Math Chapter Wise

EnglishTGT 2011

Q361.The function () () 2 -1 1+ x f x = cos sinx +sin 2x defined, if

A{ } x 1,1 ∈ − B[ ] x 1,1 ∈ − Cx R/∈ D[ ] x 1,1 ∈ −

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EnglishUP PCS (Pre) 1998

Q362.The domain of definition of the function (())) 1 2 x f x sin log 3 − = is:

A(6, 12) B(3, 12) C3,6 2 D3,6 2

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EnglishUP PCS (Pre) 1998

Q363.If ((()) x 3 f x x 1 − = +, then ((()) { { } } f f f x is:

A–x Bx C–4x D4x

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EnglishUP PCS (Pre) 1998

Q364.If f: R → → → R is defined by f (x) = x2 + 1 then f–1 ({10, 37}) equals:

A{3, –3, 6, – 6} B{3, 6} C3, 6 4 − − D{0}

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EnglishUP PCS (Pre) 1998

Q365.Which of the following statements is false:

AIn the set of odd integers 'addition' is not a binary operation BIn the set of intergers 'division' is not a binary operation CIn the set of integers, the operation 'o' defined by 1 aob ab 4 = is a binary operation DIn the set of non-zero rational numbers 'division' is a binary operation

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EnglishUP PCS (Pre) 1998

Q366.Which of the following sets forms a group under multiplication:

Athe set Z+/of positive integers Bthe set Z* of non-zero integers Cthe set Z– of negative intergers Dthe set R+ of positive real numbers

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EnglishUP PCS (Pre) 1998/ PGT 2000

Q367.If Z denotes the set of integers and A, B, C are its subsets given by: A = {x ∈ Z: x is divisible by 2} B = {x ∈ Z: x is divisible by 4} C = {x ∈ Z: x is divisible by 6} then the set A B C ∩ ∩ ∩ ∩ is:

A{x ∈ Z: x is divisible by 4} B{x ∈ Z: x is divisible by 12} C{x ∈ Z: x is divisible by 24} Dthe empty set

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EnglishUP PCS (Pre) 1998

Q368.If R is the set of real numbers and f is the relation {(x, [x]) x∈R}, where [x] denotes the greatest integer not greater than x, then:

Af is not a function on R Bf is a function from R to R which is one-one but not onto Cf is a function from R to R which is onto but not one-one Df is a function from R to R which is neither one-one, nor onto

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EnglishUP PCS (Pre) 1998

Q369.A set X has more than one element and for x, y in X, x o y = y. Then:

Ao is not a binary operation in X Bo is a binary operation on G but it is not associative Co is an associative binary operation but (X, o) has no identity element D(X, o) is a group

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EnglishUP PCS (Pre) 1995

Q370.Consider the statements:

ABoth A and B are correct BA is incorrect and B is correct CA is correct and B is incorrect DBoth A and B are incorrect

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English(GIC) Lecturer exam, 2015

Q371.The set of natural numbers is not closed for the following operation:

Aaddition Bmultiplication Csubtraction Dsquaring

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EnglishUP PCS (Pre) 1994

Q372.Let f,g: IR IR be given by f(x) 2x 3 and 2 g(x) x 5 then g(f(2)) is equal to–

A6 B9 C25 D36

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EnglishUP PCS (Pre) 1994

Q373.The function 1 sin x 1 1 f(x) 2 x x 2 − = + + = + + = + + = + + − is defined for:

A–1≤ x ≤ 1 B2 < x Cx = 0 Dnone of these

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EnglishUP PCS (Pre) 1994

Q374.For x in IR, let [x] denote the greatest integer which is ultmost equal to x, then:

A[x] < x ≤ [x] + 1 B[x] ≤ x ≤ [x] + 1 C[x] ≤ x < [x] +1 D[x] < x < [x] + 1/is completely true

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EnglishUP PCS (Pre) 1994

Q375.If a < 0 and b ≥ 0 then:

Aab > 0 Bab ≤ 0 Cab ≥ 0 DNone of these

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EnglishUP PCS (Pre) 1995

Q376.If f(x) = tan x then the value of f (x) + f (–x) is equal to–

A2 tan x B–2 tan x C∞ D0

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EnglishUP PCS (Pre) 1995

Q377.For real numbers x and y, we have–

Ax y x y Bx y x, x y, y C2 2/x y x y Dx y x, y y, x

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EnglishUP PCS (Pre) 1995

Q378.The intersection 1 1 n N, n n is–

Aφ B(–1,1) C[–1,1] D{0}

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EnglishUP PCS (Pre) 1995

Q379.If 2 x (x) 1 x f then f (sin θ) is equal to–

Acosec2/θ Bsec2/θ Ccot2/θ Dtan2/θ

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EnglishUP PCS (Pre) 1995

Q380.If p is a prime number then1 | p 1 divisible by p" This theorem is known as:

AFermat's theorem BWilsion's theorem CEuler's theorem DDivision Algorithm

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