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The areas of three faces of a cuboid are 15, 20, 12 $c{m}^2$. What are the possible values of the height of the cuboid in cms?

Find the value of x?

x + y = 5
3x - y = 3

Using quadratic formula solve the following quadratic equation: [3 MARKS]



$p^2{x}^2+(p^2-q^2)x-q^2=0,p\ne 0$

The rain water from a roof of $44m\times 20$ m drains into a cylindrical tank having diameter of base $4m$ and height $3.5m$. If the tank is just full, find the rainfall in cm.

In an AP
(i) given a=5,d=3,$a_n$=50, find n and $S_n$.
(ii) given $a_{12}$=37,d=3, find a and $S_{12}$.
(iii) given d=5,$S_9$=75, find a and $a_9$.
(iv) given a=8,$a_n$=62,$S_n$=210, find n and d.
(v) given l=28,S=144, and there are total of 9 terms. Find a.

The graph given below shows graphical representation of the following polynomials.



a) $y=x^3$

b) $y=x^7$

c) $y=x^2$

d) $y=x^6$





Identify the correct relation between the graphs $\left(1\text{to}4\right)$ and the polynomials $\left(a\text{to}d\right)$.

The volume of the largest sphere than can be cut from a cylindrical log of wood of base radius 1 m and height 4 m is:

Question 10

Shyama purchases a scooter costing Rs 36450 and the rate of sales tax is 9%, then the total amount paid by her is

(a) Rs 36490.50

(b) Rs 39730.50

(c) Rs 36454.50

(d) Rs 33169.50

The sum of the numerator and the denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fractions.

Evaluate each of the following

$co{s}^2{30}^o+co{s}^2{45}^o+co{s}^2{60}^o+co{s}^2{90}^o$

1. 7200

In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If $\angle PRQ=l$ and $\angle OPQ=m,$ then $l+m$=___.

Evaluate

$\left(i\right)\frac{{\sin }^2{63}^{\circ }+{\sin }^2{27}^{\circ }}{{\cos }^2{17}^{\circ }+{\cos }^2{73}^{\circ }}$

$\left(ii\right)\sin {25}^{\circ }\cos {65}^{\circ }+\cos {25}^{\circ }\sin {65}^{\circ }$

Prove that the lines given by the equations 3x + 2y + 5 = 0 and 3x + 2y − 1 = 0 are parallel. At what points do they intersect the x-axis? And the y-axis?

The median class for the following data is
$$\begin{array}{cccccc}\text{Marks}& Below10& Below20& Below30& Below40& Below50\\ \text{No. of students}& 5& 10& 23& 31& 40\end{array}$$

There is a solid wooden cuboidal block of length, breadth and height 10 m, 8 m and 5 m respectively. On the top face of the block is a hemispherical depression of radius 3 m. What is the surface area of the solid so obtained?

The table below shows the distance (in units) covered by 6 people.

Rosy covered three times the distance covered by all 6 people.

Calculate the distance covered by Rosy.

To get the ratio of 2 : 3, if one quantity is 8, then the other quantity is

Evaluate:

(a) ⁵C₄

(b) ¹⁰⁰C₉₈

Solve $\frac{3x}{2}$ - $\frac{5y}{3}$ = -2; $\frac{x}{2}$ + $\frac{y}{2}$ = $\frac{13}{6}$

On representing the linear equation 3x = 2y - 2 in standard form ax + by + c =0, which of the following is/are the correct values of a, b and c?

The LCM of two numbers x and y is z. What is their HCF?

A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... as shown in the figure.What is the total length of such a spiral made up of thirteen consecutive semicircles?

Two dice are thrown simultaneously. The probability of getting two numbers whose product is even, is

The three vertices of a parallelogram ABCD are A (3,-4), B (-1,-3) and C (-6, 2). Find the coordinates of vertex D and find the area of ABCD

Find the ratio in which the point P (x, 2) divides the line segment joining the points A(12, 5) and B (4, -3). Also, find the value of x.