List of practice Questions

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i)$\dfrac{1}{4} , 1$ (ii) $\sqrt 2 , \dfrac{1}{3}$ (iii) $0, \sqrt5$ (iv) $1, 1$ (v) $-\dfrac{1}{4} ,\dfrac{1}{4}$(vi) $4, 1$

Show that the points (5, –1, 1), (7, – 4, 7), (1 – 6, 10) and (–1, – 3, 4) are the vertices of a rhombus.

Find the following integral: $\int (2x^2+e^x)dx$

If $\frac{2}{11}$ is the probability of an event, what is the probability of the event ‘not A’

A coin is tossed twice, what is the probability that atleast one tail occurs?

A trust fund has Rs $30,000$ that must be invested in two different types of bonds.
The first bond pays $5$% interest per year, and the second bond pays $7$% interest per year.
Using matrix multiplication, determine how to divide Rs $30,000 $ among the two types of bonds.
If the trust fund must obtain an annual total interest of:
$A.$ Rs $1,800 $
$B.$ Rs $2,000$

A charge $10 \mu C$ is placed at the centre of a hemisphere of radius R = 10 cm as shown. The electric flux through the hemisphere (in MKS units) is

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $16x^2 + y^2 = 16$.

Which of the following can not be a valid assignment of probabilities for outcomes of sample Space $S =\{ω_1, ω_2 , ω_3, ω_4, ω_5, ω_6, ω_7\}$

Boyle's law is represented by the equation PV=K (K is not constant), K depends on

Solve the given inequality for real x: $x+\frac x2+\frac x3<11$.

Solve the given inequality for real x: 3(x – 1) ≤ 2 (x – 3)

Solve the given inequality for real x: 4x+3 < 5x+7

Let $f={(x,\frac {x^2}{1+x^2}):x∈R}$ be a function from R into R. Determine the range of f.

Let A, B and C be the sets such that $A ∪ B = A ∪ C$ and $A ∩ B = A ∩ C$. show that B = C.

The relation f is defined by

$f(x) = \begin{cases} x^2, & \quad 0≤x≤3\\ 3x, & \quad 3≤x≤10 \end{cases}$
The relation g is defined by
$g(x) = \begin{cases} x^2, & \quad 0≤x≤2\\ 3x, & \quad 2≤x≤10 \end{cases}$
Show that f is a function and g is not a function.

Find the real numbers x and y if (x-iy) (3+5i) is the conjugate of -6-24i.

Write the following intervals in set-builder form:
(i) (-3, 0)
(ii) [6, 12]
(iii) (6, 12]
(iv) [-23, 5)

Which of the following statements is incorrect regarding the polar satellite?

The hypotenuse of a right-angled triangle has its ends at the points (1, 3) and (-4, 1). Find the equation of the legs (perpendicular sides) of the triangle.

Average energy density of electromagnetic field of a wave having amplitude of 48 $V m^{-1}$ is

Find the sum to n terms of the sequence, 8, 88, 888, 8888… .

Show that the function given by $f(x)=e^{2x}$ is strictly increasing on R.

$Find$ $\frac {dy}{dx}$: $2x+3y=sin \ y$

Show that the points (–2, 3, 5), (1, 2, 3) and (7, 0, –1) are collinear.