SAMPLE QUESTION PAPER Class X Session 2023 24 MATHEMATICS STANDARD Code No 041 MAX MARKS 80 TIME 3 hours General Instructions 1 This Question Paper has 5 Sections A B C D and 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 An internal choice has been provided in the 2marks questions of Section E 8 Draw neat figures wherever required Take 22 7 wherever required if not stated SECTION A Section A consists of 20 questions of 1 mark each If two positive integers a and b are written as a x3y2 and b xy3 where x y are prime 1 numbers then the result obtained by dividing the product of the positive integers by the LCM a b is a xy b xy2 c x3y3 d x2y2 1 The given linear polynomial y f x has a 2 zeros b 1 zero and the zero is 3 c 1 zero and the zero is 4 d No zero 1 2 Page 1 of 10 3 The lines representing the given pair of linear equations are non intersecting Which of the 1 following statements is true a cid 3028 cid 2869 cid 3028 cid 2870 cid 3029 cid 2869 cid 3029 cid 2870 b cid 3028 cid 2869 cid 3028 cid 2870 cid 3029 cid 2869 cid 3029 cid 2870 c d cid 3028 cid 2869 cid 3028 cid 2870 cid 3028 cid 2869 cid 3028 cid 2870 cid 3030 cid 2869 cid 3030 cid 2870 cid 3030 cid 2869 cid 3030 cid 2870 cid 3030 cid 2869 cid 3030 cid 2870 cid 3030 cid 2869 cid 3030 cid 2870 cid 3029 cid 2869 cid 3029 cid 2870 cid 3029 cid 2869 cid 3029 cid 2870 4 The nature of roots of the quadratic equation 9x2 6x 2 0 is 1 a No real roots b 2 equal real roots c 2 distinct real roots d More than 2 real roots 5 Two APs have the same common difference The first term of one of these is 1 and that of 1 the other is 8 The difference between their 4th terms is a 1 b 7 c 7 d 9 6 What is the ratio in which the line segment joining 2 3 and 5 6 is divided by x axis 1 a 1 2 b 2 1 c 2 5 d 5 2 7 A point x y is at a distance of 5 units from the origin How many such points lie in the third 1 quadrant a 0 b 1 c 2 d infinitely many 8 In ABC DE AB If AB a DE x BE b and EC c 1 Then x expressed in terms of a b and c is a b c d cid 3028 cid 3030 cid 3029 cid 2878 cid 3030 cid 3028 cid 3029 cid 3029 cid 2878 cid 3030 cid 3028 cid 3030 cid 3029 cid 3028 cid 3029 cid 3030 P then the angle subtended by the chord at the centre is a 130 b 100 c 50 d 30 A B P O D E Q 9 If O is centre of a circle and Chord PQ makes an angle 50 with the tangent PR at the point of contact 1 C R Page 2 of 10 10 A quadrilateral PQRS is drawn to circumscribe a circle If PQ 12 cm QR 15 cm and RS 14 cm then find the length of SP is a 15 cm b 14 cm b c 12 cm d 11 cm 11 Given that sin cid 3028 cid 3029 then cos is 1 1 cid 3029 a cid 3029 cid 3118 cid 2879 cid 3028 cid 3118 b cid 3029 cid 3028 c cid 3029 cid 3118 cid 2879 cid 3028 cid 3118 cid 3029 d 12 sec A tan A 1 sin A equals a sec A b sin A c cosec A d cos A 13 If a pole 6 m high casts a shadow 2 3m long on the ground then the Sun s elevation is 1 a 60 b 45 c 30 d 90 14 If the perimeter and the area of a circle are numerically equal then the radius of the circle 1 cid 3028 cid 3029 cid 3118 cid 2879 cid 3028 cid 3118 1 is a 2 units b units c 4 units d 7 units 15 It is proposed to build a new circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality The radius of the new park is a 10m b 15m c 20m d 24m 16 There is a square board of side 2a units circumscribing a red circle Jayadev is asked to 1 keep a dot on the above said board The probability that he keeps the dot on the shaded 17 2 cards of hearts and 4 cards of spades are missing from a pack of 52 cards A card is drawn at 1 random from the remaining pack What is the probability of getting a black card a b c d cid 2872 cid 2879 cid 3095 cid 2872 cid 2870 cid 2870 cid 2872 cid 2874 cid 3095 cid 2879 cid 2872 cid 2872 cid 2870 cid 2872 cid 2873 cid 2870 cid 2872 cid 3095 cid 2870 cid 2872 cid 2872 cid 2874 b c d 18 The upper limit of the modal class of the given distribution is 1 Below 140 Below 145 Below 150 Below 155 Below 160 Below 165 4 11 29 40 46 51 region is cid 3095 cid 2872 a cid 2870 cid 2870 cid 2873 cid 2870 Height in cm Number of girls Page 3 of 10 cone a 165 b 160 c 155 d 150 19 DIRECTION In the question number 19 and 20 a statement of assertion A is followed by 1 a statement of Reason R Choose the correct option Statement A Assertion Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the Statement R Reason Top is obtained by joining the plane surfaces of the hemisphere and cone together of assertion A a Both assertion A and reason R are true and reason R is the correct explanation b Both assertion A and reason R are true and reason R is not the correct explanation of assertion A c Assertion A is true but reason R is false d Assertion A is false but reason R is true 20 Statement A Assertion 5 cid 2879 cid …