Let `X` and `Y` be Banach spaces. Then the product space `X × Y` , with the norm defined by: `∥ (x,y)∥=∥x∥+∥y∥,∀(x,y)∈X×Y`

1. Banach space
2. Normed space
3. Linear space
4. All of these
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Answer: B
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Let `f(x)=[x]`, greatest integer `≤ x` ; be integrable function on [0,4], then `∫_0^4[x]dx` is equal to:

1. 3

2. 7

3. 6

4. 4

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Answer: C
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Solution of `(△^2=2△+1)u_x=3x+2` is:

1. `u_x=3x+4`

2. `u_x=4x+3`

3. `u_x=3x-4`

4. `u_x=4x-3`

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Answer: B
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The sequence `{ (2ni)/(n+i)−((9−12i)n+2)/(3n+1+7i)}` converges to :

1. `3+6i`
2. `-3-6i`
3. `-3+6i`
4. `3-6i`
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Answer: D
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Which of those is not an analytical method to solve partial differential equation?

1. Change of variable
2. Superposition principle
3. Finite element method
4. Integral transform
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Answer: B
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Order of convergence of Newton's method is :

1. Quadratic
2. Cubic
3. 4^th
4. Undefined
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Answer: A
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After discretizing the partial differential equations take which if these forms?

1. Exponential equations
2. Trigonometric equations
3. Logarithmic equations
4. Algebraic equations
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Answer: A
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For a function `f, if f_(x x)=f_(xy)=f_(yy)=0`, the point (x,y) will be multiple point of order:

1. Lower than two
2. Two
3. Higher
4. Higher than the two
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Answer: D
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Suppose that `X` and `Y` are closed subspaces of a Hilbert space `H` such that `X⊥Y`, then `X+Y` is :

1. A closed subspace
2. `X^⊥+Y^⊥`
3. `X^⊥+Y`
4. Normed subspace
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Answer: A
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The function `f(x)=x^((−1))` is not:

1. Uniform continuous on `(0,1)`
2. Continuous on `(0,1)`
3. Differentiable on `[0,1)`
4. Both A and B
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Answer: A
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