If R denotes the set of all real numbers, then the function f : R → R defined f(x) = x is :
one-one only
onto only
both one-one and onto
neither one-one nor onto
a . i^i^ + a . j^j^ + a . k^k^ is equal to
a
2a
3a
0
If a = 3, b = 4, then a value of λ for which a + λb is perpendicular to a - λb is
916
34
32
43
The projection of a = 2i^ + 3j^ - 2k^ on b = i^ + 2j^ + 3k^ is
114
214
14
- 214
The general solution of the differential equation dydx + 1 + cos2y1 - cos2y = 0 is given by
tany + cotx = c
tany - cotx = c
tanx - coty = c
tanx + coty = c
The degree of the differential equation 1 + dydx234 = d2ydx213 is
2
4
9
1
The area enclosed between the curves y = x3 and y = x is, (in square units)
53
54
512
125
∫0π8cos34θdθ is equal to
13
16
∫0π2cosx - sinx1 + cosx sinx dx is equal to
π2
π4
π6
∫dxxx7 + 1 is equal to
logx7x7 + 1 + c
17logx7x7 + 1 + c
logx7 + 1x7 + c
17logx7 + 1x7 + c
B.
Given that, ∫dxxx7 + 1On putting x7 = t⇒7x6dx = dt⇒ dx = 17x6dt∴ I = ∫17x7dtt + 1 = 17∫1tdtt + 1 ∵ x7 = t = 17∫1t - 1t + 1 = 17logtt + 1 + c = 17logx7x7 + 1 + c