trb.tripura.gov.in STPGT Mathematics Previous Question Paper 2017 : Selection Test for Post Graduate Teachers

Organisation : Teachers’ Recruitment Board, Tripura
Exam : STPGT – Selection Test for Post Graduate Teachers
Document Type : Previous Year Question Paper
Subject : Mathematics
Code No : AF17—XVIII
Year : 2017
Website : https://trb.tripura.gov.in/

TRB Tripura STPGT Mathematics Previous Question Paper

Question Paper of TRB Tripura Selection Test for Post Graduate Teachers Mathematics Question Paper 2017 is now available in the official website of Teachers’ Recruitment Board, Tripura.

Related : TRB Tripura STPGT Music Question Paper 2017 : www.pdfquestion.in/29520.html

Instructions for Candidates

1. Use Black Ballpoint Pen only for writing particulars of this Question Booklet and marking responses on the OMR Answer Sheet.
2. This test is of 2 hours and 30 minutes duration and consists of 75 MCQ-type questions. Each question carries 2 marks.

3. There is no negative marking for any wrong answer.
4. Rough work should be done only in the space provided in the Question Booklet.

5. The answers are to be marked on the OMR Answer Sheet only. Mark your responses carefully since there is no chance of alteration/correction.
6. Use of eraser or whitener is strictly prohibited.

Download Question Paper :
https://www.pdfquestion.in/uploads/STPGTMat.pdf

Model Questions

Direction : Answer the following questions by selecting the correct option.
1. If x satisfies the inequality |x – 1|+|x – 2|+|x – 3|³ 6 then
(A) 0 £ x £ 4
(B) x £ 0 or x ³ 4
(C) x £ – 2 or x ³ 4
(D) None of the above

2. If p2 + q2 = 1 and m2 + n 2 = 1, then
(A) |pm + qn|£ 0
(B) |pm + qn|£ 1
(C) |pq + mn|> 1
(D) |pq + mn|< 2

3. In an investigation of 1003 families of Agartala, it is found that 63 families have neither a mobile nor alaptop, 794 families have a mobile and 187 a laptop. The number of families in that group having both a mobile and a laptop is
(A) 41
(B) 40
(C) 22
(D) 20

4. Which of the following sets is not finite?
(A) P = {a :a is a colour in the rainbow}
(B) Q = { b :b is a page of Mathematics book}
(C) R = { c :c is one of the oranges produced at Jampui hill in 2016}
(D) S = { d : d is a star in the Universe}

5. Let A = { x :x is a prime number less than 21} and B = { x :x is a positive odd integer < 20 } Then B D A is
(A) Æ
(B) {1, 2}
(C) {1, 2, 9, 11}
(D) {1, 2, 9, 15}

6. The relation R = {(a, b) :a, b ÎZ and a – b is divisible by 5}, where Z is theset of all integers. Then R is
(A) symmetric only
(B) reflexive only
(C) not transitive
(D) an equivalence relation

7. Let f :R ®R and g :R ®R be defined by f (x) = 2x +1, g(x) = x 2 – 2 where R is a set of real numbers. Then g o f is
(A) 2x 2 – 3
(B) 4x 2 + 4x – 1
(C) 4x 2 – 4x
(D) None of the above

9. The smallest positive integer n for which 11 1 + – æ è ç ø ÷= i i n , is
(A) 1
(B) 2
(C) 3
(D) 4

10. If a and b are the roots of theequation (x – a)(x – b) = c, c ¹ 0; then the roots of the equation (x – a)(x – b) +c = 0 are
(A) a and c
(B) b and c
(C) a and b
(D) (a + c) and (b + c)

11. The number of different words ending and beginning with a consonant which can be made out of the letters of the word EQUATION is
(A) 5200
(B) 4320
(C) 4000
(D) None of the above

12. If n – 1P n + P = 3 1 : 3 5 :12, then n is
(A) + 7
(B) – 7
(C) – 8
(D) + 8

13. Which one of the following statements is not true?
(A) The set of all rational numbersdoes not form a group with respect to multiplication.
(B) A group may have more than one identity element.
(C) In a group, the inverse of the inverse of an element is equal to the element.
(D) The set S = { -3, – 2, -1, 0, 1, 2, 3} is not a group with the operation addition.

14. The inverse of i in the multiplicative group {1, -1, i, – i} is
(A) 1
(B) -1
(C) i
(D) -i

15. Which of the following is not true?
(A) The limit of a convergent sequence is not unique.
(B) Every convergent sequence is bounded.
(C) The sequence {1+(-1)n } is bounded but not convergent.
(D) The sequence {(-1)n (n + 1)} oscillates infinitely.

16. The series 1 1 2 13 1 4 + + + ! ! ! L is
(A) divergent
(B) convergent
(C) neither divergent nor convergent
(D) None of the above

17. The 12th and 19th terms of a harmonic progression are respectively 1/5 and 3/22 . Then the 4th term of the progression is
(A) 3/7
(B) 7/3
(C) 1/3
(D) 4/3

18. The equations
2x + 3y + 1z = 1
2x + 3y + 2z = 2
5x + 5y + 9z = 4 have
(A) unique solution
(B) in fi nitely many solutions
(C) no solution
(D) None of the above

19. If sinq + sin2 q =1, then the value of cos12 q + 3cos10 q + 3cos8 q + cos6 q – 1 is equal to
(A) 0
(B) 1
(C) -1
(D) 2

20. The equation cos2x + asinx = 2a – 7 possesses a solution if
(A) a < 2
(B) 2 £ a £ 6
(C) a > 6
(D) a is any integer

21. The equation cos2x + asinx = 2a – 7 possesses a solution if
(A) a < 2
(B) 2 £ a £ 6
(C) a > 6
(D) a is any integer

22. If D stands for the area of a triangle ABC, then a2 sin2B + b2 sin2A is equal to
(A) D
(B) 2D
(C) 3D
(D) 4D

23. The area of the triangle formed by joining the centres of the circles
x 2 + y2 +2x + 4y – 4 = 0,
x 2 + y2 + 6x + 4y + 9 = 0,
and
x 2 + y2 – 4x – 4y +2 = 0 is
(A) 4 sq. units
(B) 6 sq. units
(C) 8 sq. units
(D) 12 sq. units

24. The length of the chord intercepted by the straight line 2x – y – 3 = 0 on the parabola y2 = 8x is
(A) 4 units
(B) 4 2 units
(C) 4 5 units
(D) 5 units

25. The equation of the conic 4x 2 – 4xy + y2 + 2x – 26y + 9 = 0 represents the curve
(A) parabola
(B) ellipse
(C) hyperbola
(D) None of the above

26. If the tangent of the curve x = at 2,y = 2at is perpendicular to x-axis, then its point of contact is
(A) (a, a)
(B) (0, a)
(C) (a, 0)
(D) (0, 0)

27. x and y be two variables such that x > 0 and xy = 1, then the minimum value of (x + y) is
(A) 2
(B) 3
(C) 4
(D) 0

28. If P (x) be a polynomial of degree 3, with P (0) = 4, P ¢(0) = 3, P ¢¢(0) = 4, P ¢¢¢(0) = 6, then p¢(-1) equals to
(A) -10
(B) 10
(C) 2
(D) 1

29. The solution of the differential equation 2x 3 dy dx – y = represents
(A) straight line
(B) circle
(C) parabola
(D) ellipse

30. The vectors ra=3i$ – k$, r b = i$ + 2$j are adjacent sides of a parallelogram, then its area is
(A) 17 sq. units
(B) 14 sq. units
(C) 41 sq. units
(D) 7 sq. units