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STATEMENT 1: If f(x) is continuous on [a...

STATEMENT 1: If `f(x)` is continuous on `[a , b]` , then there exists a point `c in (a , b)` such that `int_a^bf(x)dx=f(c)(b-a)`
STATEMENT 2: For `a < b ,` if `ma n dM` are, respectively, the smallest and greatest values of `f(x)on[a , b]` , then `m(b-a)lt=int_a^bf(x)dxlt=(b-a)Mdot`
(a) statement 1 is true, statement 2 is true, Statement 2 is the correct explanation for statement 1.
(b) statement 1 is true, statement 2 is true, Statement 2 is not correct explanation for statement 1.
(c) statement 1 is true, statement 2 is not true.

(d) statement 2 is true, statement 1 is not true.

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Statement 1: A plane passes through the point A(2,1,-3)dot If distance of this plane from origin is maximum, then its equation is 2x+y-3z=14. Statement 2: If the plane passing through the point A( vec a) is at maximum distance from origin, then normal to the plane is vector vec a (a) Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1. (b) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is true , Statement 2 is false. (d) Statement 2 is true, Statement 1 is false.

Statement 1: Mass of O^16 nucleus is less than the sum of masses of 9 protons and 8 neutrons. Statement 2: Some internal energy is needed to keept the protons and neutrons bound in the nucleus. (A) Statement 1 is true, Statement 2 is true. Statement 2 is not a correct explanation for statement 1. (B) Statement 1 is true, Statement 2 is true. Statement 2 is a correct explanation for statement 1. (C) Statement 1 is true, Statement 2 is false. (D) Statement 1 is false, Statement 2 is true.

Statement I: No natural radioisotope can emit positron. Statement II: Some artifically transmuted isotopes show radioactivity - some of these may emit positrons. (A) Statement I is true, statement II is true, statement II is a correct explanation for statement I. (B) Statement I is true, statement II is true, statement II is not a correct explanation for statement I. (C) Statement I is true , statement II is false. (D) Statement I is false, statement II is true.

Statement I: Negative charges are never emitted from the nucleus of an atom. Statement II: Nucleus of an atom is constituted only of protons and neutrons. (A) Statement I is true, statement II is true, statement II is a correct explanation for statement I. (B) Statement I is true, statement II is true, statement II is not a correct explanation for statement I. (C) Statement I is true, statement II is false. (D) Statement I is false, statement II is true.

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Statement 1: The greater the decay constant of a radioactive element, the smaller is its half-life. Statement 2: An element, although radioactive, can last longer, if its decay with time is slow. (A) Statement 1 is correct, Statement 2 is correct. But, Statement 2 is not the correct explanation of Statement 1. (B) Statement 1 is correct, Statement 2 is correct. Statement 2 is the correct explanation of Statement 1. (C) Statement 1 is correct, Statement 2 is incorrect. (D) Statement 1 is incorrect, Statement 2 is correct.

Statement 1: The normals at the points (4, 4) and (1/4,-1) of the parabola y^2=4x are perpendicular. Statement 2: The tangents to the parabola at the end of a focal chord are perpendicular. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

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CENGAGE PUBLICATION-INTEGRALS-All Questions
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