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CBSE Class 10 Question Bank 2023 : Mathematics

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Dk Saraff
St. Helen's School, Howrah

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REAL NUMBERS 1) The HCF of two numbers a and b is 5 and their LCM is 200. Find the product ab. 2). The LCM of two numbers is 9 times their HCF. The sum of LCM and HCF is 500. Find their HCF. 3) Two positive integers a and b can be written as a =x 3 y2 and b= xy3, where r and y are prime numbers. Find HCF(a, b) and LCM(a, b). 4) The HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161, find the other. 5) The HCF of two numbers is 145 and their LCM is 2175. If one of the numbers is 725, find the other. ANS- 1)1000 2)50 3) HCF=XY2 LCM =X3 Y3 4)207 5)435 6)Express in form where p and q is integer and q 0: 0.134 Ans. 7) If one zero of the polynomial (a2 + 9)x + 13x + 6a is the reciprocal of the other, find the value of a a=3 POLYNOMIALS ax2+bx+c sum ( + )= - product ( ) = Equation of quadratic polynomial : X2-( + )x+ 8)Find the zeros of the polynomial f(x) = x2 + 7x + 12 and verify the relation between its zeroes and coefficients. Ans.x = -4 or x = -3 9) When x3 + 3x2 kx + 4 is divided by x 2, the remainder is k. Find the value of the constant k. Ans. : k = 8 10)What number should be added to 2x3 3x2 8x so that the resulting polynomial leaves the remainder 10 when divided by 2x + 1? Hint : Let the no be a a + 2x3 3x2 8x = 10 = = x= = 2x + 1 = 0 substitute the value of x in the above equation. GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Ans. : 7 11) Given that x + 2 and x + 3 are factors of 2x3 + ax2 + 7x b. Determine values of a and b. Ans. : a = 9, b = 6 12) If x 2 is a factor of + + and a + b =1, find the values of a and b. Ans. : = , = 13) .If one zero of the polynomial Ans. k + 3 + is 2, then find the value of k . LINEAR EQUATIONS 14)Find the values of k of the following equations which have no solution; i)kx+3y=k-3 12x+ky=k Ans. k=-6 15)For which values of , do the pair of linear equations x+y= 2 and x+ y=1 Have i)no solution ii)infinitely many solutions iii)unique solutions Ans.i) =-1 ii) =1 iii) 1;-1 16) 65x 33y = 97 Ans. x=2 y = 1 33x 65y = 1 17) + = 3 + Ans. x = 2 = y=1 PROBLEMS ON SIMULTANEOUS LINEAR EQUATIONS 18)3 men and 4 boys can do a piece of work in 14 days while 4 men and 6 boys can do it in 10 days. How long will it take 1 boy to finish the work ? Ans. 140 days 19)A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours it goes 40km upstream and 55km downstream. Determine the speed of the stream and that of the boat in still water. Ans. Speed of stream 3km/h Speed of boat in still water 8km/h 20)There are 38 coins in a collection of 20 paise coins and 25 paise coins. If the total value of the collection is Rs 8.50 how many of each are they? Ans. 20 paise= 20 coins; 25 paise =18 coins GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 21)If 1 is added to the denominator of a fraction it becomes if 1 is added to the numerator it becomes 1 find the fraction. Ans. 22)A two digit number is 7 times the sum of its digits. The number formed by reversing the digits is 18 less than the original number. Find the original number. Ans. 42 23)Taxi charges in a city consists of fixed charges and the remaining depending upon the distance travelled in km. if a person travels 70 km he pays Rs 1130 and for travelling 100 km he pays 1550 . find the fixed charges and the rate per km. Ans. charges =Rs150 14 per km 24)The present age of a woman is 3 years more than 3 times the age of her daughter. 