Add a pair of parentheses to each expression so that it evaluates to True. a) 0 == 1 == 2 b) (2 + 3) == (4 + 5) == 7 c) (1 < -1) == (3 > 4)

The expression $2x^{2}+4x+7$ has minimum value $m$ at $x=\alpha$. The ordered pair $(\alpha, m)$ is:

A) $(1, -5)$

B) $(-1, -5)$

C) $(-1, 5)$

D) $(1, 5)$

Select the correct approach for solving a pair of linear equations in 2 variables by elimination method:

• Add or subtract one equation from the other so that one variable gets eliminated.
• Multiply both the equations by any non-zero constant to make the coefficients of one variable (either x or y) numerically equal.
• Solve the equation in one variable (x or y) to get its value.
• Substitute the value of x (or y) in either of the original equations to get the value of the other variable.

Options:

• (i), (iv), (ii), (iii)
• (ii), (i), (iv), (iii)
• (ii), (i), (iii), (iv)
• (i), (ii), (iii), (iv)

Find the measure of an angle which forms a pair of supplementary angles with itself.

An unbiased coin is tossed. If the outcome is head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well shuffled pack of nine cards numbered $1, 2, \cdots, 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is:

A $\frac{19}{36}$
B $\frac{19}{72}$
C $\frac{15}{72}$
D $\frac{13}{36}$

An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well-shuffled pack of eleven cards numbered 2, 3, 4, ..., 12 is picked, and the number on the card is noted. The probability that the noted number is either 7 or 8 is:

0.244