Jeopardy

Calculus

100

Differentiate f(x)=3x³+5x²-7x+4

f(x)=9x²+10x-7

200

If y=x²e^x, find dy/dx

e^x(x²+2x)

300

Find int (3x²+2x)e^x dx

e^x(3x²-4x+4)+C

400

Evaluate int (0,1) [x²/(x²+1)²] dx

(1/4)+(pi/4)

500

If y=e^x sin x, find d³y/dy³

y'''=2e^x(cos x - sin x)

Probability

100

A fair die is rolled. Find P(0)

0

200

Two dice are rolled. Find probability that the sum is less than 7

15/36 (or) 5/12

300

An unbiased coin is tossed 4 times. Find P(exactly 2 heads)

6/16 (or) 3/8

400

Find mean and variance for a binomial distribution with n=5, p=0.3

Mean = 1.5

Variance = -1.05

500

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

Linear Algebra

100

Find det[[2,3],[1,4]].

5

200

For A = [[1,5,10],[0,11,4],[5,6,13]], find det(A).

-331

300

If A = [[1,2],[3,4]], find A⁻¹.

[[-2,1],[3/2,-1/2]]

400

Solve for x: det[[x,1,1],[1,x,1],[1,1,x]] = 0

x= 2,1,-1

500

If A = [[1,2,3],[2,5,7],[3,7,10]], find the rank of A.

rank(A)=2

Vector Algebra

100

Find the magnitude of a⃗ = 3î + 4ĵ.

₅

200

Find angle between a⃗ = 2î + 3ĵ and b⃗ = 3î + 2ĵ.

cos^-1(10/13)

300

If a⃗ = î + ĵ + k̂, b⃗ = 2î - ĵ + 3k̂, find a⃗ × b⃗.

4i-j-3k

400

Find the scalar projection of a⃗ = 2î - ĵ + 2k̂ on b⃗ = î + 2ĵ - 2k̂.

-4/3

500

a = 2i+3j-k, b=i-2j+2k, c=i+j+k

Find (a×b).c

-8

Trigonometry & Limits

100

Evaluate lim(x→0) sin x / x

1

200

Express sin2A in terms of tanA

2 tanA/(1+ tan²A)

300

Express sin^-1x in terms of cot^-1x

Cot^-1(√(1-x²) /x)

400

Evaluate lim(x→0) (1 - cos 2x)/x².

2

500

Find lim(x→0) (tan x - x)/x³.

1/3