3 years hence the woman s age will be 10 years more than twice the age of her daughter . find the present ages. Ans. woman 33 yrs daughter 10yrs 25)The equation y = mx + c is satisfied for the pair of values x= 1, y = 7 and x = -2, y = 1. Find the values of m and c. Ans. m =2 , c=5 QUADRATIC EQUATIONS 26) 2 x2 + 7x + 5 2 = 0 Ans. : 27)a2x2 + (a2 + b2)x + b2 = 0 Ans. : 1, 28) =2 Ans. : 3, 4 =2 Ans. : a + b, 30)4x4 13x2 + 9 = 0 Ans. : 1, 1, , 31)51+x + 51 x = 26 Ans. : 1, 1 32) x (x 7) = 3 2 Ans. : 2, 9 29) 33) + + + = + Ans. : , GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 , 2 34) Solve the equation: x- =6. Give your answer correct to two significant figures. Ans: 8.2,-2.2 Solve up to 2 Decimal Places 35)x2 10x + 6 = 0 Ans. : 9.36, 0.64 36)2(x 1) (x 5) = 5 Ans. : 5.55, 0.45 37) find the value of m for which the given equation has real and equal roots. x2 + 2(m - 1)x + (m + 5) = 0 Ans: 4 or -1 38) The equation 3x2 12x + (n 5)=0 has equal roots. Find the value of n. Ans . n=17 **39) Find the value of the 6+ 6+ 6 + 6 + Ans. : 3, 2 40)300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students. Ans. : 50 41)A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work. Ans. :30 days 42) The speed of an express train is x km/hr. and the speed of ordinary train is 12 km/hr. less than of the express train. If ordinary train takes one hr. longer than the express train to cover a distance of 240 km, find the speed of the express train. Ans. : x = 60 43)50 is divided into two parts such that the sum of their reciprocals is Hint: Let the first part the x 1 x + 1 50 x 1 . Find the two parts. Let the second part the 50 x = 1 Ans. : x = 30, 20 44) In a two digit number, the unit s digit exceed its ten s digit by 2 and the product of given number and the sum of its digit is equal to 144. Find the number. Hint: Let 10 s digit be x, units digit = x + 2 10x + y 10x + x + 2 = 11x + 2 GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Sum of digits = x + x + 2 = 2x + 2 A.T.P. (11x + 2) (2x + 2) = 144 Ans. : x=2 Required sum 11x + 2 = 11 2 + 2 = 24 45)The sum of the numerator and denominator of a fraction is 8. If 1 is added to both the numerator and denominator, the fraction is increased by Hint: Deno = x Fraction 1 5 . Find the Fraction. Num = 8 x 8 x 8 x+1 x x+1 8 x x = 1 5 Ans. : x = 5, Fraction 3 5 46)The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 34. Find the ages of the son and the father. Hint: Father s age = x Son s age = 45 x Father s age 5 years ago = x 5 Son s age = 45 x 5 = 40 x Ans. : Father s age = 39 years Ans. : Son s age = 6 years 47) One year ago, father was 8 times as old as his son. Now his age is the square of his son s age. Find their present ages. Hint: Son s age = x Father s age = x2 A.T.P. x2 1 = 8(x 1) Ans. : Son s = 7 years Father s = 49 years 48)Rs480 is divided equally among x children. If the number of children were 20 more than each would have got Rs12 less. Find x Hint: 480 x 480 x + 20 = 12 Ans. : x = 20, x 40 49)A shopkeeper buys a certain number of books for Rs720. If the cost per book was Rs 5 less, the number of books that would be bought for Rs720 would be 2 more. Taking the original cost of each book to be Rs x, write the equation in x and solve. GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Hint: 720 x 5 720 x =2 Ans. : x = 45 50) in an auditorium seats were arranged In rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduces by 10, the total number of seats increased by 300. Find: (i) The number of rows in the original arrangement. (ii) The number of seats in the auditorium after re arrangement Hint: ( ) = + Ans. (i) = (ii) x = 1200 Arithmetic Progressions If an AP is 11, 15, 19, 23, then first term is a = 11, d = difference 15 11 = 4 or 19 15 = 4. It will be always same. Formula: an = a + (n 1) d, where an is the general term. When last term is given L = a + (m 1) d m is the terms. Numbers in an A.P. Always difference is equal b a = c b * 2b = a + c Three numbers are taken as a d, a, a + d. Four numbers are taken as a 3d, a d, a + d, a + 3d. 51)If m times the m th term of an AP is equal to n times its n th term; then find its (m + n)th term. Ans. : (m + n)th = 0 52) The nth term of sequence is (2n - 3), find its fifteenth term Ans. : 27 53) Find the value of p, if x, 2x + p and 3x + 6 are in AP. Ans. : p=3 54)Find the sum of 28 terms of an A.P. whose nth term is 8n 5. Ans . 