GATE CE 2023 Set 1 | Calculus Question 10 | Engineering Mathematics

Consider the following definite integral $$${\rm I} = \int\limits_0^1 {{{{{\left( {{{\sin }^{ - 1}}x} \right)}^2}} \over {\sqrt {1 - {x^2}} }}dx} $$$
The value of the integral is

$${{{\pi ^3}} \over {24}}$$

$${{{\pi ^3}} \over {12}}$$

$${{{\pi ^3}} \over {48}}$$

$${{{\pi ^3}} \over {64}}$$

GATE CE 2017 Set 2

MCQ (Single Correct Answer)

-0.6

The tangent to the curve represented by $$y=x$$ $$ln$$ $$x$$ is required to have $${45^ \circ }$$ inclination with the $$x-$$axis. The coordinates of the tangent point would be

$$(1, 0)$$

$$(0,1)$$

$$(1,1)$$

$$\left( {\sqrt {2,} \sqrt 2 } \right)$$

GATE CE 2014 Set 2

MCQ (Single Correct Answer)

-0.6

The expression $$\mathop {Lim}\limits_{a \to 0} \,{{{x^a} - 1} \over a}\,\,$$ is equal to

$$\log \,x$$

$$0$$

$$x$$ $$log$$ $$x$$

$$\infty $$

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Questions Asked from Marks 2

GATE CE 2025 Set 2 (1) GATE CE 2025 Set 1 (2) GATE CE 2024 Set 2 (1) GATE CE 2023 Set 1 (1) GATE CE 2017 Set 2 (2) GATE CE 2014 Set 2 (1) GATE CE 2011 (1) GATE CE 2010 (2) GATE CE 2004 (1) GATE CE 2002 (2) GATE CE 2000 (3)

GATE CE Subjects

Engineering Mechanics

Strength of Materials Or Solid Mechanics

Structural Analysis

Construction Material and Management

Reinforced Cement Concrete

Steel Structures

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

Hydrology

Irrigation

Geomatics Engineering Or Surveying

Environmental Engineering

Transportation Engineering

Engineering Mathematics

General Aptitude