Name of the School : National Institute of Open Schooling
Name of the Exam : Senior Secondary Mathematics
Document type :Sample Question paper
Website : nios.ac.in
Download Model/Sample Question Papers : https://www.pdfquestion.in/uploads/nios.ac.in/5355-sqp311e.pdf
Mathematics Sample Question Paper :
Subject : Mathematics
Class : Senior Secondary
Time : 3 Hours
Related : National Institute of Open Schooling Senior Secondary Home Science Sample Question Paper : www.pdfquestion.in/5348.html
Maximum Marks : 100
1. Find ‘a’ and ‘b’ if ai. (3+bi) = 3 – 7i
2. Find the value of A2 + I where A = 2 5.
3. Prove that : 11n n nr r r C C C +
4. How many ways can 4 boys and 3 girls be seated in a row of 7 chairs
5. Prove that :6 sin q + cos6q =1- 3sin2q cos2q
6. Prove that :cos11 + sin 11tan 56cos11 sin 11
7. Find the value of ‘h’ in terms of q ,f and ‘a’ as shown in the figure.
8. Evaluate :0limx®sintan b
9. If 1, w, 2 w be the cube roots of unity, then prove that
10. Show that :22 2 2 2x xy xz
11. Using geometric progression, express 0.5 as rational number.
12. In what ratio does the point (3, -1) divide the join of the points (4, 2)
13. Find the equation of the circle which passes through the origin and cuts off intercepts from the axes equal to 4 and 5.
14. Find the derivative from the first principle of the function ax
15. Find the intervals in which function
16. Evaluate :
17. Find the co-efficient of x10 in the expansion of mentioning the condition under which the result holds.
18. Find the general solution of the equation sin x +sin 2x + sin 3x = 0
19. Find the vertex, focus, directrix and length of latus rectum of the parabola 5×2 + 24y = 0
20. Solve the equation
21. Of all the rectangles inscribed in a given circle, prove that square has the maximum area.
22. Find the square root of – 15 – 8i. Hence find the square root of – 15 + 8i
23. Solve the system of equations using matrices
x+ y + z = 6
2x y + z = 3
x 2y + 3z = 6
24. Prove that
26. Find the area of the region enclosed by the parabolas y2 = 4ax and x2 = 4ay for a >0.
27. Evaluate :
Option – I : (Statistics and Probability)
28. In a study to test the effectiveness of a new variety of wheat, an experiment was performed with 50 experimental fields and the following results were obtained
Yield per hectare No. of fields (in quintals)
31-35 2
36-40 3
41-45 8
46-50 12
51-55 16
56-60 5
61-65 2
66-70 2
If the mean yield per hectare is 50 quintals, find variance and standard deviation.
29. If A and B are two events, such that P (A) = 0.8, P (B) = 0.6, P(AÇ B) = 0.5 then find the value of (i) P (AÈB) (ii) P (B/A) (iii)P (A/B)
30. A pair of dice is thrown 10 times. If getting a doublet (same number on both) is considered a success, find the probability of (i) 4 successes (ii) No success
Option – II : (Linear Programming)
28. Solve the following, by simplex method Minimize z = x1 + x2
29. Four person A, B, C and D are to be assigned four jobs I, II, III and IV. The cost matrix is given as under:
Man
Job
A B C D
I 8 10 17 9
II 3 8 5 6
III 10 12 11 9
IV 6 13 9 7
Find the proper assignment.
30. Solve the following by using graphical method: Minimize z = 60×1 + 40 x2
Option – III : (Vectors and Analytical Solid Geometry)
28. In a regular hexagon ABCDEF, if AB, then express each of the following
29. Find the equation of the plane through the points (–1,1,1) and (1, –1,1) and perpendicular to the plane x + 2y + 2z – 5 = 0
30. Reduce the equations of the line given by 3x +2y –z – 4 = 0 and 4x + y –2z + 3 = 0 in symmetric form.
Mathematics : April 2015
Note :
(i) This Question Paper consists of two Sections, viz., ‘A’ and ‘B’.
(ii) All questions from Section ‘A’ are to be attempted. However, in some questions, internal choice is given.
(iii) Section ‘B’ has two options. Candidates are required to attempt questions from one option only.
Section A :
1. If 1, w, w2 are the cube roots of unity, then prove the following : 2
2. A committee of 5 is to be formed from 6 gents and 4 ladies. In how many ways this can be done if at most 2 ladies are included? 2
3. Find the equation of the circle concentric with the circle x 2 + y2 – 6x + 2y – 11 = 0 and passing through the centre of the circle x 2 + y2 = 16. 2
4. The 6th term of an AP is 20 and its 11th term is 35. Find the 25th term of the AP. 2
5. If A = {1, 2, 3, 4}, B = {2, 4, 5, 6, 7, 8} and C = {1, 3, 5, 6, 7, 8, 9, 11}, then verify that A Ç (B – C) = (A Ç B) – (B ÇC) 2
6. If the roots of the quadratic equation ax 2 + bx +c = 0 are in the ratio of 2 : 3, then prove that 6b2 = 25ac.