The following question are taken from the last year’s final exam of HSLC which is conducted by SEBA board of Assam, 2018. These are the Advance Mathematics question 2018 .Soon.. We will provide answers of these questions. It is very necessary for a HSLC candidate to know about that how he have to prepare. And also necessary to know what is the pattern of final questions. So we are providing the Previous Year questions in a easy and suitable manner so that one can understand easily, Read easily and the most important feature is one can get every where and any time whenever you need. We are trying to provide more previous years questions like 2017,16,15 etc. We are trying our label best. Our answer are written by some expert teachers.

## Advance Mathematics Previous Year Questions- 2018

#### SECTION-A

(Question Numbers 1 to 12)

In each of the following questions, four answers are provided of which only one is correct. Choose the correct answer.

1. Let A and B be two sets. If n(AUB)=120, n(A-B)=63, n(B-A)= 42, then n(A ∩ B) = ?

(a) 10

(b) 15

(c) 20

(d) 25

2. Let A {2, 3} and B {4, 5, 6}. The number of relations from A to B is

(a) 22

(b) 23

(c) 25

(d) 26

3. Find the value of:-       √-2 x √-3 x √-5
(a) √-30

(b) √30

(c) -i√30

(d) i√30

4. Let a, b, q be three positive integers such that division of a by b gives a = bq + r, where r is an integer. Then

(a) 0 ≤ r < b

(b) 0 < r < b

(c) 0 < r ≤ b

(d) 0 ≤ r ≤ b

5, One root of a quadratic equation is √3 i. The equation is

(a) x2 – 3 = 0

(b) x2 + 3 = 0

(c x2 + 9 = 0

(d) x2 – 9 = 0

6. If log 4.12 = 0.6149, then log 0.00412 = ?

(a)-2.6149

(b) 2 6149

(c) 3 6149

(d)-3.6149

7. If log 2 = 0.3010, then log √2 = ?

(a) 0.03010

(b) 0.003010

(c) 1.3010

(d) 0.1505

8. The number of three-digit odd positive integers is

(a) 450

(b) 500

(c) 550

(d) 600

9. If n-2C4 = n-2C9, then n = ?

(a) 11

(b) 13

(c) 15

(a) 17

10. Find the value of :

sin 300°

(a) 1/√2 (b) -1/√2

(c) √3/2

(d) -√3/2

11. A secant PAB and a tangent PT are drawn to a circle from an external point P . If PA = 1.2 cm and PB = 4.8 cm, then PT = ?

(a) 1.2 cm

(b) 2.4 cm

(c) 3.6 cm

(d) 24 em

12. The gradient of a line is 1/√3. The angle made by the line with the positive direction of the x-axis is

(a) 30°

(b) 45°

c) 60°

(d) 90°

SECTION-B

Each question carries 2 marks

(Question Numbers 13 to 21)

There are 100 students in a class and each of them appears in a class test. If 55 students pass in Mathematics, 46 students pass in English and 35 students pass in both the subjects, then find the number of students who fail in both the subjects.

14. Find the real numbers x and y, if (3 + i)x + (1 – 2i)y + 7i= 0, i= √-1.

15. Find the modulus of: 16. Let z1and z2be two complex numbers. Prove that

|z1z2| = |z1||z2|

17. Find the condition such that one root of the equation ax2+ bx + c = 0, a ≠ 0, is n times the other.

18. How many words (may be meaninglessj can be formed by using all the letters of the word ENGINEERING?

Or

How mang numbers less than 1000 can be formed by using the digits Q, 1, 2, 3, 4, 5 and 6 if repetition of digits is allowed?

19. Let AD be a median to the triangle ABC. Let the internal bisectors of ∠ADB, ∠ADC meet AB and AC at E and F respectively. Prove that EF is parallel to BC.

20. Prove that the tangents to a circle from an external point are equal.

21. Using the concept of gradient of a line, show that the points (6, -1), (5, 0) and (2,3) are collinear.

#### SECTION-C

Each question carries 3 marks

(Question Numbers 22 to 37)

22. Let Z be the set of integers. Let R={a, b} : a, b ∈ Z, and (a – b) is divisible by 3}. Examine whether R is an equivalence relation on Z or not.

23. Let A and B be two non-empty sets, prove that –
(i) if A = B, then A x B = B x A
(ii) if A x B = B × A, then A = B

24. Find the square root of
-4 -3i

25. Prove, with the help of a mathematical induction, that 26. Let a, b, c be integers such that a | b and b | c. Prove that a | c.

27. Find the two integers x and y, such that 30x + 72y=6.

28. If a2= 5a – 3 and b2= 5b – 3, a ≠ b; then form a quadratic equation whose roots are a/b and b/a.

29. If log2 = 0.3010, log3 = 0.4771, then find the logarithm of3√48.

30. From 4 gentlemen and 7 ladies, a committee of 5 is to be formed. In how many ways can this be done so as to include at least 2 gentlemen?

31. Prove that 32. Show that 33. Let A, B be two acute angles and A + B < 90°. Show that 34. If sin A = 3/5 and A is an acute angle, then find sin 2A, cos 2A, tan 2A.

35. If two chords of a circle cut at a point within it, prove that the rectangles contained by their segments are equal.

36. A semicirele is drawn on AB as diameter. Let X be a point on AB. From X, a perpendicular XM is drawn on AB cutting the semicircle at M. Prove that AX . XB = MX2.

37. A straight line makes intercepts a and b on the x axis and the y-axis respectively. Find the equation of the line.

#### SECTION-D

##### (Question Numbers 38 to 40)

38. Solve :- 39. Prove that the rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of two rectangles contained by its opposite sides.

40. The intercepts made by a line on the axes are equal in magnitude, but opposite in signs. If the line passes through the point (5, 7), then find the equation of the line. Express the equation of the line (i) in gradient form and (ii) in normal form.

#### SECTION-E

##### (Question Numbers 41, 42)
1. If d and m are the GCD and LCM of two positive integers a, b respectively, then prove that dm = ab.

Or

State the Fundamental Theorem of Arithmetic, Let a, b, c, d be integers and m be a positive integer (m > 1). If a ≡ b (mod m), c ≡ d (mod m), then prove that

(i) a + c ≡ b + d (mod m)
(ii) ac ≡ bd (mod m)

42. x = 5 + 4i, then evaluate x4 + 9x3 + 35x2 – x + 16. Examine whether x2 + 10x 41 is a factor of this expression or not.