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ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x
and AC = 2y, express the vectors (i) BC, (ii) PQ, (iii) PC, (iv) BQ in terms of x
and y. What can you deduce about the directed line-segments BC and PQ?
Given: x = 1 – cost and y = t – sint. Find y’.
Given: x = tan4t and y = sec4t. Find y’.
Let the proposition p be T and proposition q be F. Find the truth value of the following
a. p^›q
A pair of dice is loaded. The probability that a 4 appears on the first die is 2/7, and the
probability that a 3 appears on the second die is 2/7. Other outcomes for each die appear
with probability 1/7. What is the probability of 7 appearing as the sum of the numbers
when the two dice are rolled?
For which value of k will the vector v1=(1, −2, k) in R
3
be a linear combination of
v2 = (3, 0, −2) and v2= (2, −1, 5)?
Suppose three cellphones are tested at random.let D represent the defective cell phone and N represent the non defective cellphone.if we let X be the random variable for the number of defective cellphones,construct the probability distribution of the random variable X
Let f : G → G0 be a group epimorphism, and let H be the normal subgroup that be the Kernal of the epimorphism. Then, prove that G0 is isomorphic to G/H.
Make a study about how many sheets of paper you consumed weekly in answering
your Self Learning Modules. Record the quantity (total number of sheets) per subject, then
construct a probability distribution. Compute the mean, variance, and the standard deviation
of the probability distribution you made. Interpret the result, then find out how many weeks
you will consume 50 sheets of pad paper.
A girl is 9 years old. Her brother is 4 years older. Their mother is 4 times older than her brother. Their father is years older than the mother. How old is the father?
