10th Secondary Sent-Up Mathematics Exam 2024 PDF

## SECONDARY SENT-UP EXAMINATION - 2024 **Subject Code:** 110 **Mathematics** (Compulsory) **Total Questions:** 138 **Total Printed Pages:** 32 **Full Marks:** 100 **Time : 3 Hours 15 Minutes** **Instructions for the candidates :** 1. Candidates must enter his/her Question Booklet Serial No. (10...

## SECONDARY SENT-UP EXAMINATION - 2024 **Subject Code:** 110 **Mathematics** (Compulsory) **Total Questions:** 138 **Total Printed Pages:** 32 **Full Marks:** 100 **Time : 3 Hours 15 Minutes** **Instructions for the candidates :** 1. Candidates must enter his/her Question Booklet Serial No. (10 Digits) in the OMR Answer Sheet. 2. Candidates are required to give their answers in their own words as far as practicable. 3. Figures in the right hand margin indicate full marks. 4. 15 minutes of extra time have been allotted for the candidates to read the questions carefully. **Ans :** x² - 3 = 0 x² = 3 x = ±√3 ( +√3 )² = 3 (√3)² = 3 -√3X-√3 = +3 Ans **Ans :** a = 4, b = -1, c = -4 शून्यक का योगफल (α+β) = -b/a = -(-1)/4 =1/4 शून्यको के गुणन‌फल (αβ) = c/a = -4/4 = -1 Ans **Ans :** When x = 5 and y = -15 3x5 - ax1 - 20 15 + a = 20 a = 20 - 15 a = 5 Therefore a = 5, b = 2 **Ans :** 4x² + 7x + 3 / 4x + 3 (<u>4x² + 7x + 3</u> ) / (4x + 3) 3x + 3 / Therefore, the quotient = 4x + 3 Ans **Ans :** 455 = 84 x 5 + 35 ⇒ 84 = 35 x 2 + 14 ⇒ 35 = 14 x 2 + 7 ⇒ 19 = 7 x 2 + 5 H.C.F = 7 **Ans :** 63, 65, 67 --- a = 63, d = 2 3, 10, 17 --- a2 = 3, d = 7 nth term = a + (n - 1)d a1(n-1)d1 = a2 + (n-1)d2 63 + (n-1)2 = 3 + 7(n-1) 63 + 2n - 2 = 3 + 7n - 7 63 - 2 - 3 + 7 = 7n - 2n 65 = 5n n = 65/5 **n = 13** **Ans :** 25 + 28 + 31 + --- + 100 का योगफल क्या होगा a = t1 = 25, t2 = 28 d = t2 - t1 = 28 -25 d = 3 tn = a + ( n - 1 )d 100 = 25 + ( n - 1 )3 100 = 25 + 3n - 3 100 = 22 + 3n 100 - 22 = 3n 78 = 3n n = 78 / 3 n=26 Sn = n/2 { 2a + ( n - 1 )d } = 26/2 {2x25 + ( 26 - 1 )3} = 13 { 50 + 25x3} = 13 x ( 50 + 75) = 13 x 125 **= 1625 Ans** **Ans :** AD / BD = AE / EC ( प्रमेय प्रमाण) 1.5/1 = 1 / EC EC = 1/1.5 EC = 2/3 Therefore EC = (2/3 ) सेमी Ans **Ans :** भाग गोले कि संख्या V = 4/3 πr³ = 2 x π x 6³ = 2 x π x 216 = 432π 6 x 6 x 6 = 1 x 2 x 2 x 2 = 8 x 6 x 6 = 2 x 2 x 6 x 6 π = 22/7 **Ans :** Sin² 63° + Sin² 27° cos² 73° + cos² 73° = Sin² 63° + Sin² ( 90 - 63°) cos² ( 90 - 75°) + cos² 73° = Sin² 63° + cos² 63° = 1 Ans **Ans :** 2x + y + 4 = 0 ① 5x - 3y - 1 = 0 ② ax + by + c1 = 0 a2x + b2y + c2 = 0 x / (b1c2 - b2c1) = y / (c1a2 - c2a1) = 1 / (a1b2 - a2b1) ⇒ x / ( -1 - (-12)) = y / (20 - (-2)) = 1 / (-6 - 5) ⇒ x / 11 = y / 22 = 1 / -11 ⇒ x / 11 = 1/-11 ⇒ x = -1 **= -1 + 12 = 20 + 2 = -11** ⇒ x / 11 = y / 21 = 1 / -11 ⇒ x / 11 = 1 / - 11 ⇒ x = -1 y / 21 = 1 / -11 ⇒ y = -2 **Ans = -2** **Ans :** r = 3.5 cm वृत्त की परिधि = 2πr = 2x22/7 x 3.5 = 2 x 22 x 35/10 = 22 cm वृत्त का क्षेत्र = πr² = 22/7 x (3.5)² = 22 / 7 x 12.25 = 11/7 x 35 x 35/10 = 11/2 x 35/10 x 35/10 = 385 / 10 = 38.5 वर्ग से. Ans **Ans :** मान लीजिए दो समरूप त्रिभुज ABC तथा DEF हो तथा BC = 4 सेमी EF = 5 सेमी और ABC का क्षेत्रफल = 6 वर्ग सेमी है तो △ DEF का क्षेत्रफल ज्ञात कीजिए △ ABC ~ △ DEF BC = 4 cm △ ABC = 64 cm² EF = 5 cm △ ABC का क्षेत्र = ( BC )² / ( EF )² x △ DEF का क्षेत्र 64 = ( 4 )² / ( 5 )² x △ DEF का क्षेत्र △ DEF का क्षेत्र = 64 x 25 / 16 △ DEF का क्षेत्र = 100 cm² **Ans :** y = 9 - 4x / 6 y = 3/2 - 5/2 x y = 10 - 5x / 8 x = 2/5 y = 0 / 1