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x^{2} + y^{2 }+ 2(2K+3)x  2Ky +(2K+3)^{2} + K^{2}  r^{2} = 0 represents the family of circles with centres on the line
If the equation [(k(x+1)^{2/}3)]+[(y+2)^{2}/4]=1 represents a circle, then k=
Let (1 + x)^{n} =
C_{0} + C_{1}x + C_{2}x^{2} + ... + C_{n}x^{n} and (C_{1}/C_{0}) + (2 C_{2}/C_{1}) + (3 C_{3}/C_{2}) + .... + ((n C_{n})/(C_{n}  1)) = (1/k)n(n + 1), then the value of k is
Solution of the differential equation tan y sec^{2} x dx + tan x sec^{2} y dy = 0 is
The latus rectum of the conic 3x^{2} + 4y^{2}  6x + 8y  5 = 0 is
If the length of the major axis of an ellipse is three times the length of its minor axis, then it's eccentricity is
The maximum area of the rectangle that can be inscribed in a circle of radius r is
The equation of the normal to the curve x^{2} = 4y at (1, 2) is
The length of the latus rectum of the parabola x^{2}4x8y+12=0 is
Four numbers are chosen at random from {1, 2, 3, . . . , 40}. The probability that they are not consecutive is
A purse contains 4 copper coins and 3 silver coins, the second purse contains 6 copper coins and 2 silver coins. A coin is taken out from any purse. The probability that it is a copper coin is
If two equations x^{2}+a^{2}=12ax and x^{2}+b^{2}=12bx have only one common root, then
If 2a + 3b + 6c = 0, then at least one root of the equation ax^{2}+bx+c = 0 lies in the interval
The fourth ,seventh and tenth of a G.P. are p,q,r respectively then
The equation of lines passing through the intersection of 4x3y1=0 and 2x5y+3=0 which are equally inclined with axes, are
If α , β are different values of x satisfying a cos x + b sin x = c then tan (α + β) /2 =
In how many different ways can the letters of the word DETAIL be arranged in such a way that the vowels occupy only the odd positions?
Let d _{1} , d _{2} , d _{3} , … …, d k be all the divisors of a positive integer n including 1 and n.
Suppose d _{1} + d_{ 2} + d _{3} + … … + d k = 72 , then the
value of 1 d _{1} + 1 d_{ 2} + 1 d _{3} + … … + 1 d k is
Statement1: For every natural number
Statement2: For every natural number
Let be two unit vectors and α the angle between them. Vector → will be a unit vector is α is equal to
The quadratic equations x^{2}6x+a=0 and x^{2}cx+6=0 have one root in common. The other roots of the first and second equations are integers in the ratio 4:3. Then the common root is
Given P x = x ^{4} + a x^{ 3} + b x^{ 2} + c x + d such that x=0 is the only real root of P ′ x = 0. If P − 1 < P 1 , then in the interval [1, 1]:
The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1,2 and 3 only, is
For which of the values of m the area of the region bounded by the curve y = x − x^{2} and y = mx equal 9 2 .
Let a, b, c, d be real numbers such that
(a ^{2} + b^{ 2} − 1 )(c^{ 2} + d^{ 2} − 1 )> (a c + b d − 1 )^{2}
then which of the following statements is correct?
Let [x] = the greatest integer less than or equal to x. Then equation sinx = [1+sin x] +[1cos x] has
Let a 1, a 2, a 3, … … , a n n > 2 be real numbers such that a i = − a _{n − i + 1} for 1 ≤ i ≤ n and k = ∑ 1 ≤ i < j < k ≤ n ∑ ∑ ^{x i x j x k} , then which of the following is not true?
The solutions of are given by (where p = dy/dx and k is constant)
If A = [ α β 0 α ] is the n^{th} root of I_{2}, then choose the correct statement
3 videos10 docs54 tests

3 videos10 docs54 tests
