Mathematics Zone is India's most loved platform for All Exams

Question 1:

If \(p \tan(\theta - 30^{\circ}) = q \tan(\theta + 120^{\circ})\), then what is \((p+q)/(p-q)\) equal to?

\(\sin 2\theta\)

\(\cos 2\theta\)

\(2 \sin 2\theta\)

\(2 \cos 2\theta\)

Question 2:

What is the general solution of \( \cos^{100} x - \sin^{100} x = 1 \)?

\( n \pi \)

\( (2 n+1) \pi \)

\( 2 n \pi \)

\( (2 n+1) \pi / 2 \)

Question 3:

Let \(x>1, y>1, z>1\) be in GP. Then \(\frac{1}{1+\ln x}, \;\frac{1}{1+\ln y}, \;\frac{1}{1+\ln z}\) are

in AP

in GP

in HP

neither in AP nor in GP nor in HP

Question 4:

The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?

240

720

1440

1620

Question 5:

If \( \frac{x}{\cos \theta} = \frac{y}{\cos\bigl(\tfrac{2\pi}{3}-\theta\bigr)} = \frac{z}{\cos\bigl(\tfrac{2\pi}{3}+\theta\bigr)} \), then what is \( x+y+z \) equal to?

-1

0

1

3

Question 6:

If \(p\) times the \(p\)th term of an AP is equal to \(q\) times the \(q\)th term (\(p \neq q\)), then what is the \(p+q\)th term equal to?

0

\(p+q\)

\(p q\)

\(p q(p+q)\)

Question 7:

Let \( A \) and \( B \) be two square matrices of same order. If \( AB \) is a null matrix, then which one of the following is correct?

Both \( A \) and \( B \) are null matrices

Either \( A \) or \( B \) is a null matrix

B is a null matrix if \( A \) is a nonsingular matrix

Both \( A \) and \( B \) are singular matrices

Question 8:

If \( \omega \neq 1 \) is a cube root of unity, then what is \( (1+\omega-\omega^{2})^{100} + (1-\omega+\omega^{2})^{100} \) equal to?

\(2^{100} \omega^{2}\)

\(2^{100} \omega\)

\(2^{100}\)

\(-2^{100}\)

Question 9:

Let \( P \) and \( Q \) be two non-void relations on a set \( A \). Which of the following statements are correct? I. \( P \) and \( Q \) are reflexive \( \Rightarrow P \cap Q \) is reflexive. II. \( P \) and \( Q \) are symmetric \( \Rightarrow P \cup Q \) is symmetric. III. \( P \) and \( Q \) are transitive \( \Rightarrow P \cap Q \) is transitive.

I and II only

II and III only

I and III only

I, II and III

Question 10:

In a class of 240 students, 180 passed in English, 130 passed in Hindi and 150 passed in Sanskrit. Further, 60 passed in only one subject, 110 passed in only two subjects and 10 passed in none of the subjects. How many passed in all three subjects?

60

55

40

35

Question 11:

In an AP, the ratio of the sum of the first p terms to the sum of the first q terms is p^{2}: q^{2}. Which one of the following is correct?

The first term is equal to the common difference

The first term is equal to twice the common difference

The common difference is equal to twice the first term

The first term is equal to square of the common difference

Question 12:

In an arithmetic progression (AP), if the 5th term is 10 and the 10th term is 25, what is the common difference?

3

5

2

4

Question 13:

Consider an arithmetic progression where the sum of the first 4 terms is equal to the sum of the next 4 terms. What can be said about the common difference?

The common difference is zero.

The common difference is negative.

The common difference is positive.

The common difference is such that the average of the first 4 terms is equal to the average of the next 4 terms.

Question 14:

If the 7th term of an arithmetic progression is twice the 4th term, what is the ratio of the common difference to the first term?

1:3

1:2

2:3

3:1

Test o1

00:00:00