List of top Mathematics Questions

Let 
\(\stackrel{→}{a} = \hat{i} + \hat{j} + \hat{2k}, \stackrel{→}{b} = \hat{2i} - \hat{3j} + \hat{k}\)
and 
\(\stackrel{→}{c}= \hat{i} - \hat{j} + \hat{k}\)
be three given vectors.
Let \(\stackrel{→}{v}\) be a vector in the plane of \(\stackrel{→}{a}\) and \(\stackrel{→}{b}\) whose projection on \(\stackrel{→}{c}\) is \(\frac{2}{\sqrt3}\).
If \(\stackrel{→}{v}.\hat{j}\) = 7 , then \(\stackrel{→}{v}.(\hat{i}+\hat{k})\) is equal to :

The boolean expression (~(p ∧q)) ∨q is equivalent to:
\(sin^{-1}\bigg(sin\frac{2π}{3}\bigg)+cos^{-1}\bigg(cos\frac{7π}{6}\bigg)+tan^{-1}\bigg(tan\frac{3π}{4}\bigg)\) is equal to:
The value of \(cos⁡(\frac{2π}{7})+cos⁡(\frac{4π}{7})+cos⁡(\frac{6π}{7})\) is equal to:
Let the equation of two diameters of a circle x2 + y2 – 2x + 2fy + 1 = 0 be 2px – y = 1 and 2x + py = 4p. Then the slope m ∈ (0, ∞) of the tangent to the hyperbola 3x2 – y2 = 3 passing through the center of the circle is equal to _______.
Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is:
Five numbers, \(x_1, x_2, x_3, x_4, x_5\) are randomly selected from the numbers \(1, 2, 3\),….., \(18\) and are arranged in the increasing order \((x_1<x_2<x_3<x_4<x_5)\). The probability that \(x_2 = 7\) and \(x_4 = 11\) is:
Let \(f :R→R\) and \(g : R→R\) be two functions defined by \(f(x) = log_e(x^2 + 1) – e^{–x} + 1\) and \(g(x)=\frac {1−2e^{2x}}{e^x}\). Then, for which of the following range of α, the inequality \(f(g((\frac {α−1)^2}{3}))>f(g(α−\frac 53))\) holds?
The sum of diameters of the circles that touch (i) the parabola \(75x^2 \)= \(64(5y – 3)\) at the point (\(\frac{8}{5}\), \(\frac{6}{5}\)) and (ii) the y-axis is equal to _______.
 
Let \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\), \(a_i>0,\ i=1, 2, 3\) be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of \(\vec a\) on the vector \(3\hat i+4\hat j\) be 7. Let \(\vec b\) be a vector obtained by rotating \(\vec a\) with 90°. If \(\vec a,\vec b\) and x-axis are co-planar, then projection of a vector \(\vec b\) on \(3\hat i+4\hat j\) is equal to :
The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :

If the inverse trigonometric functions take principal values, then
\(cos^{-1} ( \frac{3}{10} cos (tan^{-1} (\frac{4}{3})) + \frac{2}{5} sin (tan^{-1} (\frac{4}{3})))\)
is equal to :

Let \(y = y(x)\) be the solution of the differential equation \((x + 1)y' – y = e^{3x}(x + 1)^2\), with \(y(0)=\frac 13\). Then, the point \(x=−\frac 43\) for the curve \(y = y(x)\) is :
If \(y = m_1x + c_1 \)and \(y = m_2x + c_2\), \(m_1≠m_2\) are two common tangents of circle \(x_2 + y_2 = 2\) and parabola \(y^2 = x\), then the value of \(8|m_1m_2|\) is equal to :
Let \(Q\) be the mirror image of the point \(P(1, 0, 1)\) with respect to the plane \(S\): \(x + y + z = 5\). If a line L passing through \((1, –1, –1)\), parallel to the line \(PQ\) meets the plane \(S\) at \(R\), then \(QR_2\) is equal to :
If the solution curve \(y = y(x)\) of the differential equation\( y^2dx + (x^2 – xy + y^2)dy = 0\), which passes through the point \((1,1)\) and intersects the line \(y=\sqrt 3x\) at the point \((α,\sqrt 3α)\), then value of \(log_e(\sqrt 3α)\) is equal to :
Let \(x=2t,\ y=\frac {t^2}{3}\) be a conic. Let S be the focus and B be the point on the axis of the conic such that SA⊥BA, where A is any point on the conic. If k is the ordinate of the centroid of the ΔSAB, then \(\lim\limits_{t \to 1} k\) is equal to
Let a circle C in complex plane pass through the points \(z_1 = 3 + 4i\), \(z_2 = 4 + 3i\) and \(z_3 = 5i\). If \(z(≠z_1)\) is a point on C such that the line through \(z\) and \(z_1\) is perpendicular to the line through \(z_2\) and \(z_3\), then \(arg\ (z)\) is equal to:
Let \(C_r\) denote the binomial coefficient of \(x^r \)in the expansion of \((1 + x)^{10}\). If for \(α, β∈R\), \(C_1 + 3⋅2 C_2 + 5⋅3 C_3 + …\) upto 10 terms =\(\frac {α×211}{2^β−1}(C_0+\frac {C_1}{2}+\frac {C_2}{3}…..\)upto 10 terms) then the value of \(α + β\) is equal to _______.

If 
\(\sum\limits_{k=1}^{31}\) \((^{31}C_k) (^{31}C_{k-1})\) \(-\sum\limits_{k=1}^{30}\) \((^{30}C_k) (^{30}C_{k-1})\) \(= \frac{α (60!)} {(30!) (31!)}\)
where \(α ∈ R\), then the value of 16α is equal to

If the system of linear equations
2x + 3y – z = –2
x + y + z = 4
x – y + |λ|z = 4λ – 4
where λ ∈ R, has no solution, then
The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is ________.
Let \(θ\) be the angle between the vectors \(\vec a\) and \(\vec b\), where \(|\vec a|=4\), \(|\vec b|=3\) and \(θ(\frac \pi 4,\ \frac \pi3)\) . Then \(|(\vec a−\vec b)×(\vec a+\vec b)|^2+4(\vec a.\vec b)^2\) is equal to ______.
Let the abscissae of the two points \(P\) and \(Q\) be the roots of \(2x^2 – rx + p = 0\) and the ordinates of \(P\) and \(Q\) be the roots of \(x^2 – sx – q = 0\). If the equation of the circle described on \(PQ\) as diameter is \(2(x^2 + y^2) – 11x – 14y – 22 = 0\), then \(2r + s – 2q + p\) is equal to _________.
The number of values of x in the interval \((\frac \pi 4, \frac {7\pi }{4})\) for which \(14cosec^2x – 2sin^2x = 21 – 4cos^2x\) holds, is ______.