List of top Mathematics Questions

The angle θ between the vectors \(\rm \vec{a} = 5\hat{i} - \hat{j} +  \hat{k}\) and \(\rm \vec{b} = \hat{i} + \hat{j} -  \hat{k}\) equals to

If an be the nth  term of the GP of positive numbers. Let ∑n=100100a2n=α and ∑n=1100a2n−1=β such that α≠β then the common ratio is:
Form the differential equation of y=ae3xcos⁡(x+b) Where y′=dydx and yn=d2ydx2?
Let $R$ be a relation on $R$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$Then $R$ is
If sin 5x+sin 3x+sin x = 0, then the value of x other than zero, lying between π0≤×≤π2 is;
Find the centre and radius of x2+y2+6y=0.
If the orthocentre of the triangle, whose vertices are $(1,2),(2,3)$ and $(3,1)$ is $(\alpha, \beta)$, then the quadratic equation whose roots are $\alpha+4 \beta$ and $4 \alpha+\beta$, is
The angle θ between the vectors a→=5i^−j^+k^ and b→=i^+j^−k^ is:
If 4x2 + py2 = 45 and x2 - 4y2 = 5 cut orthogonally, then the value of p is:
If a→,b→,c→ are non-coplanar vectors and λ is a real number, then[λ(a→+b→)λ2b→λc→]=[a→b→+c→b→] for
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
Differentiate w.r.t. x the function:\(x^x+x^a+a^x+a^a\), for some fixed \(a>0\) and \(x>0\)
The value of $\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots +\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$ is :

The equation $e ^{4 x}+8 e ^{3 x}+13 e ^{2 x}-8 e ^x+1=0, x \in R$ has :

For any two statements p and q, the negation of the expression p∨(∼p∧q) is:

If ABCD is a parallelogram, vector AB = 2i + 4j - 5k and vector AD = i + 2j + 3k, then the unit vector in the direction of BD is

If A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a} then find the number of elements present in the range of R?

Let $y=y(x)$ be the solution of the differential equation $\left(x^2-3 y^2\right) d x+3 x y d y=0, y(1)=1$.Then $6 y^2( e )$ is equal to

Find the value of \( x \) that satisfies the equation \( \frac{3x - 4}{2} = 5 \).
Find the sum of the roots of the quadratic equation \( 2x^2 - 3x - 5 = 0 \).
Solve for \( x \) in the equation \( 3x + 5 = 2x + 7 \).
Find the value of \( x \) in the quadratic equation \( x^2 - 5x + 6 = 0 \).
Write all the factors of the following numbers:
  1. 24
  2. 15
  3. 21
  4. 27
  5. 12
  6. 20
  7. 18
  8. 23
  9. 36
Explain the concept of a limit. Why is it important in calculus?
Find the equation of the tangent line to the curve \( y = x^2 - 3x + 2 \) at the point \( (1, 0) \).