Test: Comprehension Based Questions: Definite Integrals and Applications of Integrals - Airforce X Y / Indian Navy SSR MCQ
16 Questions MCQ Test - Test: Comprehension Based Questions: Definite Integrals and Applications of Integrals
Let the definite integral be defined by the formula 
For more accurate result for c ∈ (a, b), we can use 
that for 
Q. 
For more accurate result for c ∈ (a, b), we can use that for 
Let the definite integral be defined by the formula For more accurate result for c ∈ (a, b), we can use that for
Q. 
then f(x) is of maximum degree
For more accurate result for c ∈ (a, b), we can use that for then f(x) is of maximum degree
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Let the definite integral be defined by the formula For more accurate result for c ∈ (a, b), we can use that for
Q. 
and c is a point such that a < c < b, and (c, f(c)) is the point lying on the curve for which F(c) is maximum, then f '(c) is equal to
For more accurate result for c ∈ (a, b), we can use that for and c is a point such that a < c < b, and (c, f(c)) is the point lying on the curve for which F(c) is maximum, then f '(c) is equal to
PASSAGE - 2
Consider the functions defined implicitly by the equation y3 – 3y + x = 0 on various intervals in the real line. If x ∈(-∞, - 2) ∪ (2,∞) , the equation implicitly defines a unique real valued differentiable function y = f (x). If x ∈(-2, 2) , the equation implicitly defines a unique real valued differentiable function y = g(x) satisfying g(0) = 0.
Q. 
PASSAGE - 2
Consider the functions defined implicitly by the equation y3 – 3y + x = 0 on various intervals in the real line. If x ∈(-∞, - 2) ∪ (2,∞) , the equation implicitly defines a unique real valued differentiable function y = f (x). If x ∈(-2, 2) , the equation implicitly defines a unique real valued differentiable function y = g(x) satisfying g(0) = 0.
Q. The area of the region bounded by the curve y = f (x), the x-axis, and the lines x = a and x = b, where -∞ < a <b <-2 , is
PASSAGE - 2
Consider the functions defined implicitly by the equation y3 – 3y + x = 0 on various intervals in the real line. If x ∈(-∞, - 2) ∪ (2,∞) , the equation implicitly defines a unique real valued differentiable function y = f (x). If x ∈(-2, 2) , the equation implicitly defines a unique real valued differentiable function y = g(x) satisfying g(0) = 0.
Q. 
PASSAGE - 3
Consider the function f : ( -∞,∞) →(-∞,∞) defined by
Q. Which of the following is true?
PASSAGE - 3
Consider the function f : ( -∞,∞) →(-∞,∞) defined by
Q. Which of the following is true?
PASSAGE - 3
Consider the function f : ( -∞,∞) →(-∞,∞) defined by
Q. 
Which of the following is true?
PASSAGE - 4
f (x) = 1 + 2x + 3x2 + 4x3.
Let s be the sum of all distinct real roots of f (x) and let t = |s|.
Q. The real numbers lies in the interval
and hence 
PASSAGE - 4
f (x) = 1 + 2x + 3x2 + 4x3.
Let s be the sum of all distinct real roots of f (x) and let t = |s|.
Q. The area bounded by the curve y = f (x) and the lines x = 0, y = 0 and x = t, lies in the interval
PASSAGE - 4
f (x) = 1 + 2x + 3x2 + 4x3.
Let s be the sum of all distinct real roots of f (x) and let t = |s|.
Q. The function f'(x) is
PASSAGE - 5
Given that for each 
dt exists. Let this limit be g(a). In addition, it is given that the function g(a) is differentiable on (0, 1).
Q. The value of 
PASSAGE - 5
Given that for each dt exists. Let this limit be g(a). In addition, it is given that the function g(a) is differentiable on (0, 1).
Q. 
PASSAGE - 6
be a thrice differentiable function. Suppose that F(1) = 0, F(3) = –4 and F(x) < 0 for 
Q. The correct statement(s) is(are)
PASSAGE - 6
be a thrice differentiable function. Suppose that F(1) = 0, F(3) = –4 and F(x) < 0 for
Q. 
...(i)
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