List of top Mathematics Questions asked in CBSE CLASS XII

By using the properties of definite integrals, evaluate the integral: \(∫^{\frac{π}{2}}_0\frac{cos^5xdx}{sin^5x+cos^5x}\)

By using the properties of definite integrals, evaluate the integral: \(\int^{\frac{π}{2}}_0 \frac{sin^{\frac{3}{2}}xdx}{sin^{\frac{3}{2}}x+cos^{\frac{3}{2}}x}\)

By using the properties of definite integrals, evaluate the integral: \(∫_0^\frac{π}{2}\frac{\sqrt{sinx}}{\sqrt{sinx}+\sqrt{cosx}}dx\)

By using the properties of definite integrals, evaluate the integral: \(∫_0^{\frac \pi2}cos^2x\ dx\)

Evaluate the integral: \(∫_1^2(\frac 1x-\frac {1}{2x^2})e^{2x}\ dx\)

Evaluate the integral: \(∫_{-1}^1\frac {dx}{x^2+2x+5}\)

Evaluate the integral: \(\int_{0}^{2}\frac{dx}{x+4-x^2}\)

Evaluate the integral: \(∫_0^{\frac \pi2} \frac {sinx}{1+cos^2x}dx\)

Evaluate the integral: \(\int^2_0 x\sqrt{x+2}\)

Evaluate the integral: \(\int_{0}^{4} \sin^{-1} \frac{2x}{1+x^2}\,dx\)

Evaluate the integral: \(\int_{0}^{π/2} \sqrt{\sin \phi}\cos^5 \phi\, d\,\phi\)

A factory manufactures two types of screws,A and B each type of screw requires the use of two machine,an automatic and a hand operated.It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A,while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screw B.Each machine is available for at the most 4 hours on any day.The manufacturer can sell a package of screw A at a profit of Rs7 and screw B at profit of Rs10.Assuming that he can sell all the screws he manufactures,how many packages of each type should the factory owner produce in a day in order to maximize his profit?Determine the maximum profit.

Evaluate the definite integral: \(∫_0^1(xe^x+sin\frac{πx}{4})dx\)

Evaluate the definite integral: \(∫_0^π(sin^2\frac{x}{2}-cos^2\frac{x}{2})dx\)

Evaluate the definite integral: \(∫^3_2\frac{xdx}{x^2+1}\)

Evaluate the definite integral: \(∫^3_2 \frac{dx}{x^2-1}\)

Evaluate the definite integral: \(∫_1^0\frac{dx}{1+x^2}\)

Evaluate the definite integral: \(∫^\frac{π}{4}_\frac{π}{6} cosec x dx\)

Evaluate the definite integral: \(∫_0^\frac{π}{4} tanxdx\)

Evaluate the definite integral: \(∫_4^5 e^x dx\)

Evaluate the definite integral: \(∫^2_1(4x^3-5x^2+6x+9)dx\)

Evaluate the definite integral: \(∫^3_2 \frac{1}{x}dx\)

Evaluate the definite integral: \(∫^1_{-1}(x+1)dx\)

Evaluate the definite integral as limit of sums: \(∫^4_0(x+e^{2x})dx\)