The area bounded by the curve y = x3, x-axis and two ordinates x = 1 to x = 2 is equal to
If x is so small that x3 and higher power of x may be neglected, then [(1+x)3/2 - [1+(1/2)x]3] / [(1-x)1/2] may be approximated as
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Area of the triangle in the Argand diagram formed by the complex numbers z, iz and z + iz is
The solution of differential equation (dy/dx)=[((1+x)y)/((y-1)x)] is
The eccentricity of the ellipse 9x2 + 5y2 - 30y = 0 is
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): is discontinuous for integral values of x.
Reason(R): f(x) is not defined for integral values of x.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): The function f (x) ≡ x5 − 5x3 − 20x + 7 attains its maximum at x = − 1 .
Reason(R) : f ′ (−1) = 0
In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-
Tangents are drawn from the point (17,7) to the circle x2+y2=169.
Statement-1:
The tangents are mutually perpendicular.
Statement-2:
The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x2+y2=338.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): If the 21st and 22nd terms in the expansion of (1+x)44 are equal, then the value of x is 7/8.
Reason(R): In the expansion of (x+y)n, (r+1)th term , Tr+1 = nCr+1xn-r+1 yr+1.
The number of solutions of 2x + y = 4, x - 2 y = 2, 3x + 5y = 6 is