Suppose f(x) = x(x + 3)(x - 2), x ∈ [- 1, 4]. Then, a value of c in (- 1, 4) satisfying f'(c) = 10 is
2
52
3
72
The area included between the parabola y = x24a and the curve y = 8a3x2 + 4a2 is
a22π + 23
a22π - 83
a2π + 43
a22π - 43
If a, b, c are distinct positive real numbers, then the value of the determinant abcbcacab is
< 0
> 0
0
≥ 0
The equations x - y + 2z = 43x + y + 4z = 6x + y + z = 1 have
unique solution
infinitely many solutions
no solution
two solutions
If x =sin2tan-12 and y = sin12tan-143, then
x > y
x = y
x = 0 = y
x< y
If coshx = 54, then cosh3x = ?
6116
6316
6516
6163
In a∆ABC, if <A = 90°, then cos-1Rr2 + r3 = ?
90°
30°
60°
45°
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
all real numbers
B.
We have,fx = 1 - x, x < 11 - x2 - x, 1 ≤ x ≤ 23 - x, x > 2∵ By defination of continuitylimx→1-fx = limx→1+fx = f1⇒ limx→1-1 - x = limx→1+1- x(2 - x)= (1 - 1)(2 - 1) = 0∴ f(x) is continuous at x = 1Now, limx→2-fx = limx→2+fx = f2⇒limx→2-1 - x2 - x = limx→2+3 - x= 1 - 22 - 2⇒ 1 - 22 - 2 = 3 - 2 = 0⇒ 0 ≠ 1 ≠ 0 ∴ f(x) is discontinuous at x = 2Hence, fx is con tineous for all real numbers except 2
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