List of top Mathematics Questions

The function f(x) = \(|x - 1|\) is

If \(2\sin2\theta=\sqrt3\), where 0 ≤ 2θ ≤ 90°, then find the value of cos 3θ

Let\[f(x)=\begin{cases} 2x-1, x<1\\ 1, x=1 \\ x^2,x>1 \end{cases}\]then at x = 1

Match List - I with List II. If \(A = \begin{vmatrix}3&-2&3 \\2 &1 &-1 \\4 &-3 &2\end{vmatrix}\)

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The points of discontinuity of the function \(f\) defined by \(f(x) = \begin{cases} x+2 & x≤1 \\ x-2 &1<x<2\\ 0& x≥2\end{cases}\) are:

If |\(\vec{a}\)| = 5, |\(\vec{b}\)| = 2 and |\(\vec{a}\) · \(\vec{b}\) | = 8 then the value of |\(\vec{a} \)×\(\vec{b} \)| is:

The value of C which satisfies Rolle's Theorem for f(x) = sin⁴x + cos⁴x in \([0, \frac{π}{2}]\). Then C is:

The value of \(\int_1^4|x-1|dx \)  is :

The value of tan(cos^-1x) is:

If A is a square matrix of order 3 and |A|=5, then |adj(adjA)| is:

Choose the wrong statement from the following:

The value of the determinant \(\begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix}\) is :

The quantity of water that must be added to 36 litres of milk at 2 ½ litres for ₹120 so as to have mixture worth ₹36 for a litre is:

Maximum slope of the curve \(y = -2x^3 + 6x^2 + 5x - 20\) is:

The function f(x) - x³ , x ∈ R has :

If \(A = \begin{bmatrix} 4&5&2\\ 3&-1&7\end{bmatrix}\), then the sum of the elements of the matrix AA^T is:

If A is a non-identity invertible symmetric matrix, then \(A^{-1}\) is:

The ratio of speeds of a motor boat and that of current of water is 35:6. The boat goes against the current in 6 hours 50 minutes. The time taken by boat to come back is :

If \(A=\begin{bmatrix} -2&6\\-5&-1\end{bmatrix}\) then \(A^{-1}\) is:

A. \(\begin{bmatrix}1& 2& 3   \\[0.3em]2 & 4 & 5   \\[0.3em]3 & 5&6   \\[0.3em] \end{bmatrix}\) is a Symmetric matrix. 
B. \(\begin{bmatrix}0 &0 &0   \\[0.3em]0& 0&0   \\[0.3em] \end{bmatrix}\) is a Null matrix.
C. \(\begin{bmatrix}1& 0& 0   \\[0.3em]0 & 2 & 0\\[0.3em]0 & 0&3\\[0.3em] \end{bmatrix}\) is an Identity matrix.
D. \(\begin{bmatrix}0& 1&2   \\[0.3em]-1 & 0 & 3   \\[0.3em]-2 & 3&0\\[0.3em] \end{bmatrix}\) is a Skew symmetric matrix.
E. \(\begin{bmatrix}\sqrt{3} &0& 0\\[0.3em]0 & \sqrt{3} & 0   \\[0.3em]0 & 0&\sqrt{3}   \\[0.3em] \end{bmatrix}\) is a Scalar matrix
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Arun covers first 28 kms of his journey in 45 minutes and the remaining 32 kms in 35 minutes. What is his average speed in m/s ?

If \(y=sin^{-1}x \) and \((1-x^2)\frac{d^2y}{dx^2} -x \frac{dy}{dx}=K\),then value of K is:

If the mean of 5 observations x, x+2, x+4, x+6 and x+8 is 11, then value of x

A telephone exchange receives on an average 5 calls per minute. The probability of receiving 3 or less calls per minute is :