List of practice Questions

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax + b) (cx + d)²

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers):\(\frac{(ax+b)}{(cx+d)}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{1+\frac{1}{x}}{1-\frac{1}{x}}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers):\(\frac{1}{ax^2+bx+c}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers):\(\frac{ax+b}{px^2+qx+r}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{a}{x^4}-\frac{b}{x^2}\) + cosx

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{px^2+qx+r}{ax+b}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): 4\(\sqrt x\) -2

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax +b)ⁿ

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax +b)ⁿ (cx + d)^m

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): sin (x + a)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): cosec x cot x

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{cos\,x}{1+sin\,x}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{sin\,x+cos\,x}{sin\,x-cos\,x}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{sec\,x-1}{sec\,x+1}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{a+b\,sin\,x}{c+d\,cos\,x}\)

Is there any difference between the two roads as the poet describes them:
(i) in stanzas two and three?
(ii) in the last two lines of the poem?

The text you read is a travelogue where the author, Vikram Seth, talks about his visit to two sacred places in Kathmandu. Imagine that you were with Vikram Seth on his visit to Pashupatinath temple, and you were noting down all that you saw and did there, so that you could write a travelogue later.
Record in point form • what you see when you reach the Pashupatinath temple • what you see happening inside the temple • what you do when inside the temple • what you see outside the temple • what your impressions are about the place.

Prove that \((cos x+cos y)^2+(sin x – sin y)^2 = 4 cos^2\,\frac{x+y}{2}\)

Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for \(x^2 = -9y\)

Reduce the following equations into slope-intercept form and find their slopes and the y-intercepts. 
(i) \(x + 7y = 0 \)
(ii) \(6x + 3y - 5 = 0 \)
(iii) \(y = 0\)

Prove that \((cos\,x-cos\, y)^2 + (sin\,x – sin\,y)^2 = 4sin^2 \frac{x-y}{2}\)

For what values of x, the numbers \(\frac{-2}{7}\), x , \(\frac{-7}{2}\) are in G.P.?

Find the equation of the parabola that satisfies the following conditions: Focus \((6, 0)\); directrix \(x = -6\).