If ddxx + 1x2 + 1x4 + 1x8 + 1= 15xp - 16xq + 1x - 1 - 2, then p, q = ?
(12, 11)
(15, 14)
(16, 14)
(16, 15)
limx→01 + x2 - 1 - x + x23x - 1 = ?
1loge3
loge9
1loge9
loge3
If y = tan-11 + a2x2 - 1ax, then 1 + a2x2y'' + 2a2y' = ?
- 2a2
a2
2a2
0
If x2 + y2 = t + 1t and x4 + y4 = t2 + 1t2, then dydx = ?
-xy
-yx
x2y2
y2x2
If x = at2 and y = 2at, then d2ydx2 at t = 12 is
- 2a
4a
8a
- 4a
The equations x - y + 2z = 43x + y + 4z = 6x + y + z = 1 have
unique solution
infinitely many solutions
no solution
two solutions
B.
We have, x - y + 2z = 43x + y + 4z = 6x + y + z = 1Let D = 1 - 12314111= 11 - 4 + 13 - 4 + 23 - 1= - 3 - 1 + 4 = 0and Dx = 4 - 12614111= 41 - 4 + 16 - 4 + 26 - 1= - 12 + 2 + 10 = 0Now, D = 0 and Dx = 0∴ These equations have infinitely many solutions.
The value (s) of x for which the function
f(x) = 1 - x, x < 1=1 - x2 - x, 1 ≤ x ≤ 23 - x, x > 2fails to be continuous is (are)
1
2
3
all real numbers
If y = log2log2x, then dydx = ?
loge2xlogex
1loge2xx
1xlogexloge2
1xlog2x2
The angle of intersection between the curves y2 + x2 = a22 and x2 - y2 = a2 is
π3
π4
π6
π12
If the function fx = k1x - π2, x ≤ πk2cosx, x > π is twice differentiable, then the ordered pair (k1, k2) is equal to
12, - 1
12, 1
(1, 0)
(1, 1)