3108 GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 55) Which term of the AP: 23,44,65,86, ., is 212? Ans: 10 56)The ratio of the 11th term to the 18th term of an A.P is 2 : 3. Find the ratio of the 5th term to 21st term and also the ratio of the sum of first five terms to the sum of first 21 terms. Ans. : , 57)If Sn denotes the sum of first n terms of an AP; prove that S12 = 3(S8 S4) 58)Find the sum of integers between 100 and 200 that are divisible by 9 Ans. : 1683 59)The sum of first 7 terms of an AP is 49 and that of first 17 terms of it is 289. Find the sum of first n terms Ans. : a = 1, d = 2 , 60) in an AP, the first term is 25, nth term is -17 and the sum of n terms is 132. Find n and the common difference. Ans. : = , = 61)The sum of n natural numbers is 5n2+ 4n. Find its 8th term Ans. : 79 62) Solve the equation: 4 + ( 1) + 2+. . . + = 437 Ans. : x = 50 63) In an AP,18th term is 48 and 32nd term is 104. find (i) the first term and the common difference. (ii) the sum of first 50 terms. Ans: (i) -20 (ii) 3900 64) Find three numbers in A.P. whose sum is 24 and whose product is 440. Ans 5,8,11 or 11,8,5 65) The sum of first n terms of an AP is . find the 25th term. Ans: 76 GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 CO-ORDINATE GEOMETRY Section Formula Section Formula : The co-ordinates of the point which divides internally, the line segment joining the points P(x 1 y1) and Q(x2 y2) in ratio m1 : m2 are , Mid-point formula P(x1 y1) Q(x2 y2) = , In unknown ratio we will take k : 1 Centroid Formula : , 66)In the given figure, M(3,-2) is the midpoint of AB. if A and B are on x-axis and y-axis . find the coordinates of A and B. Ans: A(6,0) , B (0,-4) 67) Find the co-ordinates of the centroid of a triangle whose vertices are A( 1, 3) B(1, 1) C(5, 1). Ans. : ( , 1) 68) In the given figure, the line segment AB meets X-axis at A and Y-axis at B. The point P(-3,4) on AB divides it in the ratio 2:3. Find the coordinates of A and B. Ans: A(-5,0), B(0,10) 69) P divides the line segment joining A(1,-6) and B(6,4) in the ratio 2:3. find the coordinates of P. Ans: (3,-2) GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 70)Find the ratio in which C(p, 1) divides the join of A( 4, 4) and B(6, 1). Hence find the value of p. Ans. : 3 : 2; p = 2 71)If the line joining the points A(4, 5) and B(4, 5) is divided by the point P such that = find the co- ordinates of P. HINT. = 5AP = 2AB 5AP = 2 (AP + PB) AP : PB = 2 : 3 72) The line segment joining the points (2, 1) and (5, 8) is trisected at the points P and Q. If the point P lies on the line 2x y + k = 0, find value of k. Ans. : k = 8 73)Find all possible values of x for which the distance between the points A(x,-1) and B (5, 3) is 5 units. Ans. a = 2 or 8 74)If the point A(x, 2) is equidistant from the points B(8,-2)and C(2,-2) find the value of x. Also, find the value of x. Also, find the length of AB. Ans. X=5 AB=5 75)Find the point on the X axis which is equidistant from the points (2,- 5) and (- 2, 9). Ans. (-7,0) 76)If the P(x, y) is point equidistant from the points A(5,1) and B(-1,5) Prove that 3x=2y. 77)Using the distance formula, show that the given points are collinear: (4,2) (7,5) (9,7) 78)Show that the points A (3, 0), B(6, 4) and C(- l, 3) are the vertices of an isosceles right triangle. 