Simplify $\sec\theta - \cos\theta$?

C. $\frac{\sin^2\theta}{\cos\theta}$

A. $\frac{1 - \cos\theta}{\sin\theta}$

B. $\frac{1 - \cos^2\theta}{\cos\theta}$

C. $\frac{\sin^2\theta}{\cos\theta}$

Mathematics · Algebra · page 6 of 17

Algebraic Expressions MCQs with Answers

Includes 34 past paper MCQs (marked).

Timed quizzes, instant results, track your progress — free

Practice these MCQs in the app

All Mathematics chapters

Algebraic Expressions and Identities MCQs (51–60)

10 MCQs with answers and a short one-liner. Hide answers to test yourself.

Past paper MCQs in this chapter · See all past papers

Answers and one-liners are hidden. Tap an option to check that question, or show all.

51.
If $AB = BA$, then the matrices are commutative to each other.
Correct Answer: B. Multiplicative
One-liner
If $AB = BA$, then the matrices are multiplicative commutative to each other.
52.
For any number $x$, the value of $[\pm x] =$ _?
Correct Answer: A. $\pm x$
One-liner
For any number $x$, the value of $[\pm x]$ is $\pm x$.
53.
Simplify $\sec\theta - \cos\theta$?
Correct Answer: C. $\frac{\sin^2\theta}{\cos\theta}$
One-liner
$\sec\theta - \cos\theta = \frac{1}{\cos\theta} - \cos\theta = \frac{1 - \cos^2\theta}{\cos\theta} = \frac{\sin^2\theta}{\cos\theta}$, so the simplified form is $\frac{\sin^2\theta}{\cos\theta}$.
54.
Which product is the smallest among the following?
Correct Answer: C. $8008 \times 2001$
One-liner
The smallest product is $8008 \times 2001$ because for a fixed sum, the product is minimized when the two numbers are farthest apart.
55.
If $\sin \theta + \cos \theta = 1$, then $\sin \theta - \cos \theta$ is equal to:
Correct Answer: B. $\pm 1$
One-liner
The value of $\sin \theta - \cos \theta$ is $\pm 1$.
56.
What is the value of $1 - \sin^2 \theta$?
Correct Answer: C. $\cos^2 \theta$
One-liner
The value of $1 - \sin^2 \theta$ is $\cos^2 \theta$.
57.
Past Paper MCQ
What is the value of $(892)^2$?
Correct Answer: D. $795,664$
One-liner
The value of $(892)^2$ is $795,664$.
58.
What is the remainder when the polynomial $2x^4 - 3x^2 + 5x - 7$ is divided by $x + 2$?
Correct Answer: A. $3$
One-liner
By the Remainder Theorem, substituting $x = -2$ into $2x^4 - 3x^2 + 5x - 7$ gives the remainder $3$.
59.
If $xy^2 + xy = 8x$, then at the point $(1, 2)$, what is $\frac{dy}{dx}$?
Correct Answer: B. $\frac{2}{5}$
One-liner
The derivative $\frac{dy}{dx}$ at $(1,2)$ is $\frac{2}{5}$.
60.
Let $Z_1 = 2 - i$ and $Z_2 = 3 - i$, then find $Z_1 Z_2$.
Correct Answer: D. $5 - 5i$
One-liner
The product $Z_1 Z_2 = (2 - i)(3 - i) = 6 - 2i - 3i + i^2 = 6 - 5i - 1 =$ $5 - 5i$.

Previous chapter: Problems on Ages Next chapter: Linear Equations

Algebraic Expressions MCQs with Answers

Algebraic Expressions and Identities MCQs (51–60)

Subjects

Exams

Platform

Legal