List of top Questions asked in CBSE CLASS XII

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\(\begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}\)

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

Consult internet and find out how to make orally active protein pharmaceutical. What is the major problem to be encountered?

Which of the following differential equations has y=x as one of its particular solution?

Can you suggest a method to remove oil (hydrocarbon) from seeds based on your understanding of rDNA technology and chemistry of oil?

What are Cry proteins? Name an organism that produces it. How has man exploited this protein to his benefit?

What is gene therapy? Illustrate using the example of adenosine deaminase (ADA) deficiency.

Compare and contrast the advantages and disadvantages of production of genetically modified crops.

Area bounded by the curve y=x³, the x-axis and the ordinates x=2 and x=1 is