Title cbjemapl01.pdf ✅

Page 1 Sample Paper 01 Solutions Sample Paper 01 Solutions Class- X Exam - 2023-24 Mathematics - Standard Time Allowed: 3 Hours Maximum Marks : 80 General Instructions : 1. This Question Paper has 5 Sections A-E. 2. Section A has 20 MCQs carrying 1 mark each 3. Section B has 5 questions carrying 02 marks each. 4. Section C has 6 questions carrying 03 marks each. 5. Section D has 4 questions carrying 05 marks each. 6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the values of 1, 1 and 2 marks each respectively. 7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of 2 marks has been provided. 8. Draw neat figures wherever required. Take 7 22 π = wherever required if not stated. Section - A Section A consists of 20 questions of 1 mark each. 1. Two APs have the same common difference. The first term of one of these is -1 and that of the other is - .8 Then the difference between their 4th terms is (a) -1 (b) -8 (c) 7 (d) -9 Ans : (c) 7 4th term of first AP, a4 =− +1 4( ) − 1 d =− +1 3d and 4th term of second AP, al4 =− +8 4( ) − 1 d =− +8 3d Now, the difference between their 4th terms, a a l4 4 - = ( )( ) − +13 83 d d − − + =−+ +− 13 83 d d = 7 Hence, the required difference is 7. Thus (c) is correct option. 2. For the following distribution: Marks Number of students Below 10 3 Below 20 12 Below 30 27 Below 40 57 Below 50 75 Below 60 80 The modal class is (a) 10-20 (b) 20-30 (c) 30-40 (d) 50-60 Ans : [Board Term-1 Comp 2017] Marks Number of students 0-10 3 0 − = 3 10-20 12 − 3 9 = 20-30 27 12 15 − = 30-40 57 27 30 − = 40-50 75 57 18 − = 50-60 80 75 5 − = Class 30-40 has the maximum frequency 30, therefore this is model class. Thus (c) is correct option.
Page 2 Sample Paper 01 Solutions 3. If one zero of the polynomial ( ) 3 8 x x k 2 + + is the reciprocal of the other, then value of k is (a) 3 (b) -3 (c) 3 1 (d) 3 1 - Ans : [Board 2020 OD Basic] Let the zeroes be α and 1 α . Product of zeroes, 1 a $ a tant coefficient of cons x = 2 1 k 3 = & k = 3 Thus (a) is correct option. 4. x x 1 0 2 2 2 ^ h + − = has (a) four real roots (b) two real roots (c) no real roots (d) one real root Ans : [Board Term - 2 Comt. 2015] We have x x 1 2 2 2 ^ h + − = 0 x x 1 2 x 4 2 2 + + − = 0 x x 1 4 2 + + = 0 x x 1 2 2 2 ^ h + + = 0 Let x2 = y then we have y y 1 2 + + = 0 Comparing with ay by c 2 + + = 0 we get a = 1, b = 1 and c = 1 Discriminant, D b a4 c 2 = − 1 4 1 1 2 = ^ h − ^ ^h h =− 3 Since, D < 0, y y 1 2 + + = 0 has no real roots. i.e. x x 1 4 2 + + = 0 or x x 1 0 2 2 2 ^ h + − = has no real roots. Thus (c) is correct option. 5. The LCM of smallest two digit composite number and smallest composite number is (a) 12 (b) 4 (c) 20 (d) 44 Ans : [Board 2020 SQP Standard] Smallest two digit composite number is 10 and smallest composite number is 4. LCM ( , )10 4 = 20 Thus (c) is correct option. 6. Which of the following statement is false? (a) All isosceles triangles are similar. (b) All quadrilateral are similar. (c) All circles are similar. (d) None of the above Ans : Isosceles triangle is a triangle in which two side of equal length. Thus two isosceles triangles may not be similar. Hence statement given in option (a) is false. Thus (a) is correct option. 7. If a regular hexagon is inscribed in a circle of radius r, then its perimeter is (a) 3r (b) 6r (c) 9r (d) 12r Ans : Side of the regular hexagon inscribed in a circle of radius r is also r , the perimeter is 6r . Thus (b) is correct option. 8. If 4 3 tan θ = , then sin cos sin cos 4 4 q q q q + − c m is equal to (a) 3 2 (b) 3 1 (c) 2 1 (d) 4 3 Ans : Given, tan4 θ = 3 tan θ 4 3 = ...(i) sin cos sin cos 4 4 q q q q + − 4 1 4 1 cos sin cos sin = + − q q q q tan tan 4 1 4 1 q q = + − 4 1 4 1 4 3 4 3 = + ` − ` j j 3 1 3 1 = + − 4 2 = 2 1 = Thus (c) is correct option. 9. The top of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30c with the horizontal, then the length of the wire is (a) 12 m (b) 10 m (c) 8 m (d) 6 m Ans : [Board 2018] Height of big pole CD = m20 Height of small pole AB = m14
Page 3 Sample Paper 01 Solutions DE = CD CE − = CD AB − [AB CE = ] = 20 14 − = m6 In 3BDE , sin 30c BD DE = 2 1 BD 6 = & BD = m12 Thus length of wire is 12 m. Thus (a) is correct option. 10. A ladder, leaning against a wall, makes an angle of 60c with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder. (a) 5 m (b) 5.5 m (c) 2.5 m (d) 4.5 m Ans : [Board Term-2 2011] As per given in question we have drawn figure below. In TACB with +C = 60c, we get cos 60c . AC 2 5 = 2 1 . AC 2 5 = AC = = 2 2 # .5 5 m Thus (a) is correct option. 11. In the figure, PQ is parallel to MN. If PM KP 13 4 = and KN = 20 4. cm then find KQ. (a) 4.8 cm (b) 4.6 cm (c) 4.4 cm (d) 4.2 cm Ans : [Board Term-1, 2013] In the given figure PQ || MN , thus PM KP QN KQ = (By BPT) PM KP KN KQ KQ = − 13 4 . KQ KQ 20 4 = − 4 2 # 0 4. - 4KQ = 13KQ 17KQ = 4 2 # 0 4. KQ . 17 = 20 4 4 # = 4 8. cm Thus (a) is correct option. 12. Ratio of lateral surface areas of two cylinders with equal height is (a) 1 : 2 (b) H h: (c) R r: (d) None of these Ans : [Board Term-2 Delhi 2017] 2 2 p p Rh : rh = R r: Thus (c) is correct option.