79)If p(x, y) is point equidistant from the points A(6,-1) and B(2,3) show that x- y = 3 GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 80)If the points A(4,3) and B(x,5) lies on a circle with the centre O (2,3) . Find the value of x. Ans. 2 81)Show that the points A(-3, 2), B(-5, -5), C (2, -3) and D(4,4). Are the vertices of a rhombus. Find the area of this rhombus. Ans. 45 square units. 82)Find the point on X axis which is equidistant from point A(-1,0) and B (5 , 0). Ans. x = 2 GEOMETRY 83)In ABC, PQ || BC and AP : PB = 2:3.If AQ = x + 1 QC = x + 5 ,find the value of x. Ans: 7 84)In the given figure, ABC and AMP are right angled at B and M. given AC = 10 cm, AP = 15 cm and PM = 12 cm (i) prove that ABC ~ AMP. (ii) find AB and BC. Ans: 6 cm and 8 cm 85)In ABC, PQ || BC. IF AP : PB=2:3 ,find i) the length of PQ , IF BC = 7.5 cm. Ans: 3 cm 86)AB and ED are perpendiculars to BD. AE meets BD at C. if AB = 16 cm, BC = 12 cm, CD = 3 cm, find: the lengths of DE and CE. GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Ans: 4 cm, 5 cm 87)In the given figure, AB = 9 cm ,BC = 12 cm and AC = 15 cm . BP AC. (i) what is the measure of ABC? (ii) Prove that APB ~ ABC. (iii) Find the lengths of BP and AP. Ans : 90 , 7.2 cm, 5.4 cm 88)In the given figure, AB || CD || EF , AB = 5 cm, AC = 4 cm, EF = 7.5 cm , CF = x and CD = y. (i) prove that FEC ~ ABC. (ii) solve for x and y. Ans: 6 cm , 3 cm 89) The perimeter of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangle is 9 cm long, find the length of the corresponding side of the second triangle. Ans 6 90). A pole of length 10 m casts a shadow 2 m long on the ground. At the same time a tower casts a shadow of length 50 m on the ground. Find the height of the tower. Ans 250m 91) If tan 3x = sin 450cos 450 + sin 300 , find the values of x. GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Ans. 150 92)If sin 3x = 1 and 00 3x 900 find the value of I)sin x0 Ans. II)cos 2x Ans. 93)If cos (A + B) = = sin (A B) , 00 < A + B 900 , A > B , find the value of A and B. Ans. A = 450 , B = 150 94) If is an acute angle and sin = cos , find the value of 2 tan 2 + sin2 -1 Ans. 95) If sin (A + B) = = cos (A B) , o0 < A + B 900(A > B) , find the values of A and B. Ans. A = 450 , B = 150 96) Given tan = , find cos + sin in terms of p and q. Ans. + / 97) In triangle ABC , B = 900, find (I) sin A Ans. (II) tan A Ans. (III) cosec2A (IV) cos C Ans. (V) cotC Ans. (VI) cosec C Ans. 98) 99) 1 sin + cos 1 + sin 1 sin + cot2A 1 sin cos = Ans. 1 2 sin 1 2cos = sec + tan GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 100) tanA + secA 1 tanA secA + 1 = 1 + sinA cosA 101) sec2 + cosec2 = tan + cot 102)sin4 + cos4 = 1 2 sin2 cos2 103)tan2A tan2B = sin2 A sin2 B cos2 A cos2 B = sec2A sec2B 104) show that (1- + )2 = 2(1+ ) (1 ). 105)If tanx+ cotx =2 find the value of tan7 x + cot7 x ans=2 Heights and Distances 106)If the length of a shadow cast by a pole is 3 times the length of the pole, find angle of elevation of the sun. Ans. : 300 107) A man on the top of a tower observes a car moving at a uniform speed towards it. if it takes 12 minutes for the angle of depression to change from 30 to 45 , how soon will the car reach the tower? give the answer correct to nearest second. Ans: 16 minutes 24 seconds 108)A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 600. When he moves 50 m away from the bank he finds that the angle of elevation is to be 300. Calculate. (i) The width of the river (ii) height of the tree Ans. : (i) 25 m, (ii) 43.3 m 109)The shadow of a vertical tower on a level ground increases by 10 m, when the altitude of the sun changes from 450 to 300. Find the height of the tower, correct to two decimal