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Let a1, a2, a3................... be in A.P. And q1, q2, q3................ be in G.P, such that a1=q1=2 and a10=q10=3 then:
aa1q19 Is not an integer
ba19q7 Is an integer
ca7a18=a19q10
d None

Answer
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Hint – In this question first calculate the common difference and common ratio of A.P and G.P respectively using the formula of nth term of an A.P and G.P later on using these values calculate all the given terms so, use these concepts to reach the solution of the question.

Complete step-by-step solution -
As you know the general formula of an A.P is an=a1+(n1)d and the general formula of G.P is qn=q1rn1 where a1 and q1be the first term of A.P and G.P respectively, while, d and r are the common difference and common ratio respectively.
It is given that a10=q10=3
an=a1+(n1)da10=a1+(101)d=a1+9d=3qn=q1rn1q10=q1r101=q1r9=3
Now it is also give that a1=q1=2
a1+9d=32+9d=3d=19q1r9=32r9=3r9=32
Now from A.P general equation an=a1+(n1)d, the value of
a19=a1+(191)da19=a1+18d=2+18×19=4a7=a1+(71)da7=a1+6d=2+6×19=83a18=a1+(181)da18=a1+17d=2+17×19=359
Now from G.P general equation qn=q1rn1, the value of
q19=q1r191q19=q1r18=2(r9)2=2(32)2=92q7=q1r71q7=q1r6r9=32r=(32)19r6=(32)69q7=2(32)69=2(32)23
Now check out option (a) which is a1q19
a1q19=2×92=9
Which is an integer so option (a) is ruled out.
Now check out option (b) which is a19q7
a19q7=4×2(32)23=8(32)23
Which is not an integer so option (b) is also ruled out.
Now check out option (c) which is a7a18=a19q10
a7a18=a19q1083(359)=4(3)
Which is also not true
Hence, option (d) is correct none of these.

Note: - In such types of question the key concept we have to remember is that always remember the general formulas of A.P and G.P, then according to given conditions calculate the values of common difference and common ratio, then calculate the terms which is given in options, then check out every option we will get the required answer.