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In the following questions, a question is followed by data in the form of two statements labelled as I and II. You must decide whether the data given in the statements are sufficient to answer the questions.
Find the values of x and y.
I) $$2x + 3y = -2$$
II) $$-x - \frac{3y}{2} = 1$$
What is the value of $$\cos^{2} \theta - \sin^{2} \theta$$?
I) $$\sin^{2} \theta = \frac{7}{25}$$
II) $$\theta$$ lies in first quadrant
A is a non-empty set and R,S are two relations defined on A. Is R $$\cap$$ S a reflexive relation?
I) R and S are reflexive relations
II) R is symmetric relation
R is a relation defined on A, where A is the set {a,b,c,d,e}.
Is R symmetric?
I) $$R \subseteq A \times A$$
II) $$R = \left\{(x,y) \mid x \ is \ vowel \ and \ y = e \right\}$$
How many colors have been used to paint the outer surface of the cube?
I) Each face of the cube is painted using only one color, and no two adjacent faces have the same color.
II) At least two pairs of opposite faces have the same color.
Is 5 a root of the poly1101nial $$p(x)$$?
I) $$p\left(p\left(p(7)\right)\right) \neq 0$$
II) $$p(7) = 21$$ and $$p(21) = 5$$
What is the value of the positive two digit number?
I) The number is six times the sum of its digits.
II) The number obtained by reversing the digits is less than the original number by nine.
What will be the population in the city A in 2025?
I) In 2020 the population of the city A was 10 million.
II) In 2015 the population of the city A was much less than that of 2020.
If a and b are two digit numbers that share the same digits except in reverse order, then what is the sum of a and b ?
I) a - b = 45
II) The difference between the two digits in each number is 5
Is $$\frac{1}{a_{1}},\frac{1}{a_{2}},\frac{1}{a_{3}} ...$$ a Geometric Progression?
I) $$a_{1},a_{2},a_{3}$$.....is an Arithmetic Progression.
II) $$a_{1},a_{2},a_{3}$$.....is a Geometic Progression..
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