List of top Mathematics Questions

If $ A=\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right], $ then the value of the determinant $ |{{A}^{2009}}-5{{A}^{2008}}| $ is
Given: \[ \vec{a} = \hat{j} - \hat{k}, \quad \vec{c} = \hat{i} - \hat{j} - \hat{k} \] The vector \( \vec{b} \) satisfies: \[ \vec{a} \times \vec{b} + \vec{c} = \vec{0} \quad \text{and} \quad \vec{a} \cdot \vec{b} = 3 \] Find the vector \( \vec{b} \).
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree.

If \(f(x) = \sin x e^{\sin x}\), find \(f'(x)\)

If \(tan(x - y) = \frac{4}{5}\), \(\tan(x + y) = \frac{6}{5}\), then \(\tan(2x) =\)

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?
If sin 5x+sin 3x+sin x = 0, then the value of x other than zero, lying between π0≤×≤π2 is;
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 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 equation $e ^{4 x}+8 e ^{3 x}+13 e ^{2 x}-8 e ^x+1=0, x \in R$ has :