CMAT Data Sufficiency questions

Given below are two statements:
Statement I : A coin is tossed three times. The probability of getting exactly two heads is 3/8
Statement II: In tossing of 10 coins, the probability of getting exactly 5 heads is 63/256

In the light of the above statements, choose the correct answer from the options given below.

Which of the following statements regarding quadratic equations are true?
(A) Solution set for the equation $$6x^{2}-5x=4$$ is $$\left\{-\frac{1}{2},\frac{4}{3}\right\}$$
(B) The nature of the roots of the equation $$9x^{2}+6x+1=0$$ is equal, real and rational.
(C) If one root of $$4x^{2}-3x+K=0$$ is 3 times the other, then $$K=\frac{27}{256}$$

Given below are two statements
Statement I: In the sequence of numbers 30, 90, 182, 306, 462,P........ . the term P is 650.
Statement II : There are 8 digits in $$9^{8}$$ when it is expressed in decimal form.
In light of the above statements, choose the correct answer from the options given below

Given below are two statements
Statement I : $$(543)_6$$ is equivalent to $$(317)_8$$
Statement II : The last 4 bits in the binary representation of a multiple of 16 is 1000.
In light of the above statements, choose the correct answer from the options given below

Given below are two statements
Statement I : The set of numbers(5,6, 7, p, 6, 7, 8, q) has an arithmetic mean of 6 and mode (most frequently occurring number) of 7. Then $$p\times q=16$$.
Statement II: Let p and q be two positive integers such that $$p+q+p\times q=94$$. Then $$p+q=20$$.
In light of the above statements, choose the correct answer from the options given below

Given below are two statements:
Statement I: $$\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}=2$$
Statement II: If $$a+b+c=0$$, then $$(a^{3}+b^{3}+c^{3})\div abc=3$$
In light of the above statements, choose the correct answer from the options given below