Higher Secondary Education First Year [HSE +1], 2023 - 24

Which of the following equation is the locus of (at², 2at)?

The HM of two positive numbers whose AM and GM are 16, 8 respectively is ______

• 4

• 5

• 6

• 10

Find a, so that the sum and product of the roots of the equation 2x² + (a − 3) x + 3a − 5=0 are equal is

• 1

• 0

• 4

• 2

In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is _________.

• ¹⁰C₃

• 110

• 116

• 120

The coordinates of the four vertices of a quadrilateral are (−2,4), (−1,2), (1,2) and (2,4) taken in order. The equation of the line passing through the vertex (−1,2) and dividing the quadrilateral in the equal areas is _____________.

• x − y + 3 = 0

• x + 1 = 0

• x + y = 1

• x + y + 3 = 0

• None of these

• cos 3x

• 2 cos x

• cos 2x

• cos x

Equation of the straight line perpendicular to the line x – y + 5 = 0, through the point of intersection the y-axis and the given line

• x + y + 10 = 0

• x − y – 5 = 0

• x + y – 5 = 0

• x + y + 5 = 0

The number of solutions of x² + |x − 1| = 1 is

• 0

• 2

• 3

• 1