Consider the following expressions [G16S2Q11]

Explanation

Let f(x) be a polynomial and g(x) = f 0 (x) be its derivative. If the degree of (f(x)+ f(−x)) is 10, then the degree of (g(x)−g(−x)) is [G16S2Q12]

Explanation

The minimum number of colours that is sufficient to vertex-colour any planar graph is [G16S2Q13]

Explanation

Consider the systems, each consisting of m linear equations in n variables. [G16S2Q14]

Explanation

Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. [G16S2Q15]

Explanation

Suppose that the eigenvalues of matrix A are 1,2,4. The determinant of [G16S2Q16]

Explanation

A binary relation R on N×N is defined as follows: (a,b)R(c,d) if a ≤ c or b ≤ d. Consider the following propositions: [G16S2Q36]

Explanation

Which one of the following well-formed formulae in predicate calculus is NOT valid? [G16S2Q37]

Explanation

Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of 9 compounds, each of which reacts with exactly 3 compounds of U. [G16S2Q38]

Explanation

Let A1,A2,A3, and A4 be four matrices of dimensions 10 × 5,5 × 20,20 × 10, and 10 × 5, respectively. The minimum number of scalar multiplications required to find the product A1A2A3A4 using the basic matrix multiplication method is [G16S2Q48]

Explanation

Let p,q,r,s represent the following propositions [G16S1Q11]

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Let an be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for an? [G16S1Q12]

Explanation

lim [G16S1Q13]

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A probability density function on the interval [a,1] is given by 1/x 2 and outside this interval the value of the function is zero. The value of a is [G16S1Q14]

Explanation

Two eigenvalues of a 3 × 3 real matrix P are [G16S1Q15]

Explanation

Consider the Boolean operator # with the following properties: x# 0 = x, x# 1 = x¯, x#x = 0 and x# ¯x = 1. Then x#y is equivalent to [G16S1Q16]

Explanation

The coefficient of [G16S1Q36]

Explanation

Consider the recurrence relation a1 = 8, an = 6n 2 +2n+an−1. Let a99 = K ×104 . The value of K is [G16S1Q37]

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A function f : N + → N +, defined on the set of positive integers N +, satisfies the following properties: [G16S1Q38]

Explanation

Consider the following experiment. [G16S1Q39]

Explanation