List of top Mathematics Questions asked in CBSE CLASS XII

Find the equation of all lines having slope −1 that are tangents to the curve y=\(\frac{1}{x-1}\) , x≠1.

Find the point on the curve y = x³ − 11x + 5 at which the tangent is y = x − 11.

Find points at which the tangent to the curve y = x³ − 3x² − 9x + 7 is parallel to the x axis.

Find the slope of the normal to the curve \(x = 1 − a\, sin θ,\, y = b\, cos^2 θ\) at θ=\(\frac{π}{2}\).

Find the slope of the normal to the curve x = acos³ θ, y = asin³ θ at θ=π/4.

Find the slope of the tangent to the curve y = x³ − 3x + 2 at the point whose x-coordinate is 3.

Find the slope of the tangent to curve y = x³ − x + 1 at the point whose x-coordinate is 2

Find the slope of the tangent to the curve,y = \(\frac{x-1}{x-2}\), x ≠ 2 at x = 10.

Find the slope of the tangent to the curve y = 3x⁴ − 4x at x = 4.

By using properties of determinants,show that:
(i)\(\begin{vmatrix} a-b-c & 2a & 2a\\ 2b & b-c-a & 2b \\ 2c&2c&c-a-b\end{vmatrix}\)=(a+b+c)³ 
(ii)\(\begin{vmatrix} x+y+2z & x & y\\ z & y+z+2x & y\\ z &x&z+x+2y \end{vmatrix}\)=2(x+y+z)³

By using properties of determinants, show that:
(i)\(\begin{vmatrix} x+4 & 2x & 2x\\ 2x & x+4 & 2x \\2x &2x&x+4\end{vmatrix}\)=(5x+4)(4-x)² 
(II)\(\begin{vmatrix} y+k & y & y\\ y & y+k & y \\y &y&y+k\end{vmatrix}\)=k²(3y+k)

By using properties of determinants,show that:I\(\begin{vmatrix} x & x^2 & yz\\ y & y^2 & zx\\z&z^2&xy \end{vmatrix}\)=(x-y)(y-z)(z-x)(xy+yz+zx)

Using the property of determinants and without expanding,prove that:\(\begin{vmatrix} b+c & q+r & y+z\\ c+a & r+p & z+x\\ a+b&p+q&x+y \end{vmatrix}\)=2\(\begin{vmatrix} a & p & x\\ b & q & y\\c&r&z \end{vmatrix}\)

Evaluate the determinants 
(i) \(\begin{vmatrix}3 & -1 & -2\\ 0 & 0 & -1 \\ 3&-5&0\end{vmatrix}\)(iii) \(\begin{vmatrix} 3 & -4 & 5\\ 1 & 2 & -2 \\ 2&3&1\end{vmatrix}\)
(ii)\(\begin{vmatrix} 0 & 1 & 2\\ -1 & 0 & -3 \\ -2&3&0\end{vmatrix}\) (iv)\(\begin{vmatrix} 2 & -1 & -2\\ 0 & 2 & -1\\3&-5&0 \end{vmatrix}\)

If A is square matrix such that A²=A,then (I+A)³-7A is equal to

Choose the correct answer in the following questions: If \(\begin{bmatrix} α & β  \\ \gamma & -\alpha \end{bmatrix}\) is such that A²=I then  

If A= \(\begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}\) show that A²-5A+7I=0

Show that the matrix \(B'AB\) is symmetric or skew symmetric according as A is symmetric or skew symmetric.

Find the inverse of each of the matrices,if it exists.\(\begin{bmatrix} 1 & 3 & -2\\ -3 & 0 & -5\\ 2&5&0 \end{bmatrix}\)

Find the inverse of each of the matrices, if it exists\(\begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}\)

Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 2 & -3\\ -1 & 2 \end{bmatrix}\)

Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 2 & -6 \\ 1 & -2 \end{bmatrix}\)

Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 3 & -1 \\ -4 & 2 \end{bmatrix}\)

Find the inverse of each of the matrices, if it exists.
\(\begin{bmatrix} 3 & 10\\ 2 & 7\end{bmatrix}\)

Prove \(tan^{-1}\sqrt{x}=\frac{1}{2}cos^{-1}(\frac{1-x}{1+x}),x∈[0,1]\)