CBSE Exam Paper

General Instructions: Read the following instructions very carefully and strictly follow them: This question paper contains 14 questions.  (i) All questions are compulsory. (ii) This question paper is divided into three sections - Sections A, B and C. (iii) Section A comprises of 6 questions (Q.no. 1 to 6) of 2 marks each. Internal choice has been provided in two questions.  (iv) Section B comprises of 4 questions (Q.no. 7 to 10) of 3 marks each. Internal choice has been provided in one question. (v) Section C comprises of 4 questions (Q.no. 11 to 14) of 4 marks each. Internal choice has been provided in one question. It also contains two case study based questions. (vi) Use of calculator is not permitted. SECTION A Question numbers 1 to 6 carry 2 marks each. 1. (a) In an AP, if a = 50, d= –4 and S n  = 0, then find the value of n. OR (b) Find the sum of the first twelve 2 digit multiples of 7, using an AP.  2. A solid metallic sphere of radius 3 cm is melted and rec...

CBSE Class 10 Term 2 Mathematics Standard 2022, Solution: Paper Code-30/1/1, Set 1 Section A Q.1 Find the sum of first 30 terms of AP: –30, –24, –18,/.. Solution:  a= –30, d= 6 S30 = 15 [–60 + 29 (6)] = 15 [–60+174] = 15 [114] = 1710  OR Q:  If an AP is Sn = n(4n+1), then find the AP Solution:  S1 = T1 = 5 S2= T1 + T2= 18 S2–S1 = T2= 13 AP= 5, 13, 21, 29, … Q.2: A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.  Solution:   r1 = 10.5 cm (sphere) and  r2 (cone)= 3.5 cm,  h2= 3cm 4/3πr³ = n x 1/3πr2² h 4r³ = nr2² h 4 x (105/10)³= n x 35/10 x 35/10 x 3 21 x 6= n  Number of cones formed= 126 Q. 3 (a) Find the value of m for which the quadratic equation  (m–1) x² + 2(m–1)x + 1 = 0 Solution:  D= 0 4 (m–1)² – 4(m–1) = 0 4 (m–1) [(m–1)–1]= 0 (m–1) (m–2)= 0 m= 1 and m= 2 m = 1, 2 (b) Solve the following quadratic equation f...

SECTION A Question numbers 1 to 6 carry 2 marks each. 1. (a) Find the sum of first 30 terms of AP: -30,- 24,- 18,......                  (2) OR (b) In an AP if Sn = n (4n+ 1), then find the AP.                                     (2) 2. A solid metallic sphere of radius 105 cm is melted and recast into a number of smaller cones, each of radius 3-5 cm and height 3 cm. Find the number of cones so formed.    (2) 3. (a) Find the value of m for which the quadratic equation  (m-1) x² + 2 (m-1)x + 1= 0  has two real and equal roots.        (2) OR (b) Solve the following quadratic equation for x : √3 x² + 10x +7√3 = 0                  (2) 4. Find the mode of the following frequency distribution : Class.        Frequency 10-20        ...