If 6i3i- 143i- 1203i = x + iy, then
x = 3, y = 1
x = 1, y = 3
x = 0, y = 3
x = 0, y = 0
1logbalogab1 is equal to
1
0
logab
logba
If A = 12- 30 and B = - 1023, then
A2 = A
B2 = B
AB ≠ BA
AB = BA
If A = abba and A2 = αββα, then
α = a2 + b2, β = ab
α = a2 + b2, β = 2ab
α = a2 + b2, β = a2 - b2
α = 2ab, β= a2 + b2
If matrix A = 1- 111, then
A' = 111- 1
A- 1 = 11- 11
A . 11- 11 = 2I
λA = λ- λ- 11, where λ is a non- zero scalar
If for AX = B, B = 9520 and A- 1 = 3- 1/2- 1/2- 43/45/42- 1/4- 3/4, then X is equal to
135
- 1/2- 1/22
- 423
33/4- 3/4
If cos-1xa + cos-1yb = αx2a2 - 2xyabcosα + y2b2, then x2a2 - 2xyabcosα + y2b2 is equal to
sin2α
acos2α
atan2α
acot2α
The two curves x3 - 3xy2 + 2 = 0 and 3x2y - y3 - 2 = 0
cut at right angle
touch each other
cut at an angle π3
cut at an angle π4
The domain of the function sin-1log2x22 is
- 2, 2 ~ - 1, 1
- 1, 2 ~ 0
[1,2]
- 2, 2 ~ 0
If the function f(x) = 1 + sinπx2, for - ∞ < x ≤ 1ax + b, for 1 < x < 36tanπx12, for 3 ≤ x < 6 is continuous in the interval (- ∞, 6), then the values of a and b are respectively
0, 2
1, 1
2, 0
2, 1
C.
Given, fx = 1 + sinπx2, for - ∞ < x ≤ 1ax + b, for 1 < x < 36tanπx12, for 3 ≤ x < 6and f(x) is continuous in the mterval (- ∞, 6).Therefore, f(x) will be continuous at x = 1 and at x= 3.For continuity at x = 1 f1 = limx→1fx⇒ 1 + sinπ4 = limx→1ax + b⇒ a + b = 2 ...iFor continuity at x= 3 f3 = limx→3fx⇒ 6tanπ2 = limx→3ax + b⇒ 3a + b = 2 ...iiOn solving Eqs. (i) and (ii), we get
a = 2, b = 0