Two coins R and S are tossed. The 4 joint events H_{R}H_{S},
T_{R }T_{S},H_{R }T_{S},T_{R }H_{S} have
probabilities 0.28, 0.18, 0.30, 0.24, respectively, where H represents head and T
represents tail. Which one of the following is TRUE?

**A. ** The coin tosses are independent

**B. ** R is fair, R it not.

**C. ** S is fair, R is not

**D. ** The coin tosses are dependent

**Answer : ****Option D**

**Explaination / Solution: **

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Roots of the algebraic equation x^{3} + x^{2} + x + 1 = 0 are

**A. ** (+1, +j, −j)

**B. ** (+1, −1, +1)

**C. ** (0,0,0)

**D. ** (−1, +j, −j)

**Answer : ****Option D**

**Explaination / Solution: **

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Let X and Y be finite sets and f : X → Y be a function. Which one of the following
statements is TRUE?

**A. ** For any subsets A and B of X, |f (A ∪ B)| = |f(A)| + |f(B)|

**B. ** For any subsets A and B of X, f (A ∩ B) = f(A) ∩ f(B)

**C. ** For any subsets A and B of X,|f (A ∩ B)| = min {|f(A)|,|f(B)|}

**D. ** For any subsets S and T of Y, f^{-1}(S ∩ T) = f^{-1}(S) ∩ f^{-1}(T)

**Answer : ****Option D**

**Explaination / Solution: **

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Choose the correct expression for f(x) given in the graph.

No Explaination.

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In the solution of the following set of linear equations by Gauss elimination using
partial pivoting 5x + y + 2z = 34; ay - 3z = 12; and 10 - 2y + z = -4; the pivots
for elimination of x and y are

**A. ** 10 and 4

**B. ** 10 and 2

**C. ** 5 and 4

**D. ** 5 and -4

**Answer : ****Option A**

**Explaination / Solution: **

No Explaination.

No Explaination.

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In shear design of an RC beam, other than the allowable shear strength of concrete (τ_{c}),
there is also an additional check suggested in IS 456-2000 with respect to the
maximum permissible shear stress (τ_{c max}). The check for τ_{c max }max is required to
take care of

**A. ** additional shear resistance from reinforcing steel

**B. ** additional shear stress that comes from accidental loading

**C. ** possibility of failure of concrete by diagonal tension

**D. ** possibility of crushing of concrete by diagonal compression

**Answer : ****Option D**

**Explaination / Solution: **

No Explaination.

No Explaination.

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The two vectors [1,1,1] and [1, a, a^{2}], where a = , are

**A. ** Orthonormal

**B. ** Orthogonal

**C. ** Parallel

**D. ** Collinear

**Answer : ****Option B**

**Explaination / Solution: **

Dot product of two vectors = 1 + a + a2 = 0

Dot product of two vectors = 1 + a + a2 = 0

So orthogonal

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The value of the integral given below is

**A. ** − 2π

**B. ** π

**C. ** −π

**D. ** 2π

**Answer : ****Option A**

**Explaination / Solution: **

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A path AB in the form of one quarter of a circle of unit radius is shown in the figure. Integration of (x + y)^{2} on path AB traversed in a counter-clockwise sense is

**A. ** (π/2) - 1

**B. ** (π/2) + 1

**C. ** π/2

**D. ** 1

**Answer : ****Option B**

**Explaination / Solution: **

No Explaination.

No Explaination.

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Which of the following is a solution to the differential equation

**A. ** X(t) = 3e^{-t}

**B. ** X(t) = 2e^{-3t}

**C. ** X(t) = -3/2 t^{2}

**D. ** X(t) = 3t^{2}

**Answer : ****Option B**

**Explaination / Solution: **

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