places. Ans. : 13.66 m 110)The angles of elevation of the top of a tower from two points P & Q at distances a & b respectively, from the base and in the same straight line with it, are complementary. Prove that the height of the tower is ab . Ans. : n = ab 111)The length of a shadow of a tower standing on a level plane is found to be 2x metres longer when Sun s altitude is 300 then it is 450. Prove that the height of the tower is x ( 3 + 1) m. 112)The angle of elevation of a Jet Plane from a point A on the ground is 60 0. After a flight of 15 seconds, the angle of elevation changes to 300. If the Jet is flying at a constant height of 1500 3 m. Find the speed of the Jet Plane in km/hr. Ans. : Speed = 720 km/hr. 600 300 GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 1500 3 1500 3 CIRCLE DISTANCE2 + CHORD2 = Radius2 2 2 2 AB + BC = AC Where Chord is Half A R R Distancee C Chord SUMS 113)The centre of a circle of radius 13 units is the point O (3, 6) P(7, 9) is a point inside the circle. APB is a chord of the circle such that AP = PB. Calculate the length of AB. OP = 5 units AP = 12 units Ans. : 24 O (3, 6) A B P(7, 9) 114)Chords AB and CD of a circle are parallel to each other and lie on opposite sides of a centre. In AB = 36 cm, CD = 48 cm and the distance between the chords is 42 cm. Find radius of the circle. 18 42 X r r X B 24 Ans. : Radius = 30 cm 115)AB and CD are two parallel chords of a circle of length 24 cm and 10 cm respectively and lie on the same side of its centre O. If the distance between the chords is 7 cm, find the radius of the circle. Ans. : Radius = 13 cm r A C 116) ABC with AB = AC = 10 cm and BC = 12 cm has been inscribed in a circle. Find the radius of the circle. O L r M A Ans. : r = 6.25 cm O B GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 B D L C 117)In the figure given below AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24 cm and 18 cm respectively. A M B O C D N Ans.MN=21 118) In the figure given below, O is the centre of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD. AB = 24 cm, OM = 5 cm, ON = 12 cm. Find the : (i) radius of the circle. (ii) Length of chord CD. D N C O A M B Ans.(i) 13cm; (ii)10cm ##119) A chord 4x cm long is (x - 1) cm away from the centre of the circle whose radius is (2x + 1)cm long. Find the radius and length of the chord. Ans. 13, 24 120) PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and CAB = 30 , find PCA. Ans. 60 121) .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. Ans. 2a 122) 5.A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC+ DA PART-II THEOREM GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Two equal chords AB and CD of a circle, with centre O, when produced meet at a point P, as shown in the given figure, Prove that PA = PC and PB = PD. Given: AB and CD are equal chords of a circle with centre O. When produced AB and CD at P. To prove PA = PC and PB = PD SOL. Draw OL AB and OM CD. Join OP. OL = OM Equal Chords A OLP & OMP i) ii) B O OL = OM iii) OP = OP Common OLP OMP R.H.S. PL = PM P M C OLP = OMP L D c.p.c.t. AB = CD 1 2 AB = 1 2 CD` 1 2 BL = DM 1 2 BL = AB, DM = CD. PL BL = PM DM PB = PD AB = CD & PB = PD PB + AB = PD + CD PA = PC Properties I Double Angle P P B A O O A B AOB = 2 APB Reflex AOB = 2 APB Property II GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Angles in the same segment of a circle are equal. C D C A ACB = ADB O A DAB = DCB O B B Property III ADC = ABC B D 5 cm 4 cm O BAD + BCD = 1800 C A ADC + ABC = 1800 D The opposite angles of a cyclic quadrilateral inscribed in a circle are supplementary. C Property IV O A The angle in a semi-circle is a right angle. B ACB = 900 TYPE -2 123)In the following figure O is the centre of the circle and AB is a tangent to