Math Chapter Wise

EnglishUKPSC Lecturer (Mains) 2020

Q81.The area of the region {(x,y):0≤y≤x2 +1,0 ≤y≤1+x,0≤x≤2} is:

A23/6 B23/7 C31/6 D43/6

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EnglishUKPSC Lecturer (Mains) 2020

Q82.The solution of the d 1+ ∫ x is:

A1 tan c − − + x x B1 tan c − + + x x C() 1 2 tan c − − + x x D() 1 2 tan c − + + x x Where c is an arbitrary constant.

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EnglishHaryana PGT 2019 JDD-75-PGT TIER-II-X-15 28.06.2015

Q83.∫ 3 1 2 -1 x + x +1 dx x + 2 x +1 is equal is:

Alog 2 B2log 2 C1 log2 2 D4log2

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EnglishPGT 2010

Q84.If f '(x) =2x∀ ∀ ∀x and f (0)=0 then the value of f(2) will be

A16 B2 C6 D4

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English(GIC) ØeJeòeâe hejer#ee, 2015

Q85.If a function f(x) is defined in internal (0,2) as follows:– 2 f(x) x x, when x is rational. 2 3 x x, = + = + when x is irrational. Then the values of upper and lower Riemann integrals in internal (0,2) are respectively–

A83 53, 12 12 B20 14, 3 3 C49 5, 12 6 DNone of these

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EnglishTGT 2004

Q86.If 2a a 0 0 f(x)dx = 2 f(x)dx ∫ ∫ ∫ ∫, then

Af(x) is even Bf(x) is odd Cf(x) is periodic Df(2a–x) = f (x)

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EnglishHaryana PGT 2019

Q87.() () ∫ 7/8 9/8 1 dx x + 5 x – 3 is equal to:

A1/8 x 5 c x 3 + − B1/8 x 4 c x 4 + − C1/8 x 5 c x 3 + − + − D1/8 x 4 c x 4 + − + −

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EnglishHaryana PGT 2019

Q88.The area of the region described by R = {(x,y) x2 + y2 ≤ 1 and y2 ≤ 1 – x} is:

A2 2 3 π − B2 2 3 π + C4 2 3 π + D4 2 3 π +

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EnglishHaryana PGT 2019

Q89.()() ∫ 5 4 3 2 3 2 4 2 2x + x – 2x + 2x +1 dx x +1 x – 1 is equal to:

A1 1 log6 2 5 + + B1 1 log6 2 5 + − C1 1 log6 2 5 − + D1 1 log6 2 5 − −

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EnglishUP PGT 2011 Haryana PGT 2019

Q90.2 2 2 2 0 x dx a cos x b sin x π + ∫ is equal to:

A2 ab π B2 2ab π C2 4ab π D2 9ab π

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EnglishHaryana PGT 2019

Q91.3 1 dx cos x sin2x ∫ is equal to:

A5/ 2 1 2 cot x tan x c 5 + + B5/ 2 1 2 tan x tan x c 5 + + C5/ 2 1 2 cot x tan x c 5 − + D1 2 cot x tan x c 5 + +

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EnglishHaryana PGT 2019

Q92.The area of the region bounded by the parabola (y – 2)2 = x–1, the tangent to the parabola at the point (2, 3) and the x-axis is:

A6 B9 C12 D3

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EnglishHaryana PGT 2019

Q93.If () ∫ 2 x x 3/2 2 x – x +1 e dx = e f(x)+c x +1, then,

Af(x) is an even function. Bf(x) is not bounded. CRange of f(x) is [0, 1]. DNone of these

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q94.Find the value of () ∫ 3 4 cot x cosec x dx

A–[cosec4 (x) ÷4+ cot6 x÷ 6] B–[cosec4 (x) ÷ 4+cosec6 (x) ÷ 6] C–[cot4 (x)÷ 4 + cosec6 ÷6] D–[cot4 (x) ÷ 4 + cot6 (x) ÷ 6]

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q95.What is the area inside function (2x3 +5x2 –4) ÷ ÷x2 from x = 1 to a.

A– 11÷2 Ba2/+5a+4÷a–10 Ca2/÷2+4ln Da2/÷2 + 5a – 11 ÷2

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q96.A function g: [0, π÷ ÷ ÷2]→ → →R by g(x)=(cos2 x, if x∈Q Q Q 0, otherwise.) Find the upper Riemann integrals of gover [0, π÷ ÷ ÷2]

Aπ Bπ÷3 Cπ÷4 Dπ÷2

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q97.A function on [ ] 0,1 by f (x) (1, if x= 1 ÷ ÷ ÷ n for some n ∈ N, 0, otherwise) Find ∫ ∫ ∫f with limits 0 to 1.

A–1 Bn C0 D1

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EnglishUK SSSC LT 2020

Q98.The value of 2 2 sin x cos x dx sin x.cos x − ∫ ∫ is:

Atan x + cot x + c Btan x + cosec x + c C–tan x + cot x + c Dtan x + sec x + c

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EnglishHaryana PGT 2020

Q99.If y = () ∫ 2 e log x dx satisfies the point (1, 2), then:

A() e e y 2 log x log x 2 x − = + B() e e y 2 log x log x 2 x + = + C() e e y 2 log x log x 2 x − = − D() e e y 2 log x log x 2 x + = −

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EnglishHaryana PGT 2020

Q100.The area bounded by the parabola (y – 2)2 = x – 1, the tangent to the parabola at (2, 3), x = 0 and y = 0 is:

A4 sq. unit B5 sq. unit C3 sq. unit D2 sq. unit

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