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The maximum coefficients in the expansion of (1+x)^{(2n+2)} is :
The angle between the tangents drawn from (0,0) to the circle x^{2} + y^{2} + 4x  6y + 4 = 0 is
The solution of the equation cosylog(secx+tanx)dx=cosxlog(secy+tany)dy is
The equation of the ellipse whose focus is at (4, 0) and whose eccentricity is 4/5 is
The line p = x cos α + y sin α. becomes tangent to x^{2}/a^{2}  y^{2}/b^{2} = 1 is
If cot⁻^{1}[(cos α)^{1}∕^{2}]  tan⁻^{1}[(cot α)^{1}∕^{2}] = x, then sin x =
If the equation x  sin x = k has a unique root in , , then the range of values of k are
The equation of the parabola whose focus is the point (0,0) and the tangent at the vertex is xy+1=0 is
Out of 15 students studying in a class, 7 are from Maharashtra, 5 are from karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karantaka?
From a box containing 10 cards, numbered 1, 2,3,......,10. Four cards are drawn together, what is the probability of their sum is even ?
A and B play 12 games of chess of which 6 are won by A. 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately is,
If b,c and sinB are given such that ∠B is acute and b<c sinB, then
For what value of p, the difference of the roots of the equation x^{2}  px + 8 = 0 is 2 ?
Let α and β be the roots of the equation x^{2}+x+1=0, then the equation whose roots are α^{19},β^{7} is
If f : R → R is continuous and differentiable function such that
Then, value of f'(4) is
if A, G and H are respectively the A.M., the G.M and the H.M. between two positive numbers 'a' and 'b', then the correct relationship is
If x, y, z are positive real numbers, then (x^{3}/z) < (x^{3} + y^{3} + z^{3})/(x + y + z) < (z^{3}/x) if
If A = {x : x^{2 } 5x + 6 = 0}, B = {2, 4}, C = {4, 5} then A x (B ∩ C) is
The condition for the roots of the equation (c^{2}ab)x^{2}2(a^{2}bc)x+(b^{2}ac)=d are equal, is
The equation of the curves for which the tangent is of constant length, is
The remainder left out when 8^{2n} − (62)^{2n }+ 1 is divided by 9 is:
Let f x be an odd function in the interval with a period T, then is
If f x = x^{5} − 20^{x3} + 240 x , then f x satisfies which of the following?
If , then value of x, y, z are respectively (where m , n , r ∈ I )
The area of the region bounded by the parabola (y − 2 )^{2} = x − 1 , the tangent to the parabola at the point (2, 3) and the xaxis is:
The direction ratios of two lines are a, b, c and . The lines are
The number of functions f from the set A = {0, 1, 2} in to the set B = {0, 1, 2, 3, 4, 5, 6, 7} such that f(i) ≤ f(j) for i < j and i, j ∈ A is
A fair coin is tossed 9 times the probability that at least 5 consecutive heads occurs is
Let f(x) is a quadratic expression with positive integral coefficients such that for every
Let d has local extrema at x = α and β such that α , β < 0, f α , f β > 0 ; Then the equation f(x)=0
The equation x^{2 } − 6 x + 8 + λ (x^{2} − 4 x + 3) = 0 , λ ∈ R has
3 videos10 docs54 tests

3 videos10 docs54 tests
