GATE CE 2002


Question 1
Eigen values of the following matrix are:
\begin{bmatrix} -1 &4 \\ 4&-1 \end{bmatrix}
A
3 and -5
B
-3 and 5
C
-3 and -5
D
3 and 5
Engineering Mathematics   Linear Algebra
Question 2
The value of the following definite integral is:
\int_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{sin2x}{1+cosx}dx
A
-2 ln2
B
2
C
0
D
(ln 2)^{2}
Engineering Mathematics   Calculus
Question 2 Explanation: 
Since the givem function is odd function therefore in the given limits the integral will be zero.


Question 3
The following function has a local minima at which value of x?
f(x)=x\sqrt{5-x^{2}}
A
-\frac{\sqrt{5}}{2}
B
\sqrt{5}
C
\sqrt{\frac{5}{2}}
D
-\sqrt{\frac{5}{2}}
Engineering Mathematics   Calculus
Question 3 Explanation: 
\begin{aligned} f\left ( x \right )&=x\sqrt{5-x^{2}} \\ {f}'\left ( x \right )&=\sqrt{5-x^{2}}+\frac{x\times -2x}{2\sqrt{5-x^{2}}} \\ 5-x^{2}&=x^{2} \\ 2x^{2}&=5 \\ x&=\pm \sqrt{\frac{5}{2}}\end{aligned}
Question 4
For the loading given in the figure below, two statements (I and II) are made.

I. Member AB Carries shear force and bending moment.
II. Member BC carries axial load and shear force.

Which of the following is true?
A
Statement I is true but II is false
B
Statement I is false but II is true
C
Both statements I and II are true
D
Both statements I and II are false
Solid Mechanics   Shear Force and Bending Moment
Question 4 Explanation: 


Member AB carries shear force and bending moment both. Hence statement-I is true

Member BC carries axial load and bending moment only. Hence statement-II is false.
Question 5
Read the following two statements

I. Maximum strain in concrete at the outermost compression fibre is taken to be 0.0035 in bending
II. The maximum compressive strain in concrete in axial compression is taken as 0.002.

Keeping the provisions of IS 456-2000 on limit state design in mind, which of the following is true?
A
Statement I is true but II is false
B
Statement I is false but II is true
C
Both statement I and II are true
D
Both statements I and II are false
RCC Structures   Working Stress and Limit State Method


There are 5 questions to complete.

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