it at point B. BDC = 650, B Find BAO. D Ans. : 400 650 A O E C 124)In the given figure O is the centre of the circle. Tangents A and B meet at C. If ACO = 300, find (i) BCO Ans. : (i) 300 (ii) AOB (ii) 1200 A (iii) APB (ii)600 P 4 300 O B C 125) In the figure given below, O is the centre of the circle and SP is a tangent. If SRT = 650, find the value of x, y and z. GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Ans. : x = 250 , y = 500 , z = 400 TANGENT PROPERTY THEOREM If two tangents are drawn from an external point to a circle, then i) The tangents are equal in length. ii) The tangents subtend equal angles at the centre of the circle. iii) The tangents are equally inclined to the line joining the point and the centre of the circle. Given: P is an external point to a circle with centre C. PA and PB are two tangents drawn from P to the circle, A and B being points of contact. To prove : (i) PA = PB (ii) ACP = BCP A P C (iii) APC = CPB In APC & BPC B Radii of same circle. 1) CA = CB Each = 900 radius through the point of contact is to tangent. 2) CAP = CBP 3) CP = CP Common 4) APC BPC R.H.S. 5) PA = PB ACP = BCP APC = CPB B c.p.c.t. 27 cm SUMS 126)In the adjoining figure a circle is inscribed in the quadrilateral ABCD. Given that BC = 38 cm QB = 27 cm and DC = 25 cm an AD is to DC find the radius of the circle. GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 A P D 38 cm Q O 25 cm R C A Ans. : OP = DS = 14 cm. 4 cm x 127)In the figure given below triangle ABC is circumscribed. 5 cm Find x. B Ans. : x = 7 cm C 8 cm P 128)In triangle PQR, PQ = 24 cm, QR = 7 cm and PQR = 900. Find radius of the inscribed circle. A O Ans. : x = 3 cm. x Q R 129)In the given figure 1, PA and PB are tangents to the circle, CE is a tangent to the circle at D. If AP = 15 cm, find the perimeter of PEC. E A FIG 1 P D Ans. : 30 cm. C D B 130)In the given figure 2, quadrilateral ABCD is circumscribed. Find the perimeter of quad, ABCD FIG - 2 4 R C S A Ans. : 36 cm. 3 Q 6 P 5 B FIG 3 131)In Fig - 3 Three circles with A, B, C, centres touch each other externally. Ans. : A = 2 cm, B = 3 cm, B A C C = 4 cm GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 If AB= 5 cm, BC = 7 cm CA = 6 cm find radii of the three circles. CHAPTER 16 Mensuration FORMULAE 1) Cuboid :V = L b h Area of 4 walls = 2h(l + b) TSA = 2(lb + bh + Lh) 2) Cube : VOL = a3 TSA = 6a2 3) Right Circular Cylinder : Diag = 3 a V = r2h CSA = 2 rh (Lateral) TSA = 2 r (h + r) L 4) V = r h 2 Right Circular Cone h CSA = rL TSA = r (r + L) r L2 = r 2 + h2 5) V = r3 Sphere TSA or SA 6) 7) 4 r2 Hemisphere V= r3 CSA = 2 r2 TSA = 3 r2 Spherical shell with outer radius & inner radius. V = (R3 r3) SUMS 132)The surface area of a solid metallic sphere is 616 cm 2. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained? Ans. : 64 133)A hemispherical bowl of diameter 7.2 cm is completely filled with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone. 134)The volume of a conical tent is 1232 m3 and area of the base floor is 154 m2. Calculate the : i) Radius. GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 ii) Height of the tent iii) Length of the canvas required to cover conical tent if its width is 2 m. Ans. : (i) r = 7 m (ii) 24 m (iii) 275 m 135)A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Find the number of cones recast. Ans. : 270 136) An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85 m and height of the cylindrical part is 50 m. If the diameter of the base is 168 m,find the quantity of canvas required to make the tent. Allow 20% extra for folding and for stitching.Give your answer to the nearest m2. Ans: 60509 m2 137) In the given figure a hemisphere is surmounted by a conical block of wood .The diameter of their bases is 6 cm each