class 10 2015
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161)A bag contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is: Mathematics CBSE class 10 2015
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162)Construct tangents to each circle from the centre of the other circle. Mathematics CBSE class 10 2015
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163)The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap? Mathematics CBSE class 10 2017
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164)If a tower 30 m high, casts a shadow 10 root(3) m long on the ground, then what is the angle of elevation of the sun? Mathematics CBSE class 10 2017
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165)If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP. Mathematics CBSE class 10 2015
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166)What is the common difference of an A.P. in which a21 – a7 = 84? Mathematics CBSE class 10 2017
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167)A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA Mathematics CBSE class 10 2017
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168)Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord. Mathematics CBSE class 10 2017
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169)A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the midpoint of PQ, then find the coordinates of P and Q. Mathematics CBSE class 10 2015
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170)If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y. Mathematics CBSE class 10 2017
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171)Find the value of p, for which one root of the quadratic equation px^2 – 14x + 8 = 0 is 6 times the other. Mathematics CBSE class 10 2017
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172)For what value of n, are the nth terms of two A.Ps 63, 65, 67,.... and 3, 10,17,..... equal? Mathematics CBSE class 10 2017
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173) If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower. Mathematics CBSE class 10 2017
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174)A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag. Mathematics CBSE class 10 2017
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175)Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region. Mathematics CBSE class 10 2017
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176)In what ratio does the point (24/11,y) divides the line segment joining the points P(2, -2) and Q(3, 7)? Also find the value of y. Mathematics CBSE class 10 2017
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177)How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation? Mathematics CBSE class 10 2017
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178)In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region.Mathematics CBSE class 10 2017
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179)The dimensions of a solid iron cuboid are 4.4 m × 2.6 m × 1.0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe. Mathematics CBSE class 10 2017
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180)A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy. Mathematics CBSE class 10 2017
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181)How many terms of an A.P. 9, 17, 25, .... must be taken to give a sum of 636? Mathematics CBSE class 10 2017
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182)If the roots of the equation (a^2 + b^2) x^2 – 2(ac + bd) x + (c^2 + d^2) = 0 are equal, prove that a/b = c/d Mathematics CBSE class 10 2017
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183)If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear, then find the value of k. Mathematics CBSE class 10 2017
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184)Construct a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are 3 / 4 times the corresponding sides of the triangle ABC. Mathematics CBSE class 10 2017
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185)Two different dice are thrown together. Find the probability that the numbers obtained have Mathematics CBSE class 10 2017
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186)In the given figure, XY and X’Y’ are two parallel tangents to a circle with centre O and another tangents AB with point of contact C, is intersecting XY at A and X’Y’ at B. Prove that ∠AOB = 90°. Mathematics CBSE class 10 2017
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187)Write your views on water conservation. Mathematics CBSE class 10 2017
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188)If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms. Mathematics CBSE class 10 2017
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189)Solve for x: Mathematics CBSE class 10 2017
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190)A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it? Mathematics CBSE class 10 2017
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191)Find the distance between the cars. Mathematics CBSE class 10 2017
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192)In the given figure, O is centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region. Mathematics CBSE class 10 2017
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193)In the Fig PQ is a tangent at a point C to a circle with centre O. if AB is a diameter and ∠CAB = 30°, find ∠PCA. Mathematics CBSE class 10 2016
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194)For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms of an A.P? Mathematics CBSE class 10 2016
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195)A ladder leaning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder. Mathematics CBSE class 10 2016
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196)A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen. Mathematics CBSE class 10 2016
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197)If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x)k = 0 has equal roots, find the value of k. Mathematics CBSE class 10 2016
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198)Let P and Q be the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4) such that P is nearer to A. Find the coordinates of P and Q. Mathematics CBSE class 10 2016
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199)In Fig., a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that AB + CD = BC + DA. Mathematics CBSE class 10 2016
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200)The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30 degree. The distance of the car from the base of the tower (in m.) is: Mathematics CBSE class 10 2013
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201)The probability of getting an even number, when a die is thrown once, is: Mathematics CBSE class 10 2013
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202)A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime-number less than 23, is: Mathematics CBSE class 10 2013
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203)The radius of the circle (in cm) is:Mathematics CBSE class 10 2013
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204)The length of each tangent is: Mathematics CBSE class 10 2013
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205)In fig., the area of triangle ABC (in sq. units) is: Mathematics CBSE class 10 2013
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206)If the difference between the circumference and the radius of a circle is 37 cm, then using pie = 22/7, the circumference (in cm) of the circle is: Mathematics CBSE class 10 2013
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207)Prove that the parallelogram circumscribing a circle is a rhombus. Mathematics CBSE class 10 2013
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208)Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm 7 cm. Find the area of the remaining card board. Mathematics CBSE class 10 2013
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209)How many three-digit natural numbers are divisible by 7? Mathematics CBSE class 10 2013
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210)the following quadratic equation for x: Mathematics CBSE class 10 2013
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211)Find the total surface area of the vessel. Mathematics CBSE class 10 2013
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212)Find the volume of wood in the toy. Mathematics CBSE class 10 2013
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213)In a circle of radius 21 cm, an arc subtends an angle of 60 degree at the centre. Find: Mathematics CBSE class 10 2013
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214)Find the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (10, 12). Also, find the coordinates of the point of division. Mathematics CBSE class 10 2013
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215) If the height of the second pole is 24 m, find the height of the first pole. Mathematics CBSE class 10 2013
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216)For what values of k, the roots of the quadratic equation (k + 4) x2 + (k+ 1)x + 1 = 0 are equal? Mathematics CBSE class 10 2013
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217)The sum of first n terms of an AP is 3n^2 + 4n. Find the 25th term of this AP. Mathematics CBSE class 10 2013
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218)Construct a tangent of a circle of radius 4 cm from a point on the concentric circle of radius 6 cm. Mathematics CBSE class 10 2013
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219)Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right triangle. Mathematics CBSE class 10 2013
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220)What is the sum of any two? (a) Odd numbers (b) Even numbers-Mathematics-cbse-std 6th
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221)A farmer has a rectangular field of length and breadth 240m and 160m respectively. He wants to fence it with 5 rounds of rope. What is the total length of rope he must use? Also find the cost of rope at the rate of Rs. 100 per meter. -Mathematics-cbse-std 6th
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222)If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A. Mathematics-CBSE-class-10
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223)Find the value of y for which the distance between the points (2, –3) and (10, y) is 10 units. Mathematics-CBSE-class-10
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224)Write whether the rational number 13 3125 has a decimal expansion which is terminating or non-terminating repeating. Mathematics-CBSE-class-10
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225)DE is drawn parallel to the base BC of a triangle ABC, meeting AB at D and AC at E. If AB BD = 4 and CE = 2 cm, find AE. Mathematics-CBSE-class-10
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226)The 5th and 15th terms of an A.P. are 13 and –17 respectively. Find the sum of first 21 terms of the A.P. Mathematics-CBSE-class-10
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227)Show that 1, 1 2 and –2 are the zeroes of the polynomial 2x 3 + x 2 – 5x + 2. Mathematics-CBSE-class-10
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228)The 4th and the last terms of an A.P. are 11 and 89 respectively. If there are 30 terms in the A.P., find the A.P. and its 23rd term. Mathematics-CBSE-class-10
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229)Sudhakar donated 3 cylindrical drums to store cereals to an orphanage. If radius of each drum is 0.7 m and height 2 m, find the volume of each drum. If each drum costs ` 350 per m3, find the amount spent by Sudhakar for orphanage. What value is exhibited in the question. Mathematics-CBSE-class-10
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