List of practice Questions

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola \( \dfrac{x^2}{16}-\dfrac{y^2}{9}=2\)

Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?
How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
Which of the following is the correct method of preparation of methyl fluoride?

Find the equation for the ellipse that satisfies the given conditions: Vertices \((±5,0),\)foci (±4,0)

Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity, and the length of the latus rectum of the ellipse \(16x^2+y^2=17\)

Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for \(y^2 = - 8x\)

Find the integrals of the function: \(sin^4 x\)
Find the integrals of the function: \(\frac{cos x}{1+cos x}\)
Find the integrals of the function: \(\frac{1-cosx}{1+cosx}\)
Find the integrals of the function: \(sin\, 4x\,\, sin\, 8x\)
Find the integrals of the function: \(sin\, x\,\, sin\, 2x\,\, sin\, 3x\)
Find the integrals of the function: \(sin^3 x\, cos^3 x\)
Find the integrals of the function: \(sin^2 (2x + 5)\)
Integrate the function: \(\frac{x^3 \sin(\tan^{-1}x^4)}{1+x^8}\)
Integrate the function: \(\frac{(x+1)(x+log x)^2}{x}\)
Integrate the function: \(\frac{(1+\log x)^2}{x}\)
Integrate the function: \(\frac{\sqrt {\tan x}}{\sin x \cos x}\)
Integrate the function: \(\frac {1}{1-tan \ x}\)
Integrate the function: \(\frac {1}{1+cot \ x}\)
Integrate the function: \(\frac {sin \ x}{(1+cos\  x)^2}\)
Integrate the function: \(\frac {sin\  x}{1+ cos \ x}\)
Integrate the function: \(\frac {cos \ x}{\sqrt {1+ sin \ x}}\)