STPGT TRB Tripura Mathematics 2017 Paper
If an investigation of 1003 families of Agartala, it is found that 63 families have neighter a mobile nor a laptop, 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
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
Which one of the following statments is NOT true ?
(a) The set of all rational numbers does 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.
The inverse of i in the multiplicative group {1, -1, i, -i} is
(a) 1
(b) -1
(c) i
(d) -i
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
The equations
x + 2y + 3z =1
2x+ y + 3z = 2
5x + 5y + 9z = 3
have
(a) unique solution
(b) infinitely many solutions
(c) no solution
(d) None of the above
The equation of the plane which is parallel to the line
(x-2)/3= (y-3)/4=(z-4)/5 is
(a) 3x + 4y + 5z = 7
(b) 2x+ y – 2z = 0
(c) x + y – z = 2
(d) 2x + 3y + 4z = 0
The centre of the sphere which passes through the points (0,0,0), (1,0,0), (0,1,0) and (0,0,1) is
(a) ( -1/2, -1/2, -1/2)
(b) ( 1/3,1/3, 1/3)
(c) (1/2, -1/2, -1/2)
(d) (1/2, 1/2, 1/2)
Vector multiplication of two vectors is
(a) vector only
(b) scalar only
(c) a scalar or a vector
(d) None of the above
Which of the following statements is correct ?
(a) The intersection of two convex sets is not a convex set
(b) a hyperplane is not a convex set
(c) The union of two convex sets may or may not be a convex set
(d) None of the above
The geometric mean of 4, 6, 9 with frequency 1, 2, 1 is
(a) 5
(b) 6
(c) 7
(d) 8
The highest value 97.5 of a set of 100 observations is changed to 197.5. Then which of the following statements is correct ?
(a) Mean, median and mode are unchanged
(b) Mean and median are changed only
(c) Mean is raised by 1, median and mode are unchanged
(d) Median and mode are raised by 1, mean is unchanged
If the standard deviation of 3, 5, 8, 7, 5, 7 is 1.675, then the standard deviation of 25, 27, 30, 29, 27, 29 will be
(a) 1.675
(b) 3.35
(c) 22.675
(d) 23.675
From 4 apples, 2 mangoes and 4 bananas, 4 are selected. The probability that there are exactly 2 apples among the selected fruits is
(a) 3/7
(b) 11/21
(c) 10/21
(d) None of the above
The probability of occurrence of an event is 5/9. The probability of non-occurrence of the event B is 5/11. The probability that at least one of them will occur is
(a) 6/11
(b) 5/9
(c) 4/9
(d) 79/99
In a throwing of two unbiased dice, the probability that the sum of the points on the two dice will be multiple of 4 is
(a) 1/9
(b) 1/3
(c) 1/4
(d) None of the above
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