What is the digit in the ten's place of 2¹⁰⁰¹?

If x is even integer, which of the following must be an odd integer?

­In a class of 80 students, 40% of the students play basketball, 50% play football, and 30% play table tennis. If 5 students play both football and table tennis but not basketball, what is the maximum possible number of students who play both basketball and football, but not table tennis?

In a class of 80 students, each of them studies at least one language - English, French and German. It was found that 65 studied English,60 studied French and 55 Studied German. Find the Maximum number of people who studied all the 3 languages.

How many ordered pairs of positive integers (m,n) satisfy GCD (m³,n²)=2²∗3² and LCM (m²,n³)=2⁴∗3⁴∗5⁶ where, GCD- Greatest common divisor and LCM- least common multiple

If x and y are integers such that 5 < |y| < 9 and 4 < |x|< 10, which of the following represents all possible values of xy ?

­If a + b = 10, what is the maximum value of ?

Ordinary automobile engines can be converted to run on ethanol, which can be produced from corn and other grains. In the United States, ethanol is currently much more expensive than gasoline, and there is no prospect that the price of ethanol will decrease. Perhaps, though, as petroleum reserves continue to dwindle, the price advantage of gasoline will diminish and eventually disappear, and ethanol will displace gasoline as the primary automobile fuel. However, few people in the United States could afford to use their automobiles as they do now if gasoline were as expensive as ethanol. So, if ethanol does replace gasoline, a major change in transportation habits would be bound to occur in the United States.

In the argument given, the two boldfaced portions play which of the following roles?

Macrophages are cells that play a role in the response of the immune system of mice and other mammals to invasive organisms such as bacteria.  Unlike other mice, mice that are genetically incapable of making these particular cells do not show elevated levels of nitrates when infected with bacteria.

The statements above, if true, provide the most support for which of the following conclusions?

Among all the pebbles in a bag, 17% were blue pebbles, 18% were green pebbles, and 31% were red pebbles. The number of green pebbles was increased by 20% and resulted in 216 green pebbles. The count of red pebbles and the count of blue pebbles were also increased by the same number as the increase in the count of green pebbles. To the nearest 0.1%, by what percentage did the combined count of blue, green, and red pebbles increase?