Ncert Solutions Maths class 12th
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Let f: (-1, ∞) → R be defined by f(0) = 1 and f(x) = (1/x)log?(1+x), x≠0. Then the function f:
Let f: (-1, ∞) → R be defined by f(0) = 1 and f(x) = (1/x)log?(1+x), x≠0. Then the function f:
f' (x)= (x- (1+x)ln (1+x)/ (x² (1+x). Let h (x)=x- (1+x)ln (1+x).
h' (x)=-ln (1+x). h' (x)>0 for x∈ (-1,0), <0 for x∈ (0, ∞).
h (0)=0, so h (x)≤0. f' (x)≤0. f is decreasing.
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A plane passing through the point (3,1,1) contains two lines whose direction ratios are 1, -2, 2 and 2, 3, -1 respectively. If this plane also passes through the point (α, -3, 5), then α is equal to
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A plane passing through the point (3,1,1) contains two lines whose direction ratios are 1, -2, 2 and 2, 3, -1 respectively. If this plane also passes through the point (α, -3, 5), then α is equal to
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Normal to plane is n= (-4i+5j+7k).
Plane: -4 (x-3)+5 (y-1)+7 (z-1)=0 ⇒ -4x+5y+7z=0.
Passes through (α, -3,5) ⇒ -4α-15+35=0 ⇒ α=5.
Upvote Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is:
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Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is:
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Let B? be the event where Box-I is selected and B? →where box-II selected
P (B? )=P (B? )=1/2
Let E be the event where selected card is non prime.
For B? : Prime numbers: {2,3,5,7,11,13,17,19,23,29}
For B? : Prime numbers: {31,37,41,43,47}
P (E)=P (B? )×P (E/B? )+P (B? )P (E/B? )
= 1/2×20/30+1/2×15/20
Requ
Upvote The plane passing through the points (1,2,1), (2,1,2) and parallel to the line, 2x = 3y, z = 1 also passes through the point:
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The plane passing through the points (1,2,1), (2,1,2) and parallel to the line, 2x = 3y, z = 1 also passes through the point:
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Two points on the line (say) x/3 = y/2, z=1 are (0,0,1) and (3,2,1)
So dr's of the line is (3,2,0)
Line passing through (1,2,1), parallel to L and coplanar with given plane is r = i+2j+k + t (3i+2j), t∈R (-2,0,1) satisfies the line (for t=-1)
⇒ (-2,0,1) lies on given plane.
Answer of the question is (B)
Upvote Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD=8m, BC=11m and AB=10m; then the distance (in meters) of a point M on AB from the point A such that MD²+MC² is minimum is [numerical value].
Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD=8m, BC=11m and AB=10m; then the distance (in meters) of a point M on AB from the point A such that MD²+MC² is minimum is [numerical value].
MD²+MC² is minimum when M is the midpoint of projection of CD on AB.
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