Condition for Coplanarity of Four Points
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Q. List IList II (I)The value of limn→∞3√n2⋅sin(n!)n+1 is (P) −1 (II)If x∈[0, 2π] and log2tanx+log2tan2x=0, then the number of solutions is (Q) 0(III)An unbaised dice is thrown and the numberappear is put in the place of ′p′ in equationx2+px+2=0. If the probability of theequation having real roots is ab, (a, b∈N)then the least possible value of (a+b) is (R) 1(IV)Three lines through origin having directionratios (1, a, a2);(1, b, b2);(1, c, c2) are non-coplanar. But the lines with direction ratios(a, a2, 1+a3);(b, b2, 1+b3);(c, c2, 1+c3) arecoplanar, then the value of ′abc′ is (S) 2(T) 4(U) 5
Which of the following option is CORRECT ?
Which of the following option is CORRECT ?
- (I)→(R)
- (II)→(U)
- (III)→(T)
- (IV)→(P)
Q. Let S be the set of all real values of λ such that plane passing through the points (−λ2, 1, 1), (1, −λ2, 1) and (1, 1, −λ2) also passes through the point (−1, −1, 1). Then S is equal to :
- {√3}
- {1, −1}
- {3, −3}
- {√3, −√3}