and the slant height is 5 cm . Find : (i) height. (ii)the volume. Ans: 4 cm, 94.2 cm3 138) The following figures represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. their common radius is 7 cm. the height of the cylinder and cone are each of 4 cm. find the volume of the solid. GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Ans: 1540 cm3 139)A hemispherical and a conical hole is scooped out of a solid wooden cylinder. find the volume of the remaining solid where the measurement are as follows: the height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm, height of cone is 3 cm. give your answer correct to the nearest whole number . Ans: 113 cm3 140)The diagonals of a rhombus are 30cm and 16cm. find the area and perimeter. Ans. area = 240cm2 , perimeter = 68cm 141)The area enclosed between 2 concentric circles is 770cm 2. If the radius of the outer circle is 21cm. calculate the radius of the inner circle. Ans. 14cm 142)Find the area of the unshaded portion of the given figure within the rectangle. (take = 3.14) Ans. 19.35cm2 143)3 cubes each of side 6cm are joined end to end. Find the surface area of the resulting cuboid. Ans. 504cm2 144)2 cubes each of volume 512cm3 are joined together. Find the surface area of the resulting cuboid. Ans. 640cm2 GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 145)The dimensions of a metallic cuboid are 100cm X 80 cm X 64cm. it is melted and recasted into a cube. Find the edge and surface area of the cube. Ans. 80cm , 38400cm2 146)How many times will the wheel of a car rotate in a journey of 88km if its known diameter of the diameter of the wheel is 56cm? = Ans. 50000 147)The area of a circular ring enclosed between 2 concentric circles is 286cm2. Find the radii of the 2 circles given that their difference is 7cm. = . Ans. 10cm and 3cm 148)The parallel sides of an isosceles trapezium are in the ratio 2 : 3. If its height is 4cm and area is 60cm2 find perimeter. Ans. 40cm 149) In a rain-water harvesting system, the rain-water from a roof of 22 m 20 m drains into a cylindrical tank having diameter of base 2 m and height 3:5 m. If the tank is full, find the rainfall in cm. Ans 2.5cm 150) A cylinder and a cone have equal radi of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the ratio of radius of each of its height is 3:4 151)A cylindrical tub, whose diameter is 12cm and height 15cm is full of ice cream. The whole ice cream is to be divided into 10 children in equal ice cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical part of ice cream cone. Ans r =3cm d=6cm Measures of Central Tendency * Mean ungrouped = x n For discrete data * Direct Method Fx f GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 f.d. * Short cut Method = A + * Step deviation method = A + f f.d. f C * Note : The answer will be same of Mean in all cases whether we use any of the 3 methods. * Median ungrouped First arrange in ascending order : n+1 th If n is odd; then 2 n+1 th Median = 2 value. If n is even; then Median = * 1 2 n+1 th 2 observation+ n 2 +1 th observation Mode for ungrouped : Which occurs maximum number of times 2, 3, 3, 4, 5, 3, 3, 7, 6 Ans. : = 3 (Since it has occurred maximum times). * Relationship between Mean, Median, Mode Mode = 3(Median) 2 Mean Empirical Formula. * * Middle Quartile is also known as Median = Q 2. 152)Weight of 50 eggs were recorded as given below : Weight in gm No. of eggs 80-84 85-89 90-94 95-99 100-104 105-109 110-114 5 10 12 12 8 2 1 Ans. : 94 gm 153)Calculate the mean, the median and the mode of the following nos. 3, 1, 5, 6, 3, 4, 5, 3, 7, 2 Ans. : Mean = 3.9, Median = 3.5, Mode = 3 154)The mean of the following frequency distribution is 50 and the sum of all frequencies is 120. Find the values of p and q. Class Intervals Frequency 0-20 20-40 40-60 60-80 80-100 17 p 32 q 19 GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Ans. : p = 28, q = 24 155) Find the mode of the data using an empirical formula when it is given that median = 41.25 and mean = 33.75 Ans . 