Objective Questions

Let A = {1,2,3,4}, B = {3,4,5,6}, find (A − B) ∪ (B − A).

Find the sum of the first 77 terms of the arithmetic progression 4, −3, −10, ...

Find the sum of the first 200 terms of the arithmetic progression 1.1, 1.2, 1.3…

Prove by induction that 1 + 2 + 3 + ... + n = n(n+1)/2 for n≥1 and use it to fi…

In expansion of (1 + 2x)^4, find coefficient of x^3.

If \( A \cap B = A \), then:

What is the value of 6P4?

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

The equation \(\log_2 x = -1\) implies:

Which of the following defines an arithmetic progression (AP)?

What is the 10th term of the arithmetic sequence 3, 7, 11, 15, ...?

If the 5th term of an AP is 19 and the 8th term is 31, find the first term.

Which of the following sequences are arithmetic progressions?

Find the sum of the first 20 terms of the arithmetic progression 2, 5, 8, 11, .…

If the sum of the first n terms of an AP is given by S_n = 3n^2 + 5n, what is t…

What is the arithmetic mean between 14 and 38?

Which term of the arithmetic progression 5, 9, 13, 17, ... equals 81?

Three numbers in an AP have a sum of 27 and a product of 504. What are the numb…

Which of the following expressions correctly compute the sum of the first n ter…

How many terms are there in the finite arithmetic progression 7, 13, 19, ..., 2…

In an AP, if the m-th term is n and the n-th term is m (where m != n), what is …

If the p-th term of an AP is q and the q-th term is p, what is the common diffe…

Which statements are universally true for any AP with first term a and common d…

Calculate the sum of all two-digit odd positive integers.

If the 7th term of an arithmetic progression is 40, what is the sum of its firs…

What are the two arithmetic means inserted between 5 and 20?

If the sum of n terms of an AP is S_n = 2n^2 + 3n, what is the 10th term?

Which selections of variables represent symmetric choices for terms in an AP?

Find the sum of the first 50 positive integers: 1 + 2 + 3 + ... + 50.

A sequence has n-th term T_n = 7 - 3n. What is its common difference?

The first term of an AP is 5, the last term is 45, and the sum of all terms is …

If the ratio of sums of n terms of two APs is (7n + 1) : (4n + 27), find the ra…

For the arithmetic progression 100, 96, 92, ..., which statements are correct?

Which term of the progression 24, 21, 18, 15, ... is the first negative term?

Find the value of k such that 2k + 1, 3k + 3, and 5k - 1 are consecutive terms …

In an AP, T_4 + T_8 = 24 and T_6 + T_{10} = 44. Find the first term a.

Which conditions are sufficient to uniquely determine an arithmetic progression?

How many terms of the AP 17, 15, 13, ... must be added to yield a sum of 72?

If the sum of the first p terms of an AP is q and the sum of the first q terms …

If x, y, and z are in AP, what is the value of (x + 2y - z)(2y + z - x)(z + x -…

What is the radius squared of the circle x² + y² + 8x - 10y + 5 = 0?

The value of tan 45° is:

What is the reciprocal of cos a?

Solve the inequality: -3x - 5 > 12

What is the value of tan 2a?

Which function is positive only in quadrant IV?

What is the discriminant of the equation x² - 4x + 4 = 0?

The exact value of cos35° cos25° - sin35° sin25°

Solve \((\frac{1}{2})^x = 8\).

Simplify: √(81x⁴y⁴)

Which of these exists only if the index is odd for a negative radical?

In a class of 100 students, 40 offer Math, 45 Biology, 35 Physics. 15 offer Mat…

Find the sum of the coefficients in the binomial expansion of (x+y)^n

If z = 1 - √3 i. Find the value of |z|.

What is (1 - cos x)/sin x?

If f(n) = 2^n + 6^n, then what is f(k+1)?

Convert 11π/4 to degrees

Which of the following equals the 5th term in the expansion of (x+y)⁶?

If cos a = 4/5, what is sin a in the first quadrant?

What is cos (-a) equal to?

What is sin (360°-a)?

What is tan (-a) equal to?

Convert 7π/5 radians to degrees.

The value of cos 15° using surds is:

Which identity is correct for complementary angles?

What is the cardinality of the power set of A = {a, b, c}?

If A = {1, 2, 3, 4}, how many subsets does A have?

If A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}, then A - B is:

What is the correct interpretation of A ⊂ B?

If A = {a, b, c}, which of the following is not a proper subset?

The complement of set A with respect to universal set U is:

If U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {0, 1, 2}, what is A'?

Which of the following sets is infinite?

Which of the following equals (A ∪ B)' using De Morgan's law?

If P(A) is the power set of A = {1,2}, which of the following is not in P(A)?

The trigonometric ratio of sin 60° is:

What does PEMDAS stand for?

Solve: 2x + 5 = -7

What is the value of log₂ 8?

What is the solution to |3x - 5| = -2?

The roots of x² + 2x + 1 = 0 are:

What is the first step in a proof by mathematical induction?

In the induction step, we assume the result is true for:

What is the goal of the induction step in mathematical induction?

If P(k) is true and we show that P(k) implies P(k+1), then:

What is the base case in proving 1+2+3+...+n = n(n+1)/2 using induction?

Which of the following is a typical assumption in the induction hypothesis?

What is the expression for the sum of the first n odd numbers?

To prove that 1+3+5+...+(2n-1)=n² using induction, the base case should verify:

Which principle justifies that if a statement holds for the base case and the i…

A quadratic equation is generally written in the form:

The expression under the square root in the quadratic formula is called:

If one root of a quadratic is 4 and the sum of the roots is 7, the other root i…

The roots of the equation x² + x - 12 = 0 are:

What is the nature of the roots of 4x² - 12x + 9 = 0?

In the quadratic formula, if b² - 4ac = 0, then the graph of the quadratic touc…

Which of the following statements is true about the roots of a quadratic equati…

A quadratic equation with rational coefficients and irrational roots will have …

The graph of a quadratic equation is a:

If a quadratic equation has roots α and β, then the equation can be written as: