List of practice Questions

Let $ \mathbf{a} $ be a non-zero vector parallel to the line of intersection of the two planes described by $ i + j + k $ and $ -i - j - k $. If $ \theta $ is the angle between the vector $ \mathbf{a} $ and the vector $ \mathbf{b} = -2i - 2j + 2k $, and $ \left| \mathbf{a} \right| = 6 $, then ordered pair $ (\mathbf{a} \cdot \mathbf{b}) $ is equal to:

Let $ f(x) = 2x^n + \lambda $, where $ \lambda \in \mathbb{R} $ and $ n \in \mathbb{N} $ . Given that $ f(4) = 133 $ and $ f(5) = 255 $, What is the sum of all the positive integer divisors of $ f(3) - f(2) $?

The total number of six digit numbers, formed using the digits 4,5,9 only and divisible by 6 , is __

If ${ }^{2 n+1} P _{n-1}:{ }^{2 n-1} P _n=11: 21$, then $n^2+n+15$ is equal to :

If ${ }^{2 n+1} P _{n-1}:{ }^{2 n-1} P _n=11: 21$, then $n^2+n+15$ is equal to :

The number of ways to distribute 20 chocolates among three students such that each student gets atleast one chocolate is

If ²ⁿC₃: ⁿC₃= 10, then $\frac{n^{2}+3n}{n^{2}-3n+4}$ is equal to

Find all the four letter words with two vowels and 2 consonants from the word UNIVERSE?

Rank of the word PUBLIC is?

Find out the rank of MONDAY in English dictionary if all alphabets are arranged in order?

Using all the letters of the word MATHS, then rank of the word THAMS is:

Using the number 1, 2, 3 ... 7, total numbers of 7 digit number which does not contain string 154 or 2367 is (Repetition is not allowed)

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k , is equal to

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways in which they can be transported is:

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is

Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is___.

The number of five-digit numbers, greater than 40000 and divis ible by 5, which can be formed using the digits 0, 1, 3, 5, 7, and 9 without repetition, is equal to:

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is:

The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is______

The number of triplets $ (x, y, z) $, where $ x, y, z $ are distinct non-negative integers satisfying $ x + y + z = 15 $, is:

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sit on the allotted seat, is:

The equations of two sides of a variable triangle are $x-0$ and $y=3$, and its third side is a tangent to the parabola $y^2=6 x$. The locus of its circumcentre is:

Let the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25}$ coincide Then the length of the latus rectum of the hyperbola is:-