Science (English Medium) Class 12 - CBSE Important Questions for Mathematics

If \[\begin{vmatrix}x & \sin \theta & \cos \theta \\ - \sin \theta & - x & 1 \\ \cos \theta & 1 & x\end{vmatrix} = 8\] , write the value of x.

If A = `[(1, 2, 0), (-2, -1, -2), (0, -1, 1)]`, find A⁻¹. Using A⁻¹, solve the system of linear equations   x − 2y = 10, 2x − y − z = 8, −2y + z = 7.

If A = `[[1,1,1],[0,1,3],[1,-2,1]]` , find A^-1Hence, solve the system of equations: 

x +y + z = 6

y + 3z = 11

and x -2y +z = 0

Write the value of `|(a-b, b- c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c)|`

On her birthday Seema decided to donate some money to children of an orphanage home. If there were 8 children less, everyone would have got ₹ 10 more. However, if there were 16 children more, everyone would have got ₹ 10 less. Using the matrix method, find the number of children and the amount distributed by Seema. What values are reflected by Seema’s decision?

Differentiate the following function with respect to x: `(log x)^x+x^(logx)`

If `y=log[x+sqrt(x^2+a^2)]` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`

If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`

If y=2 cos(logx)+3 sin(logx), prove that `x^2(d^2y)/(dx2)+x dy/dx+y=0`

If x=α sin 2t (1 + cos 2t) and y=β cos 2t (1−cos 2t), show that `dy/dx=β/αtan t`

If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`

Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`

If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t) then find `dy/dx `

Find the value of `dy/dx " at " theta =pi/4 if x=ae^theta (sintheta-costheta) and y=ae^theta(sintheta+cos theta)`

If x = cos t (3 – 2 cos² t) and y = sin t (3 – 2 sin² t), find the value of dx/dy at t =4/π.

Find the values of a and b, if the function f defined by 

If `y = sin^-1 x + cos^-1 x , "find"  dy/dx`

If e^y ( x +1)  = 1, then show that  `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`

Find `(dy)/(dx) , if y = sin ^(-1) [2^(x +1 )/(1+4^x)]`

If `(sin "x")^"y" = "x" + "y", "find" (d"y")/(d"x")`

`"If y" = (sec^-1 "x")^2 , "x" > 0  "show that"  "x"^2 ("x"^2 - 1) (d^2"y")/(d"x"^2) + (2"x"^3 - "x") (d"y")/(d"x") - 2 = 0`