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
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
B.
Given, y2 + x2 = a22 ...iand x2 - y2 = a2 ...iiOn solving eqs i and ii, we getx = a2 + 12, y = a2 - 12Now, y2 + x2 = a222ydydx1 + 2x = 0 ⇒ dydx1 = - xy∴ dydx1 = - a2 + 12 a2 - 12= - 2 + 12 - 1and x2 - y2 = a2On differentiating
dydx2 = xy = 2 + 12 - 1Then, tanθ = dydx1 - dydx21 + dydx1 dydx2= - 2 + 12 - 1 - 2 + 12 - 11 + - 2 + 12 - 1 2 + 12 - 1 = - 22 + 12 - 11 - 2 + 12 - 1= - 22 + 12 - 12 - 1 - 2 - 1= - 22 - 1 - 2 = 1∴θ = tan-11 = π4