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List IList IIP.Let y(x)=cos(3cos−1x),x∈[−1,1],x≠±√32. Then 1y(x){(x2−1)d2y(x)dx2+xdy(x)dx} equals1.1Q.Let A1,A2,⋯,An(n>2) be the vertices of a regular polygon of n sides with its centre at the origin. Let →ak be the position vector of the point Ak,k=1,2,⋯,n. If ∣∣∣∣n−1∑k=1(→ak×−−→ak+1)∣∣∣∣=∣∣∣∣n−1∑k=1(→ak⋅−−→ak+1)∣∣∣∣, then the minimum value of n is2.2R.If the normal from the point P(h,1) on the ellipse x26+y23=1 is perpendicular to the line x+y=8, then the value of h is3.8S.Number of positive solutions satisfying the equation tan−1(12x+1)+tan−1(14x+1)=tan−1(2x2) is4.9Which of the following option is correct? |
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Answer» List IList IIP.Let y(x)=cos(3cos−1x),x∈[−1,1],x≠±√32. Then 1y(x){(x2−1)d2y(x)dx2+xdy(x)dx} equals1.1Q.Let A1,A2,⋯,An(n>2) be the vertices of a regular polygon of n sides with its centre at the origin. Let →ak be the position vector of the point Ak,k=1,2,⋯,n. If ∣∣ ∣∣n−1∑k=1(→ak×−−→ak+1)∣∣ ∣∣=∣∣ ∣∣n−1∑k=1(→ak⋅−−→ak+1)∣∣ ∣∣, then the minimum value of n is2.2R.If the normal from the point P(h,1) on the ellipse x26+y23=1 is perpendicular to the line x+y=8, then the value of h is3.8S.Number of positive solutions satisfying the equation tan−1(12x+1)+tan−1(14x+1)=tan−1(2x2) is4.9 Which of the following option is correct? |
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