Schemes 1 and 2 describe sequential transformation of alkynes M and N. Consider only the major products formed in each step for both the schemes.
The correct statement with respect to product Y is
Word of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let xbe the number of such words where no letter is repeated; and let ybe the number of such words where exactly one letter is repeated twice and no other letter is repeated. The, 9xy=
Consider the circle x2+y2=9 and the parabola y2=8x. They intersect at P and Q in first and 4th quadrant,respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S.
Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 27 on y-axis is (are)
Let f[0,1]→R (the set of all real numbers be a function.Suppose the function f is twice differentiable, f(0)=f(1)=0,and satisfies f′(x)–2f′(x)+f(x)≤ex,x∈[0,1].Which of the following is true for 0<x<1?
Let f:[21,1]→R (the set of all real numbers) be a positive, non-constant, and differentiable function such that fprime(x)<2f(x)andf(21)=1 . Then the value of ∫211f(x)dx lies in the interval (a)(2e−1,2e) (b) (3−1,2e−1)(c)(2e−1,e−1) (d) (0,2e−1)
In a triangle the sum of two sides is x and the product of the same is y. If x2−c2=y where c is the third side. Determine the ration of the in-radius and circum-radius
Let [x] be the greatest integer less than or equal to x˙ Then, at which of the following point (s) function f(x)=xcos(π(x+[x])) is discontinuous? (a)x=1 (b) x=−1 (c) x=0 (d) x=2