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1. The limit is given by lim⁡x→0e2x−1x\lim_{x \to 0} \frac{e^{2x} - 1}{x}.
2. If f(x)= 3 - |sinx|, then f(x) is
3. limit x tends to 0 |x|/x
4. If f(x)=mx+cf(x) = mx+c and f(0)=f−1(0)=1f(0) = f^{-1}(0) = 1, what is the value of f(2)f(2)?
5. If x=a(1−cos⁡t)x = a(1 - \cos t) and y=a(t−sin⁡t)y = a(t - \sin t), then dydx=?\frac{dy}{dx} = ?
6. if z = (1+i), then the multiplicative inverse of z2z^2 =
7. The cube roots of -1 are
8. If both roots of the equation x2+bx+c=0x^2 + bx + c = 0 and the equation x2+dx+e=0x^2 + dx + e = 0 are common, then
9. A number exceeds its positive square root by 12. Then, the number is
10. Sum of an infinite G.P. is 5/4 times the sum of all odd terms. THe common raio is
11. How many 6 different digits telephone numbers can be formed from the integers 0,1,2 ---9, by using the integers at once, which begins with 35?
12. The Letters of the word "CALCUTTA" and "AMERICA" are arranged in all possible ways . The ratio of the number of arrangement is
13. The value of C(5,3)+C(5,2)=
14. The number of vectors of unit length perpendicular to the line joining A(1,1,0) and B(0,1,1) and passing through a point is
15. The projection of AB on CD if A(4,-3,2), B(1,-1,-1), C(2,2,2) and D(3,3,3)
16. The extremities of a diagonal of the parallelogram are the points (3,-4) and (-6,5). if the third vertex is the point (-2,1), then the coordinates of fourthe vertex are
17. if the points (2,3) and (-6,-5) are equidistant from the point (x,y) then
18. If the sum of the slopes of the lines x2+kxy−3y2=0x^2+kxy-3y^2=0 is twice the product of the slopes then k =
19. The locus of the middle points of chords of the circle x2+y2−2x−6y−10=0x^2+y^2-2x-6y-10=0 which passes through the origin is
20. The graph represented by the queation x=sin^2t and y=2cost is
21. The equation xy=0 in three dimensional space represents
22. if a=16,b=24,c=20, then cos(B/2)=
23. if 4sin⁡−1x+cos⁡−1x=π 4\sin^{-1}x + \cos^{-1}x = \pi , then the value of x is
24. The length of a minute pointer of a watch is 15cm. THe distance travelled by a pointer is 40min is
25. The period of cos3x is
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