Geometry - General Aptitude - General Aptitude (GA) Previous Year Questions

If \( y = 5x^2 + 3 \), then the tangent at \( x = 0 \), \( y = 3 \)

The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?

A scalar function in the xy-plane is given by \(\phi(x, y) = x^2 + y^2\). If \(\hat{i}\) and \(\hat{j}\) are unit vectors in the x and y directions, the direction of maximum increase in the value of \(\phi\) at (1,1) is along:

For \(0 \leq x \leq 2\pi\), \(\sin x\) and \(\cos x\) are both decreasing functions in the interval ______.