Mathematics

Q.

What is the value of $\cos 15°$?

Q.

What is the value of $\cos 75°$?

Q.

Find the zeros of the following quadratic polynomials $x^2+7x+10$ and verify the relationship between the zeros and the coefficients.

Q.

The IQ of person is given by the formula, $IQ=\frac{m}{c}\times 100$, where m is the mental age and c is the chromological age. If $80\le IQ\le 140$ for a group of 12-year children, find the range of their mental age.

Q.

Range of the function $f\left(x\right)=\frac{x^2+x+2}{x^2+x+1};xϵR$ is

1. $(1,\infty )$

2. $(1,\frac{11}{7})$

3. $(1,\frac{7}{3}]$

4. $(1,\frac{7}{5})$

Q.

How many 3-digit numbers can be formed by using the digits 1 to 9, if no digit is repeated?

Q.

One Mega-Byte is equal to:

1. 1024 Bytes

2. 1024 Kilo Bytes

3. 1024 Giga Bits

4. 1024 Bits

Q.

In how many ways can the letters of the word PERMUTATIONS be arranged if the

(i) words start with P and end with S?

(ii) vowels are all together?

(iii) there are always 4 letters between P and S?

Q. the value of theta for which sin theta = cos theta where , 180<theta<360

Q.

The value of ${\sin }^2{5}^{\circ }+{\sin }^2{10}^{\circ }+{\sin }^2{15}^{\circ }+$..............

$+{\sin }^2{85}^{\circ }+{\sin }^2{90}^{\circ }$ is equal to

1. $7$

2. $8$

3. $9$

4. $\frac{19}{2}$

Q.

If n(A) = p and n(B) = q, then how many relations are there from A to B.

1. (pq)²

2. pq

3. 2^pq

4. 3^pq

Q.

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5, assuming that:

(i) repetition of the digits is allowed?

(ii) repetition of the digits is not allowed?

Q.

Find the value of $\underset{n\to \infty }{lim}\frac{1+2+3+....n}{n^2}$

1. 2

2. 

3. 

4. 1

Q.

A box contains $2$ white balls, $3$ black balls and $4$ red balls. In how many ways can $3$ balls be drawn from the box, if atleast one black ball is to be included in the draw?

1. $64$

2. 24

3. $3$

4. $1$

Q.

What is the formula of $\cos 3\theta$?

Q.

Derivative of mod $x$ is

Q.

From 50 students taking examinations in Mathematics, Physics and Chemistry, each of the student has passed in atleast one of the subjects, 37 passed in Mathematics, 24 in Physics and 43 in Chemistry. At most 29 passed in Mathematics and Chemistry, at most 19 passed in Mathematics and Physics and at most 20 in Physics and Chemistry. Find the largest possible number of students that could have passed in all three examinations.

Q. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Q. If f(x+10)+f(x+4)=0, there f(x) is a periodic function with period 1. 2 2. 4 3. 6 4. 1

Q.

Find the domain of the real function, $f\left(x\right)=\frac{1}{\sqrt{x+|x|}}$

Q.

Which of the following is incorrect?

1. 

2. 

3. 

4. 

Q.

In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

Q.

Find the value of $\tan {45}^0$.

Q.

Find the Zeroes of the quadratic polynomial $\left(6x^2-7x-3\right)$ and verify the relation between its Zeroes and Coefficients.

Q.

Find the ${12}^{th}$ term of a G.P. whose $8^{th}$ term is $192$ and the common ratio is $2$.

Q. Find the derivative of the following function:
f(x) = $\frac{cosx}{1+sinx}$

Q.

Choose the correct statement:

1. 

2. 

3. 

4. 

Q.

From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is

(i) Red and a king

(ii) Either red or a king

Q. Find the derivative of the following function:
f(x) = $\frac{sinx+cosx}{sinx-cosx}$

Q.

What is a principal argument in complex numbers?