List of top Mathematics Questions

Which of the following can not be a valid assignment of probabilities for outcomes of sample Space \(S =\{ω_1, ω_2 , ω_3,  ω_4,  ω_5,  ω_6,  ω_7\}\)

Solve the given inequality for real x: \(x+\frac x2+\frac x3<11\).
Solve the given inequality for real x: 3(x – 1) ≤ 2 (x – 3)
Solve the given inequality for real x: 4x+3 < 5x+7
Let \(f={(x,\frac {x^2}{1+x^2}):x∈R}\)  be a function from R into R. Determine the range of f.
Let A, B and C be the sets such that \(A ∪ B = A ∪ C\) and \(A ∩ B = A ∩ C\). show that B = C.
The relation f is defined by

\(f(x) =   \begin{cases}     x^2,       & \quad  0≤x≤3\\     3x,  & \quad  3≤x≤10 \end{cases}\)
The relation g is defined by
\(g(x) =   \begin{cases}     x^2,       & \quad  0≤x≤2\\     3x,  & \quad  2≤x≤10 \end{cases}\)
Show that f is a function and g is not a function.

Find the real numbers x and y if (x-iy) (3+5i) is the conjugate of -6-24i.
Write the following intervals in set-builder form:
(i) (-3, 0)
(ii) [6, 12]
(iii) (6, 12]
(iv) [-23, 5)
The hypotenuse of a right-angled triangle has its ends at the points (1, 3) and (-4, 1). Find the equation of the legs (perpendicular sides) of the triangle.
Find the sum to n terms of the sequence, 8, 88, 888, 8888… .

Show that the function given by \(f(x)=e^{2x}\) is strictly increasing on R.

\(Find\) \(\frac {dy}{dx}\): \(2x+3y=sin \ y\)

Show that the points (–2, 3, 5), (1, 2, 3) and (7, 0, –1) are collinear.

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?

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: \(\frac{1-cosx}{1+cosx}\)