Math Chapter Wise

EnglishEMRS PGT-2023

Q01.If f(x) = cosx cos2x cos4x cos8x cos16x, then π ' 4 f is:

A1/2 B1 C3/2 D2

Show answer

EnglishEMRS PGT-2023

Q02.If f(x) = |x – 1| + |x – 3|, then d y x at x = 2 is:

A1 B2 Cnon-existent D0

Show answer

EnglishEMRS PGT-2023

Q03.If 2 1 k 1 k, () 1 0 x,0 1 2 3 2 + − − = − ≤ < ≤ + − x x f x x x x x is continuous at x = 0, then k equals:

A–2 B–3 C–4 D–1

Show answer

EnglishEMRS PGT-2023

Q04.For x > 1, if (2x)2y = 4e2x–2y, then (1 + loge 2x)2 d y x is equal to:

Ae e log 2 log 2 − x x x Bx loge 2x Cx loge2x De e log 2 log 2 + x x x

Show answer

EnglishEMRS PGT-2023

Q05.If x = 2 sinθ – sin2θ and y = 2cosθ –cos2θ, θ∈ [0, 2π], then 2 d y dx at θ = π is:

A3/4 B−3/8 C3/8 D−3/4

Show answer

EnglishEMRS PGT-2023

Q06.If x loge (loge x) – x2 +y2 = 4 (y > 0), then dy dx at x = e is equal to:

A2 2e 1 2 4 e − + B2 1 2e 4 e + C2 1 2e 2 4 e + D2 e 4 e +

Show answer

EnglishBihar (TRE 2.0)-2023

Q07.The function f (x) = xx,x > 0 has

Ano extremum point Bonly one extremum point Ctwo extrema points DMore than one of the above ENone of the above

Show answer

EnglishBihar (TRE 2.0)-2023

Q08.The value of → x 0 1 lim xsin x is

A-1 B0 C1 DMore than one of the above ENone of the above

Show answer

EnglishBihar (TRE 2.0)-2023

Q09.The value of → 2 x 0 1-cosx lim x is

A1/4 B1/2 C0 DMore than one of the above ENone of the above

Show answer

EnglishBihar (TRE 2.0)-2023

Q10.The function f (x) = x|x| is

Anot continuous at the origin Bnot differentiable at the origin Cdifferentiable at the origin DMore than one of the above ENone of the above

Show answer

EnglishBihar (TRE 2.0)-2023

Q11.The value of → 3 2 4 2 x 3 x - 7x +15x - 9 lim x - 5x + 27x - 27 is

A9 B2/9 C1/9 DMore than one of the above ENone of the above

Show answer

EnglishBihar (TRE 2.0)-2023

Q12.If f(x) =|sinx|, then

Af(x) is everywhere differentiable Bf(x) is everywhere continuous but not differentiable at x = nπ, n ∈ z Cf(x) is everywhere continuous and everywhere differentiable DMore than one of the above ENone of the above

Show answer

EnglishBihar (TRE 1.0) -2023

Q13.Evaluate →∞ ∑ n 2 2 n k=0 n lim k + n

A2/π Bπ C4/π DMore than one of the above ENone of the above

Show answer

EnglishEMRS TGT-2023

Q14.If () () 3 4 d 3 f x = 4x – dx x such that f(2) = 0, then f(x) is:

A4 3 1 129 x – x 8 + B3 4 1 129 x x 8 + + C3 4 1 129 x – x 8 + D4 3 1 129 x x 8 + +

Show answer

EnglishEMRS TGT-2023

Q15.2 d log x +1 dx equals

A2 log e x 1 + B() 2 x x 1 log 2 + C2 xlog2 x 1 + D2 1 x 1 +

Show answer

EnglishEMRS TGT-2023

Q16.The function () f x = x + x –1 is:

AContinuous at x = 0 but not at x = 1. BContinuous at x = 1 but not at x = 0. CDiscontinuous at x = 0 as well as at x = 1. DContinuous at x = 0 as well as at x = 1.

Show answer

EnglishEMRS TGT-2023

Q17.If log(x+y) – 2xy = 0, and y(0) = 1, then y'(0) is:

A–1 B2 C0 D1

Show answer

EnglishEMRS TGT-2023

Q18.If () e y = log sinx, then dy dx is:

A1 cot x e B2 cotx C1 cot x 2 De cot x

Show answer

EnglishKVS PGT 2023

Q19.If the function ƒ ƒ ƒ(x) = (x –1) (x –2) (x –3) satisfy the Lagrange's Mean Value Theorem in the interval [0, 4]. The number of values of c will be:

A0 B1 C2 D3

Show answer

EnglishKVS PGT 2023

Q20.x x 0 Lt x → is equal to:

A0 B1 C-1 D2

Show answer