The slope of the tangent to the curve y = 3x² - 5x + 6 at (1, 4) is

• - 2

• 1

• 0

• - 1

The chord joining the points (5, 5) and (11, 227) on the curve y = 3x² - 11x - 15 is parallel to tangent at a point on the curve. Then, the abscissa of the point is

• - 4

• 4

• - 8

• 8

3.

The function f(x) = sin(x) - kx - c, where k and c are constants, decreases always when

• k > 1

• $\mathrm{k} \ge 1$

• k < 1

• $\mathrm{k} \le 1$

If y = mlog(x) + nx² + x has its extreme values at x = 2 and x = 1, then 2m + 10n is equal to

• - 1

• - 4

• - 2

• - 3

If s = 2t³ - 6t² + at + 5 is the distance travelled by a particle at time t and if the velocity is - 3 when its acceleration is zero, then the value of a is

• - 3

• 3

• 4

• - 4

The domain of the function f(x) = $\sqrt{7 - 3\mathrm{x}} + {\log }_{\mathrm{e}}\left(\mathrm{x}\right)$ is

• $0 < \mathrm{x} < \infty$

• $\frac{7}{3} \le \mathrm{x} < \infty$

• $0 < \mathrm{x} \le \frac{7}{3}$

• $- \infty < \mathrm{x} < 0$

If f(1) = 1, f(2n) = f(n) and f(2n + 1) = {f(n)}² - 2 for n = 1, 2, 3, ... , then the value of f(1) + f(2) + ... + f(25) is

• 1

• - 15

• - 17

• - 1

In a class of 80 students numbered 1 to 80, all odd numbered students opt for cricket, students whose numbers are divisible by 5 opt for football and those whose numbers are divisible by 7 opt for hockey. The number of students who do not opt any of the three game is

• 13

• 24

• 28

• 52

If $∆ = \left|\begin{array}{ccc}1& 2& 3\\ 2& 3& 5\\ 3& 6& 12\end{array}\right|$ and $∆\text{'} = \left|\begin{array}{ccc}4& 8& 15\\ 3& 6& 12\\ 2& 3& 5\end{array}\right|$ then

• $∆\text{'} = 2∆$

• $∆\text{'} = - 2∆$

• $∆\text{'} = ∆$

• $∆ = - ∆\text{'}$

The roots of the equation $\left|\begin{array}{ccc}1 +\hspace{0.17em}\mathrm{x}& 3& 5\\ 2& 2 +\hspace{0.17em}\mathrm{x}& 5\\ 2& 3& \mathrm{x} +\hspace{0.17em}4\end{array}\right|$ =  0 are

• 2, 1, - 9

• 1, 1, - 9

• - 1, 1, - 9

• - 2, - 1, - 8