Maths

If x=1 is a critical point of the function f(x)=(3x²+ax-2-a)eˣ, then

Let $A$ $$ and $$ $B$ be two independent events such that $P\left(A\right)=\frac{1}{3}$ $\frac{}{}$ and $P\left(B\right)=\frac{1}{6}$ $\frac{}{}$ . Then, which of the following is TRUE?

If the mean and standard deviation of the data 3,5,7,a,b are 5 and 2 respectively, then a and b are the roots of the equation:

If $\frac{3+\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{n}\theta }{4-\mathrm{i}\mathrm{c}\mathrm{o}\mathrm{s}\theta },\theta \in \left[\mathrm{0,2}\pi \right]$ , is a real number, then an argument of $\mathrm{s}\mathrm{i}\mathrm{n}?\theta +\mathrm{i}\mathrm{c}\mathrm{o}\mathrm{s}?\theta$  is:

If the line y=mx+c is a common tangent to the hyperbola x²/100 - y²/64 = 1 and the circle x²+y²=36, then which one of the following is true?

Let $\alpha$ and $\beta$ be the roots of the equation $x^2-x-1=0$ . If $P_k=(\alpha {)}^k+(\beta {)}^k,k\ge 1$ , then which one of the following statements is not true?

If the sum of the first 20 terms of the series log₇(₁/₂)x + log₇(₁/₃)x + log₇(₁/₄)x + . is 460, then x is equal to:

Let $a_1,a_2,a_3,\dots \dots$ . be a G.P. such that $a_1<0,a_1+a_2=4$ and $a_3+a_4=16$ . If ${\sum }_{i=1}^9 a_i=4\lambda$ , then $\lambda$ is equal to:

The inverse function of $f\left(x\right)=\frac{8^{2x}-8^{-2x}}{8^{2x}+8^{-2x}},x\in (-\mathrm{1,1})$ $\frac{{}^{}{}^{}}{{}^{}{}^{}}$ , is

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is: