Calculus
Differentiate f(x)=3x³+5x²-7x+4
f(x)=9x²+10x-7
A fair die is rolled. Find P(0)
0
Find det[[2,3],[1,4]].
5
Find the magnitude of a⃗ = 3î + 4ĵ.
5
Evaluate lim(x→0) sin x / x
1
If y=x²ex, find dy/dx
ex(x²+2x)
Two dice are rolled. Find probability that the sum is less than 7
15/36 (or) 5/12
For A = [[1,5,10],[0,11,4],[5,6,13]], find det(A).
-331
Find angle between a⃗ = 2î + 3ĵ and b⃗ = 3î + 2ĵ.
cos-1(10/13)
Express sin2A in terms of tanA
2 tanA/(1+ tan²A)
Find int (3x²+2x)ex dx
ex(3x²-4x+4)+C
An unbiased coin is tossed 4 times. Find P(exactly 2 heads)
6/16 (or) 3/8
If A = [[1,2],[3,4]], find A⁻¹.
[[-2,1],[3/2,-1/2]]
If a⃗ = î + ĵ + k̂, b⃗ = 2î - ĵ + 3k̂, find a⃗ × b⃗.
4i-j-3k
Express sin-1x in terms of cot-1x
Cot-1(√(1-x²) /x)
Evaluate int (0,1) [x²/(x²+1)²] dx
(1/4)+(pi/4)
Find mean and variance for a binomial distribution with n=5, p=0.3
Mean = 1.5
Variance = -1.05
Solve for x: det[[x,1,1],[1,x,1],[1,1,x]] = 0
x= 2,1,-1
Find the scalar projection of a⃗ = 2î - ĵ + 2k̂ on b⃗ = î + 2ĵ - 2k̂.
-4/3
Evaluate lim(x→0) (1 - cos 2x)/x².
2
If y=ex sin x, find d³y/dy³
y'''=2ex(cos x - sin x)
A bag has 4 red, 6 blue and 5 green balls. Three balls are drawn without replacement. Find P(one red ball along with 2 other balls).
220/455 (or) 44/91
If A = [[1,2,3],[2,5,7],[3,7,10]], find the rank of A.
rank(A)=2
a = 2i+3j-k, b=i-2j+2k, c=i+j+k
Find (a×b).c
-8
Find lim(x→0) (tan x - x)/x³.
1/3