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Three measuring rods is 64 cm, 80 cm and 96 cm in length. Find the least length of cloth that can be measured an exact number of times, using any of the rods.

Solve the following systems of equations:

$\frac{15}{u}+\frac{2}{v}=17$

$\frac{1}{u}+\frac{1}{v}=\frac{36}{5}$

Metallic spheres of radii 12cm, 8cm and 10cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere(in cm).

What price should a shopkeeper mark on an article that costs him $Rs.600$ to gain $20\%$, after allowing a discount of $10\%$?

If R (5, 6) is the mid-point of the line segment AB joining the points A (6, 5) and B (4, y), then y equals

(a) 5 (b) 7 (c) 12 (d) 6

Is -2 a solution of the linear equations $4x-2=8$ and $2x=-4$ ?

A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is ${30}^{\circ }$. Find the length of the string(in meters), assuming that there is no slack in the string.

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled(in minutes)?

The external and internal radii of a hollow hemispherical vessel are $15\text{cm}$ and $10\text{cm}$ respectively. The approximate cost of painting it at the rate of $₹2$ per $\text{sq. cm}$ is:

Two chords AB and CD of a circle intersect each other at a point E outside the circle. If AB = 11 cm, BE = 3 cm and DE = 3.5 cm, then CD = ?

(a) 10.5 cm

(b) 9.5 cm

(c) 8.5 cm

(d) 7.5 cm

In fig, if $\angle ATO={40}^{\circ }$, find $\angle AOB$. [2 MARKS]

Find the consistent pair of linear equations from the following.

In the question, identify the equal angles in the triangles.

If a sequence whose $n^{th}$ term is given by
$t_n$ = 3.23 $n^2$– 4.81 n + 37, then which of the following is true?

Show that any positive odd integer of the form 6q+ 1 or 6Q + 3 or 6Q + 5 were q in some integer

Find the value of the following expression.
$\frac{\tan {82}^{\circ }}{\cot 8^{\circ }}+\frac{cosec{38}^{\circ }}{\sec {52}^{\circ }}+\frac{2\sin {35}^{\circ }\sec {55}^{\circ }}{{\sin }^2{50}^{\circ }+{\sin }^{2}40}$

$\sqrt{\frac{1-sinA}{1+sinA}}$ = ?

(a) sec A + tan A (b) sec A - tan A

(c) sec A tan A (d) none of these

An observer, 1.5 m tall, is 28.5 m away from a tower 30 m high. Determine the angle of elevation of the top of the tower from his eye.

Find the value(s) of k so that PQ will be parallel to RS. Given :

(i) P (2, 4), Q (3, 6), R (8, 1) and S (10, k)

(ii) P (3, -1), Q (7, 11), R (-1, -1) and S (1, k)

(iii) P (5, -1), Q (6, 11), R (6, -4k) and S (7, $k^2$)

If cotθ = ⁷/₈ , then tan²θ equals to:

The centres of two circles of radii $3cm$ and $2cm$ are $8cm$ apart. Find the length of the common tangent.

The zero of the polynomial represented by the given graph

$sin\theta$ $cos\theta$ [$sin({90}^{\circ }-\theta )$ $cosec\theta$ + $cos({90}^{\circ }-\theta )$ $sec\theta$]

Construct a triangle ABC with BC = 6.5 cm, AB = 5.5 cm and AC = 5 cm. ∠BAC is (use protractor)

If $m=asecA+btanAandn=atanA+bsecA,thenprovethat:m^2-n^2=a^2-b^2$

AB is a line segment & M is its mid- point. Semi- circles are drawn with AM, MB and AB as diameters on the same side of the line AB. A circle C (0, r) is drawn so that it touches all the three semicircles. The length of AB is 'x' times r. Find x.

$\begin{array}{ccc}5& 3& 3\\ 8& 10& 8\\ 35& 27& ?\end{array}$

Which of the given combinations is definitely correct?

Show that $3\sqrt{2}$ is irrational.

Monthly wages of 10 employees of a factory are 3000, 3500, 3800, 3200, 3600, 4000, 3100, 3900, 3000 and 4000. Find the median wage

In the given triangle right angled at B, which pair of angles is complementary?

The area of circle which encloses a square of side 10 cm is

Find the value of p such that the wuadratic equation (p-12)x² - 2(p-12)x+2=0 has equal roots

A letter is chosen at random from the word 'ENTERTAINMENT. Find the probability that the chosen letter is a vowel.

A tent consists of a frustum of a cone, surmounded by a cone. If the diameters of the upper and lower circular ends of the frustum be 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounded conical portion be 12 m, find the area of the canvas required to make the tent. Assume that the radii of the upper end of the frustum and the base of surmounted conical portion are equal. [2 MARKS]

For a body to escape from the earth, angle from horizontal at which it should be fired with the escape velocity is

In the following α is

The angle of elevation of an aeroplane from a point on the ground is 45⁰. After a flight of 15 seconds, the elevation changes to 30⁰. If the aeroplane is flying at a height of 3000 m, find the speed of the aeroplane.

In the given right angled triangle, what is the value of Sin A?

A piece of cloth costs Rs 200. If the piece was 5m longer and each meter of cloth costs Rs 2 less the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per meter?

Find the total surface area of hemisphere of radius 7 cm.(Take $\pi$ = $\frac{22}{7}$ )

The point C (–1,2) divides the line segment AB in the ratio 3:4, where the coordinates of A is (2, 5). The coordinates of B are___________.