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The figure shows the plot of y as a function of x
Differential Equations mcq question image
The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is
Consider the following properties attributed to state model of a system: 1. State model is unique. 2. Transfer function for the system is unique. 3. State model can be derived from transfer function of the system. Which of the above statements are correct?
Let h(t) denote the impulse response of a causal system with transfer function $${1 \over {s + 1}}.$$  Consider the following three statements:
S1 : The system is stable.
S2 : $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}$$  independent of t for t > 0.
S3 : A non-causal system with the same transfer function is stable.
For the above system,
A system can be represented in the form of state equations as: S (n+1) =A S (n) +B x (n) Y (n) = C S (n) +D x (n) Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system. H (z) =Y (z)/X (z) is given by:
What will be the elongation of a bar of 1250mm2 area and 90cm length when applied a force of 130kN if E = 1.05x 105 N/mm2?
A man invested x rupees for 2 years at a rate of r% simple interest. If the amount he received after 2 years is 1.05x, find the rate percentage.
A stable linear time invariant (LTI) system has a transfer function $$H\left( s \right) = {1 \over {{s^2} + s - 6}}.$$    To make this system causal it needs to be cascaded with another LTI system having a transfer function H1(s). A correct choice for H1(s) among the following options is
When a system is taken from state ‘x’ to state ‘y’ then 30 kJ of heat flows into the system and the system does 10 kJ of work. When the system is returned from state ‘y’ to state ‘x’ along another path, then work done on the system is 8 kJ. What is the amount of heat liberated?
Consider the following statements about the Scheduled Castes and the Scheduled Tribes under the provisions of the Constitution of India : 1. State can make any special provision relating to their admission to the Government educational institutions. 2. State can make any special provision relating to their admission to the private educational institutions aided by the State. 3. State can make any special provision relating to their admission to the private educational institutions not aided by the State. 4. State can make any special provision relating to their admission to the minority educational institutions as described in Article 30. Which of the statements given above are correct?
In the following question, two statements are given each followed by two conclusions I and II. You have to consider the statements to be true even if theyseem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements. Statements:
(I) Some polynomials are linear equations.
(II) Some linear equations are quadratic. Conclusion:
(I) Polynomials are quadratic.
(II) Linear equations are quadratic.