Math Chapter Wise

EnglishEMRS PGT-2023

Q01.∫ 5 2 x I = dx x +1 equals:

A() 4 2 2 x x 1 log x 1 C 4 2 2 − + + + B() 4 2 2 x x 1 log x 1 C 4 2 2 − − + + C() 4 2 2 x x 1 log x 1 C 4 2 2 + − + + D() 4 2 2 x x 1 log x 1 C 4 2 2 + + + +

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EnglishEMRS PGT-2023

Q02.The area of the region bounded by the parabola 2 y = 2x - x and the line y = x (in sq. units) is:

A2/3 B1/2 C4/3 D1/6

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EnglishEMRS PGT-2023

Q03.If ∫ dx 1 x = k log 1+ tan 1+ 2 sinx + cosx k 2 then the value of k is:

A1/2 B1/2 C2 D2

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EnglishEMRS PGT-2023

Q04.∫ π 2 sinx -π 2 1 dx 1+e equals:

A4/π Bπ C3 2 π D2/π

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EnglishEMRS PGT-2023

Q05.If 2 e 2 1- x y = log 1+ x, then dy dx is equal to:

A4 4x 1 x − B4 1 4 x − C3 4 4x 1 x − D3 4 4x 1 x −

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EnglishEMRS PGT-2023

Q06.The area of the region enclosed between the curves 3 y = x and y = x (in square units) is:

A12/5 B5/3 C5/4 D5/12

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EnglishBihar (TRE 2.0)-2023

Q07.The value of ∫ ∫ ∫[(log|x|)2 /x ]dx is

A[1 + log|x|]3/+ C B3 log x C 3 + C() 3 1 log x 1 3 3 − + DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q08.The value of ∫ ∫ ∫cot x log (sinx) dx is

A() 1 cot x.log x C 2 + B() 2 1 logsin x C 2 + C() 2 1 logcos x C 2 + DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q09.The value of ∫ 1 -1 2 0 2x -1 tan dx 1+ x - x is

A1 B0 C4/π DMore than one of the above ENone of the above

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EnglishKVS PGT 2023

Q10.The area of the region (in sq units) bounded by the lines x = 2y + 3, y = 1 and y = -1 is:

A4 B6 C3/2 D8

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EnglishKVS PGT 2023

Q11.The value of () / 2 x 0 e sin x cosx dx π − ∫ is:

A1 B0 C2/π D2

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EnglishKVS PGT 2023

Q12.The value of cos 2x cos2.dx cos x cos − θ ∫ is:

Asin x – 2x cos θ + c B2 (sin x – x cos θ) + c C2 (sin x + x cos θ) + c D2 sin x + x cos θ + c

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EnglishKVS PGT 2023

Q13.The value of ()() 2 2 2 x dx x 1 x 4 + + ∫, is:

A1 1 1 2 x tan x tan c 3 3 2 − − + + B1 1 1 2 x tan x tan c 3 3 2 − − − + + C1 1 1 1 x tan x tan c 3 3 2 − − + + D1 1 1 1 x tan x tan c 3 3 2 − − − + +

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EnglishKVS PGT 2023

Q14.If f 3x 4 x 2 3x 4 − = + +, then ()dx ∫ f x equal to:

Ax 2 3x 4 e log c 3x 4 − − + B8 2 log x 1 x c 3 3 − − + + C8 2 log x 1 x c 3 3 − + + Dx 2 3x 4 e log c 3x 4 − + + −

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EnglishKVS PGT 2023

Q15.() cos x xsin x dx x x cos x + ∫ is equal to:

Ax log c x cox + Bx cox log c x + C1 log c x cox + Dlog x cos x c/+ +

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EnglishKVS PGT 2023

Q16.If f(x) = a + bx + cx2, then 1 0 (x)d(x) ∫ f is:

A1 (0) 4 (1) 2 + + 1 f f f 2 B1 (0) 2 (1) 6 + + 1 f f f 2 C1 (0) 4 (1) 6 + + 1 f f f 2 D1 (0) 2 (0) 2 + + 1 f f f 2

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EnglishNVS PGT 2022

Q17.Which among the following is not correct?

A2 2 dx log x x a C x a = + − + − ∫ B2 2 2 2 2 2 2 x a x a dx x a log x x a C 2 2 − = − − + − + ∫ C2 2 2 2 2 1 x a x a x dx a x sin C 2 2 a − − = − + + ∫ D2 2 dx 1 x a log C x a 2a x a + = + − − ∫

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EnglishNVS PGT 2022

Q18.∫ 2 6 sin x dx, cos x is

Aa polynomial of degree 5 in sin x Ba polynomial of degree 4 in ex Ca polynomial of degree 5 in cos x Da polynomial of degree 5 in tan x

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EnglishNVS PGT 2022

Q19.The value of the integral 100 0 sin x dx π ∫ is:

A100 B1 C200 D100 π

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EnglishNVS PGT 2022

Q20.The area bounded by the curve y = x2 and y = 2 x is:

A4/3 B2/3 C8/3 D1/3

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