56.25 156) Find the mode of the following frequency distribution Class Interval: Frequency 25 30 25 30 35 34 35 40 50 40-45 42 45 50 38 50 55 14 Ans38.33 157)From the following distribution, find the median: Classes Frequency 500-600 36 600-700 32 700-800 32 800-900 20 900-1000 30 Ans721.875 GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Probability 1) SURE EVENT is 1 2) Impossible EVENT is 0 0 For eg. What is the probability of getting 7 in a single throw of a die = = 0 7 3) A pack of playing cards has in all 52 cards : 13 each of (i) Spades (ii) Clubs (iii) Hearts (iv) Diamonds. 4) Face cards are Kings, Queens & Jacks = 12 cards. 5) Honour cards are Ace, Kings, Queens, Jacks = 16 cards 6) There are 26 black cards and 26 are red cards. SUMS : 158)Two unbiased coins are tossed simultaneously, find the probability of getting (i) Two heads (ii) One head (iii) At least one head iv)At most one head, (v) No head Ans. : (i) 1 4 (ii) 1 2 (iii) 3 4 (iv) 3 4 (v) 1 4 159)An unbiased die is thrown once. Find the probability of getting: (i) A prime number (ii) An even number (iii) The number 5 (iv) A number greater than 4 (v) A number less than 3 (vi) A number greater between 3 and 6. Ans. : (i) 1 2 (ii) 1 2 (iii) 1 6 (iv) 1 3 (v) 1 3 (vi) 1 3 160)Anushka and Virat are friends. They both were born is 1975. What is the probability that they have (i) Same birthdays (ii) Different birthdays. Ans. : (i) 1 365 (ii) 364 365 161)Find the probability of having 53 Wednesday in a (i) a non-leap year, (ii) a leap year. GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 Ans. : (i) 1 7 (ii) 2 7 162)A bag contains 12 balls out of which x balls are black. (i) If a ball is drawn at random, what is the probability of drawing a black ball? (ii) If 6 more black balls are put in the bag, the probability of drawing a black ball will be double than that of (i). Find the value of x. Ans. : (i) x 12 (ii) x = 3 163)Cards numbered from 2 to 25 are put in a box and mixed thoroughly. One card is drawn at random. Find the probability that the card drawn bears: (i) (ii) (iii) (iv) (v) An odd number Not a prime number A perfect square A number greater than 17 A number divisible by 2 and 3 both Ans. (i) (ii) (iii) (iv) (v) 164) If an office works for 5 days in a week (Monday to Friday) and if two employees of the office remain absent in the same week, what is the probability that it is (i) the same day (ii) different days Ans: , 165)The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is .the probability of selecting a blue ball at random from the same jar is . If the jar contains 10 orange balls find the total number of balls in the jar. Ans. :24 balls GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 166)Two coins are tossed together 100 times and the results are as follows: No. of heads 0 1 2 frequency 28 52 20 What is the probability of (i) One head (ii) at most 1 head Ans: 167) There are 30 blue balls and x red balls in a bag. A ball is drawn at random from the bag. (i) write down, in terms of x, an expression for the probability that the ball drawn is red. (ii) given that the probability is , find x. Ans: , 35 168) A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is: (i) a spade (v) Jack or queen (ii) a red card (vi) ace and king (iii) a face card (vii) a red and a king (iv) 5 of heart or diamond (viii) a red or a king Ans. : (i) ( ) ( ) ( ) ( ) ( ) GUESS QUESTIONS BY ASHISH SARAF MO-9903312612 ( ) ( )

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