List of top Mathematics Questions asked in CBSE CLASS XII

Find \( \frac {dy}{dx}:\) \(sin^2y+cos\ xy=\pi\)

At what points in the interval [0, 2\(\pi\)], does the function sin 2x attain its maximum value?

Write two different vectors having the same direction.

The integrating factor of the differential equation \(x\frac{dy}{dx}-y=2x^{2}\) is

Which of the following functions are strictly decreasing on (0,π/2)?

Show that the function given by \(f(x) = 3x + 17\) is strictly increasing on \(R\)

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

A cylindrical tank of radius 10m is being filled with wheat at the rate of 314cubic mere per hour.Then the depth of the wheat is increasing at the rate of
Find the area of the circle 4x2+4y2=9 which is interior to the parabola x2=4y

In the matrix  A= \(\begin{bmatrix}   2 & 5 & 19&-7 \\   35 & -2 & \frac{5}{2}&12 \\   \sqrt3 & 1 & -5&17  \end{bmatrix}\),write:

 I. The order of the matrix 
 II. The number of elements
 III. Write the elements a13, a21, a33, a24, a23

Find a particular solution satisfying the given condition:\((1+x^2)\frac {dy}{dx}+2xy=\frac {1}{1+x^2}; \ y=0 \ when \ x=1\) 

On which of the following intervals is the function f given by \(f(x)=x^{100}+sin\  x-1\) strictly decreasing?

Find \(\frac{dy}{dx}\),if y=12(1-cost),x=10(t-sint),\(-\frac{\pi}{2}\)<t<\(\frac{\pi}{2}\)

Assume that each child born is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that 

  1. the youngest is a girl 
  2. at least one is a girl?
Find the angle between the lines whose direction ratios are a,b,c and b-c,c-a,a-b.
\(∫e^x secx(1+tanx)dx\) equals

Matrices A and B will be inverse of each other only if

\(\int \frac{10x^9+10^x \log_e 10}{x^{10}+10^x}dx\) equals

The numbers of arbitrary constants in the particular solution of a differential equation of third order are:

If \(\vec{a}\) and \(\vec{b}\) are two collinear vectors,then which of the following are incorrect:

The value of \(\int_{0}^{\frac{\pi}{2}}\) log(\(\frac{4+3\,sin\,x}{4+3\,cos\,x}\))dx is

\(∫\frac{dx}{x^2+2x+2}\) equals

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (i). f(x) = x2 (ii). g(x) = x3 − 3x (iii). h(x) = sinx + cos, 0 <x<\(\frac{\pi}{2}\) (iv). f(x) = sinx − cos x, 0 < x < 2π (v). f(x) = x3 − 6x2 + 9x + 15(vi) g(x)=\(\frac{x}{2}\)+\(\frac{2}{x}\)>0 (vii).g(x)=\(\frac{1}{x^2}\)+2(viii). f(x)=x√1-x,x>0

If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?

Classify the following measures as scalars and vectors. 
(i)10kg 
(ii)2metres north-west 
(iii)40° 
(iv)40watt 
(v)10-19coulomb 
(vi)20m/s2