NDA Maths Mock Test – 03

Question: What is \(\int \sin^3 x \cos x\,dx\) equal to? \(\int \sin^3 x \cos x\,dx\) किसके बराबर है? Options: \(\frac{\cos^4

Question: What is the general solution of the differential equation \(y\,dx – (x + 2y^2)dy = 0\)? अवकल समीकरण \(y\,dx

Question: What is the maximum value of the function \(f(x) = \left(\frac{1}{x}\right)^{2x^2}\)? फलन \(f(x) = \left(\frac{1}{x}\right)^{2x^2}\) का अधिकतम मान क्या

Question: What is \(\int \frac{dx}{x(x^7 + 1)}\) equal to? \(\int \frac{dx}{x(x^7 + 1)}\) किसके बराबर है? Options: \(\frac{1}{7}\ln\left|\frac{x^7 – 1}{x^7}\right|

Question: If \(y = \cot^{-1}\left[\frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} – \sqrt{1-\sin x}}\right]\), where \(0 < x < \frac{\pi}{2}\), then

Question: Consider the function \(f(x) = \left(\frac{1}{x}\right)^{2x^2}\), where \(x > 0\). At what value of \(x\) does the function attain

Question: From the top of a building of height \(h\) meters, the angle of depression of an object on the

Question: The top of a hill observed from the top and bottom of a building of height \(h\) is at

Question: If \(A + B + C = 180^\circ\), then what is \(\sin 2A – \sin 2B – \sin 2C\)

Question: What is the order of the differential equation whose solution is \(y = a\cos x + b\sin x +