Find the constant term in the binomial expansion of \((2x - \frac{3}{x})^{8}\).
90720
1296
1120
672
Correct answer is A
\((x)^{n}(x^{-1})^{8 - n} = x^{0}\)
\(x^{n} . x^{-8 + n} = x^{0} \implies n - 8 + n = 0\)
\(2n - 8 = 0 \implies n = 4\)
Constant term = \(^{8}C_{4}(2^{4})(3^{4}) = 70 \times 16 \times 81\)
= \(90720\)
(1, -2)
(0, 4)
(2, -3)
(1, -4)
Correct answer is D
Equate the equation of the curve and the line in order to find their point of intersection ie The values of y in both equations.
\(y + x = 1 \implies y = 1 - x\)
\(x^{2} + 2x - 3 = 1 - x\)
\(x^{2} + 2x + x - 3 - 1 = 0 \implies x^{2} + 3x - 4 = 0\)
\((x - 1)(x + 4) = 0\)
\(x = (1, -4)\)
If P(x - 3) + Q(x + 1) = 2x + 3, find the value of (P + Q).
0
1
2
3
Correct answer is C
No explanation has been provided for this answer.
A fair die is tossed twice. Find the probability of obtaining a 3 and a 5.
\(\frac{5}{12}\)
\(\frac{2}{3}\)
\(\frac{1}{18}\)
\(\frac{1}{36}\)
Correct answer is D
P(c and e) = \(P(c) \times P(e)\)
P(3) = \(\frac{1}{6}\)
P(5) = \(\frac{1}{6}\)
P(3 and 5) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}\)
Which of the following is nor a measure of central tendency?
Mean
Variance
Median
Mode
Correct answer is B
Variance is a measure of dispersion not central tendency.