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
D.
Let A = abcbcacabApply C1 → C1 + C2 + C3= a + b + cbca + b + ccaa + b + cab= a + b + c1bc1ca1abApply R2 → R2 - R1 and R3 → R3 - R1= a + b + c1bc0c - ba - c0a - bb - c= a + b + cc - bb - c - a - ca - b= a + b + cbc - b2 - c2 + bc - a2 + ab + ac - bc= - a + b + ca2 + b2 + c2 - ab - bc - ca= - 12a +b + ca - b2 + b - c2 + c - a2Since a, b, c are distinct positive numbers∴ The value of determinant A is less than 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