Math Chapter Wise

EnglishSECTION B PGT TIER-I 31.11.2014

Q81.The maximum value of sin x + cos x is–

A2 B1 C2 D0

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EnglishSECTION B PGT TIER-I 31.11.2014

Q82.Which of the following function is decreasing on 0, 2?

Asin 2x Btan x Ccos x Dcos 3x

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EnglishSECTION B PGT TIER-I 31.11.2014

Q83.The two curves 3 2 x 3xy 2 0 and 2 3 3x y y 2 − =

Atouch each other Bcut at right angle Ccut at an angle π/3 Dcut at an angle π/4

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EnglishSECTION B PGT TIER-I 31.11.2014

Q84.If x is real, the minimum value of 2 x 8x 17 is

A–1 B0 C1 D2

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EnglishSECTION B PGT TIER-I 31.11.2014

Q85.The function 3 2 f(x) 2x 3x 12x 4, has–

Atwo points of local maximum Btwo points of local minimum Cone maxima and one minima Dno maxima of minima

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q86.The function 4 2 y x 6x 8x 11 = − + + = − + + = − + + = − + + has a minimum at x equal to–/ 4 2 y x 6x 8x 11 = − + + = − + + = − + + = − + +

A1 B–2 C3 D4

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q87.x x has a stationary point at–

Ax e = Bx = 1/e Cx 1 = Dx e =

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q88.The absolute maximum of 3 y x 3x 2 = − + = − + = − + = − + in 0 x 2 ≤ is–

A4 B6 C2 D0

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q89.The function logx x attains its maximum at the point-

Ax e = Bx = 1/e Cx e = Dnone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q90.A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/sec, At that instant, when the radius of circular wave is 8 cm, how fast is the enclosed area increasing?

A2 6 cm /s π B2 8 cm / s π C2 8 cm /s 5 π D2 80 cm /s π

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q91.The distance moved by a particle in time t is given by 3 2 s t 6t 15t 12 = − − + = − − + = − − + = − − + The velocity when the acceleration becomes zero is–

A15 B–27 C6/5 Dnone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q92.The slope of the normal to the curve y = x2 + 3x + 2 at the point (–2, 0) is–

A–1 B1 C1/2 D−1/2

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EnglishTGT 2003

Q93.The function f defined by f(x) = (x + 2) e–x is

Adecreasing for all x Bdecreasing in (–∞, –1) and increasing in (–1, ∞) Cincreasing for all x Ddecreasing in (–1, ∞) and increasing (–∞,-1)

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EnglishTGT 2003

Q94.If x lies in the interval [0, 1], then the minimum value of x2 + x +1 is:

A3/4 B1 C3 DNone of these

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EnglishTGT 2003

Q95.For the curve y = xex, the point

Ax = –1 is a point of minima Bx = 0 is a point of minima Cx = –1 is a point of maxima Dx = 0 is a point of maxima

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EnglishPGT 2011

Q96.If x y x y 2 2 2 + + + = + = then dy dx is equal to:

Ax y 2 2 + − Bx y 2 2 1 2 + + Cy x y x 1 2 1 2 − − − Dx y x y 2 2 2 + −

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EnglishPGT 2011

Q97.If y x y x e − − = then dy dx is equal to:

A() 1 1 logx − + B() 2 1 logx − + C()2 log x 1 log x + DNone of these

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EnglishPGT 2011

Q98.The derivative of 1 2 1 sec 2x 1 − with respect to 2 1 x − − at 1 x 2 = is:

A2 B4 C3 D–2

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EnglishPGT 2011

Q99.If the tangent to the curve ((()) x a θ sinθ = + = +, (()) y a 1 cosθ = + = + at π θ 3 = makes an angle α with x–axis, then α equal to:

Aπ/3 B2π/3 Cπ/6 D5π/6

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EnglishPGT 2011

Q100.The normal at the point (1, 1) on the curve 2y = 3 – x2 is:

Ax + y = 0 Bx + y + 1 = 0 Cx – y + 1 = 0 Dx – y = 0

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