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A particle moves in the X-Y plane under the influence of a force such that its linear momentum is $p (t)=A[i^cos(kt)−j^ sin(kt)]$, where A and k are constants. The angle between the force and the momentum is

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If$α=∫_{0}(e_{9}x+3tan_{(−1)x})(1+x_{2}12+9x_{2} )dxwherηn_{−1}$takes only principal values, then the value of $((g)_{e}∣1+α∣−43π )is$

Let $X$be the set consisting of the first 2018 terms of the arithmetic progression $1,6,11,,¨ $and $Y$be the set consisting of the first 2018 terms of the arithmetic progression $9,16,23,¨$. Then, the number of elements in the set $X∪Y$is _____.

Word of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let $x$be the number of such words where no letter is repeated; and let $y$be the number of such words where exactly one letter is repeated twice and no other letter is repeated. The, $9xy =$

Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length $27 $ on y-axis is (are)

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number in which 5 boys and 5 girls stand in such a way that exactly four girls stand consecutively in the queue. Then the value of $nm $ is ____

The option(s) with the values of a and L that satisfy the following equation is (are) $∫_{0}e_{t}(sin_{6}at+cos_{4}at)dt∫_{0}e_{t}(sin_{6}at+cos_{4}at)dt =L$

Let $n_{1},andn_{2}$, be the number of red and black balls, respectively, in box I. Let $n_{3}andn_{4}$,be the number one red and b of red and black balls, respectively, in box II. A ball is drawn at random from box 1 and transferred to box II. If the probability of drawing a red ball from box I, after this transfer, is $31 $ then the correct option(s) with the possible values of $n_{1}andn_{2}$ , is(are)