List of top Mathematics Questions

If the foot of the perpendicular drawn from $(1,9,7)$ to the line passing through the point $(3,2,1)$ and parallel to the planes $x+2 y+z=0$ and $3 y-z=3$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to

The foot of perpendicular of the point $(2,0,5)$ on the line $\frac{x+1}{2}=\frac{y-1}{5}-\frac{z+1}{-1}$ is $(a, \beta, \gamma)$. Then which of the following is NOT correct?

Let $\vec{a}=\hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}$ be a vector such that $\vec{a} \times \vec{b}=2 \hat{i}-\hat{k}$ and $\vec{a} \cdot \vec{b}=3$ Then the projection of $\vec{b}$ on the vector $\vec{a}-\vec{b}$ is :-

Let $\vec{a}=-\hat{i}-\hat{j}+\hat{k}, \vec{a} \cdot \vec{b}=1$ and $\vec{a} \times \vec{b}=\hat{i}-\hat{j}$. Then $\vec{a}-6 \vec{b}$ is equal to

Let $P Q R$ be a triangle. The points $A, B$ and $C$ are on the sides $Q R, R P$ and $P Q$ respectively such that $\frac{Q A}{A R}=\frac{R B}{B P}=\frac{P C}{C Q}=\frac{1}{2}$. Then $\frac{A \text { Area }(\triangle P Q R)}{\text { Area }(\triangle A B C)}$ is equal to

Let $\vec{u}=\hat{i}-\hat{j}-2 \hat{k}, \vec{v}=2 \hat{i}+\hat{j}-\hat{k}, \vec{v} \cdot \vec{w}=2$ and $\vec{v} \times \vec{w}=\vec{u}+\lambda \vec{v}$. Then $\vec{u} \cdot \vec{w}$ is equal to

Let$\overrightarrow{ a }=2 \hat{i}-7 \hat{j}+5 \hat{k}, \overrightarrow{ b }=\hat{i}+\hat{k} and \overrightarrow{ c }=\hat{i}+2 \hat{j}-3 \hat{k}$ be three given vectors If $\overrightarrow{ r }$ is a vector such that$ \vec{r} \times \vec{a}=\vec{c} \times \vec{a} \ and \ \vec{r} \cdot \vec{b}=0,$ then $|\vec{r}|$ is equal to :

Let $\vec{a}$ = 2$\widehat{i}$+3$\widehat{j}$+4$\widehat{k}$, $\vec{b}$ = $\widehat{i}$-2$\widehat{j}$-2$\widehat{k}$, $\vec{c}$ = -$\widehat{i}$+4$\widehat{j}$+3$\widehat{k}$ and $\vec{d}$ is a vector perpendicular to $\vec{b}$ and $\vec{c}$, $\vec{a}$.$\vec{d}$ = 18, then find |$\vec{a}$x$\vec{d}$|²

The sum of all values of $ \alpha $, for which the points whose position vectors are:

\[ \mathbf{r_1} = \hat{i} - 2\hat{j} + 3\hat{k}, \quad \mathbf{r_2} = 2\hat{i} - 3\hat{j} + 4\hat{k}, \quad \mathbf{r_3} = (\alpha+1)\hat{i} + 2\hat{k}, \quad \mathbf{r_4} = \hat{j} + 2\hat{k} \]

are coplanar, is equal to:

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are three non-zero vectors and $\hat{n}$ is a unit vector perpendicular to $\vec{c}$ such that $\vec{a}$=$\alpha \vec{b}$-$\hat{n}$, $\alpha \neq 0$ and $\vec{b}$ .$ \vec{c}$=12, then |$\vec{c} \times(\vec{a} \times \vec{b})$| is equal to:

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three non-zero vectors and $\hat{\mathbf{n}}$ is a unit vector perpendicular to $\mathbf{c}$ such that: $\mathbf{a} = \alpha \mathbf{b} - \hat{\mathbf{n}}, \, (\alpha \neq 0)$ and $ \mathbf{b} \cdot \mathbf{c} = 12 $, then $ \mathbf{c} \times (\mathbf{a} \times \mathbf{b}) $ is equal to:

If $\overrightarrow a =\hat i+2\hat k,\overrightarrow b =\hat i+\hat j+\hat k,\overrightarrow c =7\hat i−3\hat j+4\hat k,r ×\hat b +\hat b ×\overrightarrow c =\overrightarrow0$ and $\overrightarrow r .\overrightarrow a =0$. Then $\overrightarrow r. \overrightarrow c$ is equal to

Let $\overrightarrow 𝑎 =4\hat 𝑖+3\hat 𝑗ˆ$ and $\overrightarrow 𝑏 =3\hat 𝑖−4\hat 𝑗$+$5\hat 𝑘$. If $\overrightarrow 𝑐$ is a vector such that $\overrightarrow 𝑐 ⋅(\overrightarrow 𝑎 ×\overrightarrow𝑏⃗ )+25=0$, $\overrightarrow𝑐 ⋅(\hat𝑖+\hat𝑗+ \hat𝑘)=4$, and projection of $\overrightarrow𝑐$ on $\overrightarrow𝑎$ is $1$ , then the projection of $\overrightarrow 𝑐$ on $\overrightarrow 𝑏$ equals

If four distinct points with position vectors $\overrightarrow a,\overrightarrow b,\overrightarrow c$ and $\overrightarrow d$ are coplanar, then $[\overrightarrow a \overrightarrow b \overrightarrow c]$ is equal to

Let for a triangle ABC,
$\vec{AB}=-2\hat{i}+\hat{j}+3\hat{k} $
$\vec{CB}=α\hat{i}+β\hat{j}+γ\hat{k} $
$\vec{CA}=4\hat{i}+3\hat{j}+δ\hat{k} $
If $δ>0$ and the area of the triangle ABC is $5\sqrt6$, then $\vec{CB}.\vec{CA}$ is equal to

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:

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

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

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

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

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

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

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) $?