Engineering Mathematics
Probability and Statistics
Marks 1Marks 2
Differential Equations
Marks 1Marks 2
Transform Theory
Marks 1Marks 2
Complex Variable
Marks 1Marks 2
Linear Algebra
Marks 1Marks 2
Vector Calculus
Marks 1Marks 2
Numerical Methods
Marks 1Marks 2
1
GATE CE 2022 Set 2
Numerical
+1
-0

The components of pure shear strain in a sheared are given in the matrix form:

$$\varepsilon = \left[ {\matrix{ 1 & 1 \cr 1 & { - 1} \cr } } \right]$$

Here, Trace ($$\varepsilon $$) = 0. Given, P = Trace ($$\varepsilon$$8) and Q = Trace ($$\varepsilon $$11).

The numerical value of (P + Q) is ___________. (in integer)

Your input ____
2
GATE CE 2022 Set 2
MCQ (More than One Correct Answer)
+1
-0

P and Q are two square matrices of the same order. Which of the following statements is/are correct?

A
If P and Q are invertible, then$${[PQ]^{ - 1}} = {Q^{ - 1}}{P^{ - 1}}$$.
B
If P and Q are invertible, then $${[PQ]^{ - 1}} = {P^{ - 1}}{Q^{ - 1}}$$.
C
If P and Q are invertible, then $${[QP]^{ - 1}} = {P^{ - 1}}{Q^{ - 1}}$$.
D
If P and Q are not invertible, then $${[PQ]^{ - 1}} = {Q^{ - 1}}{P^{ - 1}}$$.
3
GATE CE 2022 Set 1
MCQ (More than One Correct Answer)
+1
-0

The matrix M is defined as

$$M = \left[ {\matrix{ 1 & 3 \cr 4 & 2 \cr } } \right]$$

and has eigenvalues 5 and $$-$$2. The matrix Q is formed as

Q = M3 $$-$$ 4M2 $$-$$ 2M

Which of the following is/are the eigenvalue(s) of matrix Q?

A
15
B
25
C
$$-$$20
D
$$-$$30
4
GATE CE 2022 Set 1
MCQ (Single Correct Answer)
+1
-0.33

The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45$$^\circ$$ clockwise rotation of the coordinate system about the positive x-axis are

A
(1, 0, $$\sqrt 2 $$)
B
(1, 0, $$-$$$$\sqrt 2 $$)
C
($$-$$1, 0, $$\sqrt 2 $$)
D
($$-$$1, 0, $$-$$$$\sqrt 2 $$)
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