www.plusacademy.in | www.facebook.com/plusacademy Guess paper proof B 13 – 03 – 2015 Part – III MATHEMATICS, Paper – I (A) (English version) Time: 3 hours Max. Marks: 75 Section – A Very short answer types questions. i) ii) Answer all questions Each questions carries two marks 1. f: defined by , then this function is injection or not? Justify. concept 2. Find the range of the real valued function . plus academy – guess √ problem -Method 3. Construct a matric, whose elements are defined by 4. Find the rank of the matrix [ | | ] plus academy – guess problem -Method 5. A = 2i+5j+k and b=4i+mj+nk are collinear vectors, then find m and n. plus academy – guess problem -direct 6. OABC is a parallelogram. If OA = a and OC = c find the vector equation of the side BC. plus academy – guess problem -direct 7. Find the angle between the planes r.(2i-j+2k)=3 and r(3i+6j+k)=4. plus academy – guess problem -Method 8. Find the period of tan(x+4x+9x+…….n2x), where n is any positive integer. plus academy – guess problem -Method 9. If , where , evaluate . Concept )n= 10. Prove that ( , for any n R. plus academy – guess problem -direct Junior Intermediate | 1A IPE 2015 Question paper | [email protected] www.plusacademy.in | www.facebook.com/plusacademy Section – B Short answer types questions. (i) Attempt any five questions (ii) Each questions carries four marks 11. Examine whether the following system of equations are consistent or inconsistent and if consistent, find the complete solution x+y+z=1, 2x+y+z=2, x+2y+2z=1. plus academy – guess problem -direct 12. A,b,c are non-coplanar vectors. Prove that the following four points are coplanar 6a+6b-c, 2a-b+3c, -a+2b-4c, -12a-b-3c. plus academy – guess problem -Method 13. Find the volume of the tetrahedron, whose vertices are (1, 2, 1), (3, 2, 5), (2, -, 0) and (-1, 0, 1) 14. Of and , then find the value of tan2A. plus academy – guess problem -method 15. If are solutions of the equation , then find the value of (i) Tan (ii) ) Tan . plus academy – guess problem -direct 16. Prove that 17. Prove that +2 + = plus academy – guess problem -direct + = plus academy – guess problem -direct Section – C Long answer types questions. (i) Attempt any five questions (ii) Each questions carries seven marks 18. Let f={(1, a), (2, c), (4, d), (3, b)} and g-1 = {(2, a), (4, b), (3, d)}, then show that (gof)-1 = f-1og-1. plus academy – guess problem -Method 19. Using the principle of finite mathematical induction prove that 1.2.3+2.3.4+3.4.5+…………up to n terms = , plus academy – guess problem -direct x 2 2 x 3 3x 4 20. Find the value of x if x 4 2 x 9 3x 16 0 plus academy – guess problem – x 8 2 x 27 3x 64 direct Junior Intermediate | 1A IPE 2015 Question paper | [email protected] www.plusacademy.in | www.facebook.com/plusacademy 21. Solve the following system of equations by using Cramer’s rule x-y+3z = 5, 4x + 2y – z = 0, -x + 3y + z = 5. plus academy – guess problem -direct 22. If ̅ ̅ compute | ̅ ̅, ̅ ̅ ̅ ̅ ̅ ̅ ̅, ̅ ̅ ̅ ̅ and ̅ ̅ ̅ ̅ then ̅ |. 23. If A+B+C = , then show that ( ) plus academy – guess problem -direct 24. If r1=2, r2=3, r3=6 and r=1then show that a=3, b=4, c=5. plus academy – guess problem -direct Direct problems total scoring Method problems total scoring : 57 : 23 Plus academy guess paper Total Scoring: 57 + 23 = 80/97 www.plusacademy.in [email protected] Junior Intermediate | 1A IPE 2015 Question paper | [email protected]
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