Math Chapter Wise

EnglishUP PCS (Pre) 1994

Q301.The function 1, irrational (x) 1, rational x f x is–

ADiscontinuous at x = 0 only BDiscontinuous at rationales only CDiscontinuous at irrationals only DNone of these

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EnglishUP PCS (Pre) 1994

Q302.If x y x, then dy x dx is–

A2 y 1- ylogx B2 x 1- ylogx C2 y 1+ ylogx D2 x 1+ ylogx

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EnglishUP PCS (Pre) 1994

Q303.If 2 2 2 2 2 p a cos b sin, 2 d p p d is–

Ap/ab Bp 2 2 2 a b C3 p 2 2 a b D3 p ab

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EnglishUP PCS (Pre) 1994

Q304.What is the limit of the product 1 1 1 n n n n 1 2 n Lt 1 1..... 1? n n n

A1 B2/e C3/e D4 log e

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EnglishUP PCS (Pre) 1995

Q305.2 1/ x x 0 lim(cos x) → α is equal to –

A2/e B2 a e C2 2a e D2/ 2 2a e

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EnglishUP PCS (Pre) 1995

Q306.The value x x x 0 a b lim x of is equal to–

Aa log b Bb log a C0 D1

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EnglishUP PCS (Pre) 1995

Q307.3 2 x 2 1 sin x lim is cos x π → −

A2/3 B0 C3/2 D–3/2

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EnglishUP PCS (Pre) 1995

Q308.The limit of x x B A sin A when x and 0 A 1 is –

AB B1 CA D0

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EnglishUP PCS (Pre) 1995

Q309.If y x 2 x 4 for all x R then the value of dy dx at x = 1 is equal to:

A1 B2 C–2 DNot exist

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EnglishUP PCS (Pre) 1995

Q310.The function 2 x,when x 1 (x) 3, when x 1 ≠ = f is–

AContinous on the left only, at x = 1 BContinuous on right only, at x = 1 CContinuous at x = 1 DNone of the above is true

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EnglishUP PCS (Pre) 1995

Q311.x 0 x lim is x →

A–1 B1 C0 Ddoes not exist

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EnglishUP PCS (Pre) 1996

Q312.The function is continuous at a point, if:

AThe right hand limit exists only BThe left hand limit exists only CBoth limits exist and are equal to the value of the function at the point Dboth limits exist and are equal

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English

Q313.The value of 2 x 0 log x lim cot x is:

A1 B2 C0 D1/2

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EnglishUP PCS (Pre) 1996

Q314.The function 1 f(x) xsin,x 0 x = ≠ = ≠ 0,x 0 at x 0 is:

AContinuous and differentiable BContinuous but not differentiable CDiscontinuous but not differentiable DNone of these

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EnglishUP PCS (Pre) 1996

Q315.Let ≠ 1/x 0 1 e sin x 0 x f(x) =, x = 0 1+ e then:

Af(x) is continuous at x = 0 Bf(x) has removable discontinuity at x = 0 Cf(x) has discontinuity of second kind at x = 0 Df(x) has infinite discontinuity at x = 0

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EnglishUP PCS (Pre) 1996

Q316.The value of 1 2 2 2 n 2 2 2 2 n 1 2 3 n lim 1+ 1+ 1+... 1+ n n n n →∞ is:

A4 2 e π− B2 2e π− C4 2 2e π− DNone of these

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EnglishUP PCS (Pre) 1999

Q317.Let if is rational 1- if is irrational x x f(x) = x x Then f is:

Acontinuous everywhere on IR Bcontinuous at rational points only Ccontinuous at irrational points only Dcontinuous at only one point

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EnglishUP PCS (Pre) 1999

Q318.→ x 0 lim x log x equals:

A1 B0 C1/2 D1/3

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EnglishUP PCS (Pre) 1999

Q319.→∞ 2 2 2 3 n 1 + 2 +.......+ n lim n equals:

A1/4 B1/2 C1/6 D1/3

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EnglishUP PCS (Pre) 2000

Q320.The value of 1/n n lim n →∞ is:

A1 B–1 Ce–1 De

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