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Integrals

Multiple Choice Questions

1021.

$The integral \int_{1}^{2} e^{x} . x^{2} (2 + \log_{e} (x)) d x = ?$

e(2e - 1)
e(4e + 1)
4e² - 1
e(4e - 1)

1022.
The common difference of the A.P. b₁,b₂,....,bm is 2 more than common difference of A.P. a₁,a₂,...,a_n. If a₄₀= –159, a₁₀₀= – 399 and b₁₀₀= a₇₀, then b₁is equal to :

127

81

- 127

- 81

- 81

$Let a_{1}, a_{1} + d, a_{1} + 2 d . . . first A . P . a_{40} = a_{1} + 39 d = - 159 . . . (i) a_{100} = a_{1} + 99 d = - 399 . . . (ii) from equation (i) and (ii) d = - 4, a_{1} = - 3 now b_{100} = a_{70} \Rightarrow b_{1} + 99 D = a_{1} + 69 d b_{1} + 99 \times (- 2) = - 3 + 69 \times (- 4) (According to question D = d + 2) \Rightarrow b_{1} = - 81$

Previous Year Papers

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Test Yourself

Multiple Choice Questions

1022. The common difference of the A.P. b1,b2,....,bm is 2 more than common difference of A.P. a1,a2,...,an. If a40 = –159, a100 = – 399 and b100 = a70, then b1is equal to : 127 81 - 127 - 81

1022.
The common difference of the A.P. b₁,b₂,....,bm is 2 more than common difference of A.P. a₁,a₂,...,a_n. If a₄₀= –159, a₁₀₀= – 399 and b₁₀₀= a₇₀, then b₁is equal to :

127

81

- 127

- 81