List of top Mathematics Questions

The area of a triangle with vertices(-3,0),(3, 0) and (0, k) is 9 sq.units, the value of k is

If A =\(\begin{bmatrix}   2-k & 2 \\     1 & 3-k \end{bmatrix}\) is a singular matrix, then the value of 5k - k² is equal to

The value of
\(\cot^{-1}[\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}]\) where x ∈ \((0,\frac{\pi}{4})\) is

The contrapositive of the statement
“If two lines do not intersect in the same plane then they are parallel.” is

Let the relation R be defined in N by aRb if 3a + 2b = 27 then R is

Let f : R→R be defined by f(x)= 3x²-5 and g : R→R by g(x)=\(\frac{x}{x^2+1}\) then gof is

f : R → R and g : [0, ∞) → R are defined by f(x) = x² and g(x)=\(\sqrt{x}\). Which one of the following is not true ?

The mean of 100 observations is 50 and their standard deviation is 5. Then the sum of squares of all observations is

If n is even and the middle term in the expansion of \((x^2+\frac{1}{x})^n\) is 924 x⁶, then n is equal to

If \(\lim\limits_{x \rightarrow 0} \frac{\sin(2+x)-\sin(2-x)}{x}\)= A cos B, then the values of A and B respectively are

The distance between the foci of a hyperbola is 16 and its eccentricity is \(\sqrt2\). Its equation is

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is

A man is walking at a speed of 6 km/h. After every km he takes rest for 6 minutes. How much time will he take to cover a distance of 24 km.

Player 1 and player 2 are running around a circular field. Player 1 takes 15 minutes to take one round, while Player 2 completes the round in 25 minutes. If both start simultaneously and go in the same direction, after how much time will they meet at the starting point? (Answer to be provided only in minutes)

If \( a \) and \( b \) are the roots of the equation \( x^2 - 7x - 1 = 0 \), then the value of \( a^2 + b^2 + a^3 + b^3 is equal to:}

Let a line \( l \) pass through the origin and be perpendicular to the lines \[ l_1: \vec{r}_1 = i + j + 7k + \lambda(i + 2j + 3k), \quad \lambda \in \mathbb{R} \] \[ l_2: \vec{r}_2 = -i + j + 2k + \mu(i + 2j + k), \quad \mu \in \mathbb{R} \] If \( P \) is the point of intersection of \( l_1 \) and \( l_2 \), and \( Q (a, b, \gamma) \) is the foot of perpendicular from P on \( l \), then \( (a + b + \gamma) \) is equal to:

Let \( S = 109 + \frac{108}{5} + \frac{107}{5^2} + \frac{106}{5^3} + \cdots \). Then the value of \( (16S - (25)^{3}) \) is equal to:

The number of ordered triplets of the truth values of \( p, q, r \) and such that the truth value of the statement \[ (p \lor q) \land (p \lor r) \implies (q \lor r) \text{ is True, is equal to:} \]

For \( m, n>0 \), let \( \alpha(m,n) = \int_{0}^{1} (1 + 3t)^{n} \, dt \). If \( \alpha(10,6) = \int_{0}^{1} (1 + 3t)^{6} \, dt \) and \( \alpha(11,5) = p(14)^{5} \), then \( p \) is equal to:

Let \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 0 & 3 \\ 1 & 0 & 0 \end{bmatrix} \), where \( a, c \in \mathbb{R} \). If \( A^n = A \) and the positive value of \( a \) belongs to the interval \( (n-1, n] \), where \( n \in \mathbb{N} \), then \( n \) is equal to:

Let (\alpha, \beta, \gamma) \text{ be the image of the point } P(3, 3, 5) \text{ in the plane } 2x + y - 3z = 6. \text{ Then } \alpha + \beta + \gamma \text{ is equal to:}

For any vector \( \mathbf{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k} \), with \( 10 | \mathbf{a} |<1 \), \( i = 1, 2, 3 \), consider the following statements:

Let A be a \( 2 \times 2 \) matrix with real entries such that \( A^T = \alpha A + I \), where \( \alpha \in \mathbb{R} \setminus \{-1, 1\} \). If \( \text{det}(A^2 - A) = 4 \), then the sum of all possible values of \( \alpha \) is equal to:

The value of the integral \[ \int_{\log_2}^{-\log_2} e^x \left( \log \left( e^x + \sqrt{1 + e^{2x}} \right) \right) dx \] is equal to:

The number of elements in the set \(S = \{ \theta \in [0, 2\pi] : 3 \cos^4 \theta - 5 \cos^2 \theta - 2 \sin^2 \theta + 2 = 0 \}\) is: