List of top Mathematics Questions

If \(f(x)\) is continuous in \(\mathbb{R}\),

\[f(x) = \begin{cases} \frac{3x^2 - 12}{x - 2}, & x \neq 2 \\k, & x = 2 \end{cases}\]

 find \(k\).

If \( |x + 3| < 2 \), then \( x \) lies in
If \( 1, a, b, c, 16 \) is in G.P., then \( \sqrt[3]{abc} = \)
Evaluate \( \int \sin x \cdot \sin 2x \, dx \)
Distance between two foci of the hyperbola \( x^2 - 4y^2 = 16 \) is
P(A) = 0.4, P(B/A) = 0.9. Then P(A ∩ B) is
The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers upto 100.

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
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 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 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?
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 \( x^2 - 5x + 6 = 0 \).