List of top Mathematics Questions

The equation of tangents to the hyperbola \( 3x^2 - 2y^2 = 6 \) which is perpendicular to the line \( x - 3y = 3 \) is

The area of the region bounded by the curves \( x^2 + y^2 = 9 \) and \( x + y = 3 \) is

The area bounded by the curves \( y = \cos x \) and \( y = \sin x \) between the ordinates \( x = 0 \) and \( x = \frac{\pi}{2} \) is

If \( a = i - j + 2k \) and \( b = 2i - j + k \), then the angle \( \theta \) between \( a \) and \( b \) is given by

If \( a, b, c \) are three non-coplanar vectors, then \[ (a + b) \times (c + b) = (a - b) \times (c - b) = b \times c \]

If there is an error of \( m% \) in measuring the edge of a cube, then the percent error in estimating its surface area is

The normal at the point \( (a t^2, 2 a t) \) on the parabola meets the parabola again at the point \( (a t^2, 2 a t) \). The equation of the normal is

The given equation of rectangular hyperbola is \[ x^2 - y^2 = 6^2 \quad \text{(length of latus rectum is 16)} \] The asymptotes are parallel to each other

Let \( f(x) = 25x^{24}(1 - x)^{75} \), on the interval \( [0, 1] \), then \[ f'(x) = 25x^{24}(1 - x)^{75} - 75x^{25}(1 - x)^{74} = 25x^{24}(1 - x)^{74}[(1 - x) - 3x] \]

If \( p, q \) are simple propositions with truth values \( T, F \), then the truth value of \( (\neg p \vee q) \wedge \neg r \) is

If a line segment OP makes angles of \( \frac{\pi}{4} \) and \( \frac{\pi}{3} \) with the X-axis and Y-axis, respectively, then the direction cosines are

If \( |z| \geq 3 \), then the least value of \( |z + 4| \) is

Given lines are \[ x = my + n, \, z = py + q \] and \[ x = m'y + n', \, z = p'y + q' \] Above equations can be rewritten as \[ x - n' = p', \quad m = 1, \, p = 1 \] Lines will be perpendicular if

If \( (2, 7, 3) \) is one end of a diameter of the sphere \( x^2 + y^2 + z^2 - 6x - 12y - 2z + 20 = 0 \), then the coordinates of the other end of the diameter are

A tetrahedron has vertices at \( O(0, 0, 0) \), \( A(1, -2, 1) \), \( B(2, 1, 1) \), and \( C(1, -1, 2) \). Then, the angle between the faces \( OAB \) and \( ABC \) is

The structure \( (N_3) \) satisfies the closure property, associativity and commutativity but the identity element 0 does not belong to \( N \).

The integral \( \int \frac{dx}{\cos x + \sqrt{5} \sin x} \) equals

The correct result of the equation \( 3x^2 + 2x + 7y^2 - 14y + 4 \) is

Correct result is as follows: \[ P \, (\neg \, Q) \, \equiv (P \, \vee \, Q) \, \implies (P \, \vee \, Q) \, \implies \, R \, \implies \, S \]

If \( l = x^2 + y^2 + z^2 \) is a normal to the ellipse \[ \frac{x^2}{16} + \frac{y^2}{9} = 1, \] then

If \( \text{line} \, y = mx + c \) is a normal to the ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \] then \( c^2 \) is equal to

The differential equation \( (3x + 4y + 1) dx + (4x + 5y + 1) dy = 0 \) represents a family of

If \( A, B, C \) are three events associated with a random experiment, then \( P(A \,|\, B) \) is

The probability of getting a double six in one throw of two dice

If the complex number \( z \) lies on a circle with center at the origin and radius \( \frac{1}{4} \), then the complex number \( 1 + z \) lies on a circle with radius