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If the line lx+my=1 is a tangent line to the circle x^{2}+y^{2}=a2, the locus of (l,m) is
The coefficients of three successive terms in the expansion of (1 + x)^{n} are 165, 330 and 462 respectively, then the value of n will be
If x is positive, then the first negative terms in the expansion of 1 + x 27 5 is
If w is a cube root of unity, then the value of (1 + ω  ω)^{2} (1  ω + ω^{2}) is
The area bounded by the parabola y^{2}=4ax and the straight line y=2ax is
The particular integral of (D^{2} + 1)y = xe^{2x} is equal to
If the normal at the point P(θ) to the ellipse ((x^{2}/14)+(y^{2}/5) = 1) intersects it again at the point Q(2θ), then cosθ is equal to
The parametric equations of the hyperbola x^{2}/a^{2}  y^{2}/b^{2} = 1 are
A box contains n enumerated articles. All the articles are taken out one by one at random. The probability that the numbers of the selected articles are in the sequence 1, 2, .........n is
An unbiased coin is tossed to get 2 points for turning up a head and one point for the tail. If three unbiased coins are tossed simultaneously, then the probability of getting a total of odd number of points is
Two dice are thrown simultaneously. The probability of getting a pair of 1 is
In Δ A B C , i f b = 20 , c = 21 and sin A = 3 5 , then a =
In a Δ A B C , 2s = perimeter and R = circumradius. Then s/R is equal to
the greatest value of a nonnegative real number λ for which both the equations 2x^{2} + (λ  1)x + 8 = 0 and x2  8x + λ + 4 = 0 have real roots is :
The set of values of p for which the roots of the equation 3x^{2} + 2x + (p  1)p = 0 are of opposite sign, is
The second drivative f"(x) of the function f(x) exists for all x in [0,1] and satisfies  f ″ x  ≤ 1. If f 0 = f 1 , then for all x in [0,1]
The fourth, seventh and tenth terms of a G.P. are p, q and r respectively, then
If A.M. between two numbers is 5 and their G.M. is 4, then their H.M. is
The mean of the numbers a,b,8,5,10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?
A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. The maximum possible volume of the box is given by (in cm^{2})
Let a,b,c be any real numbers. Suppose that there are real numbers x,y,z not all zero such that x=cy+bz, y=az+cx and z=bx+ay. Then a^{2}+b^{2}+c^{2}+2abc is equal to
On the interval [0, 1] the function
f x = x ^{1005} (1 − x )^{1002 }
assumes maximum value equal to
∗
is a binary operation defined on Q. Find which of the following operation is Associative.
In a triangle X Y Z , ∠ Z = π 2 . If tan X 2 and tan Y 2 are the roots of the equation ax^{2} + bx + c = 0, a ≠ 0 then
Given the family of lines, a (3x + 4y +6) + b (x + y +2) = 0. The line of the family situated at the greatest distance from the point P(2, 3) has equation
Let P(3, 2, 6) be a point in space and Q be a point on the line
Then the value of μ for which the vector P Q → is parallel to the plane x  4y+3z = 1 is
The differential equation (x^{4} − 2 x y^{2} + y^{4} ) d x − 2x^{2} y − 4xy^{3} + sin y) dy = 0 has its solution as
If the function f(x) and g(x) are defined on R → R such that
The area bounded by the curves f (x) = sin − 1 (sin x) and (gx) = [ sin − 1 sin x ] in the interval [ 0 , π ] , where [ . ] is a greatest integer function, is
The cubes of natural number are grouped as 1 ^{3} , 2 ^{3 } , 3^{ }^{3} , 4 ^{3} , 5^{ }^{3} , 6 ^{3} ,...Let S_{n} denotes the sum of cubes in the n^{th} group, then 8S_{n} is divisible by
The solution of the equation cos ^{103} x − sin ^{103} x = 1 are
The point (0,0), (a, 11) and (b, 37) are the vertices of an equilateral triangle. Then
For three vectors u → , v → , w → which of the following expression is not equal to any of the remaining three?
If a → = i^{‸} + j ‸ + k ‸ , b → = 4 i ‸ + 3 j ‸ + 4 k ‸ and c → = i ‸ + α j ‸ + β k ‸ are linearly dependent vectors and  c  = 3 , then
3 videos10 docs54 tests

3 videos10 docs54 tests
