Objective Questions

The maximum or minimum value of a quadratic function y = ax² + bx + c occurs at:

For the quadratic y = x² - 4x + 5, the vertex is at:

The value of sin 150-5cos300+7 tan 225 --- tan 135+3sin 210 is

Given that z₁ = i and z₂ = 1-i. Find z₁/z₂

If p and q are integers and is represented in the form of p/q, then it is a:

For principle of mathematical induction to be true, what type of number should …

In how many ways can three objects be selected out of five distinct objects?

For some integer n, the odd integer is represented in the form of:

Find the coefficient of x^4 in the binomial expansion of (1 - 2x)^6

Which of the following is a necessary step for proving 1+3+5+...+(2n-1) = n²?

If θ is said to be an acute angle, and 4cosθ - 1 = 0, then what …

Find the sixth root of 64.

Find the equation of the circle which passes through the points (4,1) and (6,5)…

Simplify (9x²+6x-3)/(9x²-9)

In a class of 34 students, 24 are good in English while 15 are good in Mathemat…

What is the sum of the coefficients in the binomial expansion of (x-y)^n?

Find the equation of the normal to the circle x² + y² + 3x - 2y = 0 at the poin…

Simplify (2-i)³ - (2+i)³

Use the principle of mathematical induction to determine for which value of k t…

Out of 400 students in a International school UNILAG, 300 are offering Biology …

Find the coefficient of \(x^{-12}\) in \((x^3 - 1/x)^{24}\).

Expand: \(\sin 3\theta\)

In a survey of 290 newspapers readers, 181 read Daily Times, 142 read Guardian,…

If \(7^n - 1\) is divisible by 6, what proves induction?

The modulus and argument of \(\sqrt{3} + \sqrt{2}i\) are

The subsets P and Q of the universal set U are defined as follows: U = {x: 30 ≤…

Which of the following best describes the De Moivre's theorem of complex number…

Polar form of \(z = 4 + 4\sqrt{3}i\) is

What is the coefficient of the 3rd term in the expansion of \((3 - x)^{-3}\)?

Which of the following is not an irrational number?

In the expansion of \((x^2 - \frac{1}{x})^{12}\), the term without x is equal to

Find an expression in terms of n for the coefficient of x in \((1+4x) + (1+4x)^…

Which of the following is true about these numbers (-5, -4, -3, -2, -1)?

If \(\alpha + \beta = 90^\circ\) and \(\alpha : \beta = 2:1\), then what is the…

Obtain the modulus of the complex number (3 - 5i)(2 + i).

a + ib form of the complex number 1 + (2i)(-2 + i) is

The sum \(1^3 + 2^3 + 3^3 + \ldots + n^3\) gives

Express \(\frac{2+5i}{i} + \frac{2}{4-i}\) in the rectangular form a + ib.

Which of the following is the principal square root of 25?

If tan(t) = 13, then cot(π/4 - t) = ?

If set A = {1, 2, 3, 4, 5, ...} is given, then it represents:

Find the coefficient of x⁶y⁶ in the binomial expansion of (2x² - y²)⁶

Find the coefficient of x^3 in the expansion of (1 + 2x)^5

Evaluate (sin30°/cos30°) + (cos30°/sin30°)

If tan θ = 3, find (1 − tan²θ)/(1 + tan²θ)

Find the number of students who take at least one subject if 50 take Math, 40 t…

Find the coefficient of x^2 in (1 − 3x)^4

Evaluate cot45° − tan45°

Find the fifth term of (x + 1)^6

Which of the following sets is countably infinite?

If θ is said to be an acute angle, and 4cosθ - 1 = 0, then what is the value of…

The largest number that divides 70 and 125, which leaves the remainders 5 and 8…

Find the fourth term of (x + y)⁷

Determine the value of n if the coefficients of the sixth and eleventh terms in…

If x, y > 0, Simplify √(81x⁴y⁸) · 2x

Simplify (cosx+sinx)/cosx - (sinx-cosx)/sinx = ?

Given that z = 1 + i√3. Find the argument of z.

Find the equation of a circle whose diameter has the ends (-5, 1) and (3, -7).

Given that z = 1 + i√3. Then compute the value of |z|.

Find the equation of the normal to the circle x² + y² + 3x - 2y = 0 at the poin…

If P(k) = k²(k+3)(k-1) is true, then what is P(k+1)?

sin²x + sin²x cot²x = ?

If P(n) is the statement 1+2+...+n = n(n+1)/2, what is P(1)?

Use trigonometric identities to find the exact value of (tan40° + tan110°)/(1 -…

The inequality \( |x| > 4 \) is equivalent to:

Complex number \(\frac{3-4i}{5+2i}\) can be written in a+ib form as

If 55% like tea, 50% like coffee and 20% like both. What percentage like neithe…

If \( z = 4(\cos 110^\circ + i \sin 110^\circ) \), find \( z^3 \).

Obtain the modulus of the complex number \(\frac{3-i}{2+2i}\)

If \( n(A) = 20 \), \( n(B) = 15 \), \( n(A \cap B) = 5 \), find \( n(A \cup B)…

The sixth term in the binomial expansion of \( (2x - \frac{1}{3x^2})^{10} \) is…

Let P be the power set of the set {a,b,c,d}, what is n(P)?

The number 0.45454545... is called

What is the equivalence of \(\cos 3\theta\)?

Given that \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(3…

Which formula holds for \(\sum_{k=1}^n 2^k\) for all \( n \geq 1 \)

Find the maximum value of the function \(y = \frac{x^2}{2} - 2x + 2\).

Given that \(\log x^3 - 3\log x + 2 = 0\), find the values of x.

The solution of \( |x^2 - 1| < 1 \) is:

Find the sixth term in the expansion of \( (2x + 5y/2)^9 \).

By mathematical induction \( 1 + 3 + 5 + \dots + (2n - 1) \) is

Which law states that A ∪ (B ∪ C) = (A ∪ B) ∪ C?

Using the binomial theorem, the coefficient of x³y² in (x+y)⁵ is:

The binomial expansion of (x+y)⁴ contains how many terms?

In (x+y)ⁿ, the general term is:

Find the coefficient of x²y⁵ in (x+y)⁷

Which identity represents the number of subsets of a set with 4 elements?

Find the number of ways to arrange the word 'STATISTICS'

The sum of the coefficients in the expansion of (x+y)ⁿ is:

The term independent of x in (x² + 1/x)⁶ is:

What is the total number of terms in (x+y)ⁿ?

Which of the following is true about Pascal's Triangle?

What is the general term of an arithmetic sequence with first term a and common…

In an arithmetic progression, the 5th term is 20 and the 10th term is 40. What …

The sum of the first n terms of an arithmetic progression is given by:

Find the sum of the first 10 terms of the arithmetic series: 3, 6, 9, 12,...

The sum of the first n terms of a geometric sequence is given by:

What is the sum to infinity of the geometric series with a = 4 and r = 1/2?

The sum to infinity of a geometric series is 5 and the first term is 2. What is…

The 3rd term of a geometric sequence is 9 and the 5th term is 81. What is the c…