Math Chapter Wise

EnglishEMRS PGT-2023

Q01.If the function f given by f(x)= x3 –3 (a– 2)x2 +3ax + 7, for some a∈R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, 2 () 14 0 (1) − = − f x x (x≠1) is:

A6 B7 C5 D–7

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EnglishEMRS PGT-2023

Q02.The function -1 (x) = cot x + x f increases in the interval:

A() 1, − ∞ B(), −∞ ∞ C() 0, ∞ D[) 1, ∞

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EnglishKVS PGT 2023

Q03.The equation of tangent to the curve y = x + sinx. cosx at x = 2 π is:

Ay = π By + π = 0 C2y = π Dy = 2

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EnglishKVS PGT 2023

Q04.If f(x) = sin x + cos x, then the maximum value of f(x) is:

A2 B2 3 C2 D3 2

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EnglishKVS PGT 2023

Q05.The minimum value of the quadratic function f(x) = 3x2 - 6x + 5 is:

A1 B2 C5 D6

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EnglishKVS PGT 2023

Q06.The minimum value of () 4 3 2 x x x e − + is:

Ae B1 Ce2 D1/e

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EnglishNVS PGT 2022

Q07.f(x) = sinx + cos 2x, (x > 0) has minima for value of x equals to:

An 2 π B() 3 n 1 2 + π C() 2n 1 2 + π Dnπ

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EnglishNVS PGT 2022

Q08.The interval in which the function f(x) = 4x3 − 6x2 − 72x+ 30 decreases is:

A(−∞, −2) B(−2, 3) C(3, ∞) D(−2, −3)

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EnglishKVS PGT 2022

Q09.The slope of tangent to the curve x=3t2 +1, y=t3 −1 at x=1 is:

A0 B–2 C1/2 D∞

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EnglishKVS PGT 2022

Q10.The function f(x)=2x3 −15x2 +36x+4 has maximum value when value of x is

A3 B0 C4 D2

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EnglishDSE TGT 2022

Q11.The maximum/minimum value of f(x) = 2 x2 + x – 3 is

A–3/2 B–25/8 C3/2 D25/8

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EnglishDSE TGT 2019

Q12.The equation of the tangent to the curve (x/a)n + (y/b)n = 2, (a ≠ 0, b ≠ 0), at the point (a, b) is

Ax/a - y/b = 1 Bx + y = a + b Cx/a + y/b = 2 Dx/a - y/b = 2

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EnglishDSE TGT 2019

Q13.If the normal to the curve ay2 = x3 (a ≠ 0) at a point on it makes equal intercepts with the coordinate axes, then the x-coordinate of the point on the curve is

A4a/9 B9a C–4a/9 D4a

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EnglishOAVS TGT 2018

Q14.If b < 0, then function f(x) = bx2 + ax + c:

Ais constant Bhas the minimum value Cis positive Dhas the maximum value

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EnglishOAVS TGT 2018

Q15.f(x) = sinx is strictly increasing in the interval:

A, 2 B0, C2n, 2n 2 2 D(,)

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EnglishJSSC PGT 2018

Q16.Let f: [0, ∞ ∞ ∞] s.t. df/dx is monotonically increasing and f(0) = 0. If g (x) = f(x)/x, then g is:

AConcave function BConvex function CMonotonically decreasing DMonotonically increasing

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EnglishJSSC PGT 2018

Q17.The function sin (ex), where x > 0:

AIs bounded but does not converge BDiverges to infinity as x > ∞ CIs strictly increasing but bounded DIs bounded and converges to a real number as x > ∞

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EnglishJSSC PGT 2018

Q18.Let f (x) be a differentiable function on R such that df/dx > 0 for all x and lim f (x) ≥ 2 as x > – ∞ ∞. Which of the following is true?

Af (3) > 2 Bf (3) > = 2 Cf (3) < = 2 Df (3) = 2

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EnglishKVS TGT 2017

Q19.If 1 f(x) log(1 x), x 1 x 0 then f is–

Aan increasing function Ba decreasing function Cboth increasing and decreasing function Dneither increasing nor decreasing function

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EnglishKVS TGT 2017

Q20.The maximum value of 2 x f(x) 4 x x on 1,1 is–

A1/4 B1/3 C1/6 D1/5

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