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If $\angle Aand\angle B$ are acute angles such that tan A = tan B then prove that $\angle A=\angle B$.

the mean of 2,7,6 and x is 15 and the mean of 18,1,6,x and y is 10.What is the value of y?

(a)5 (b)10 (c)20 (d)30

Find the lengths of the medians of a $△$ABC having vertices at A (5, 1), B (1, 5), and C (-3, -1).

The mean weight of a group of five girls is 54 kg. The individual weights (in kg) of four of them are 54, 62, 58 and 56. Find the weight of the fifth girl.

The vertices of ∆ABC are A(4,6), B(1,5) and C(7,2). A line is drawn to intersect sides AB and AC at D and E respectively such that $\frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{4}$. Calculate the area of $\Delta ADE$ and compare it with the area of ∆ABC.

Let $A=\left[\begin{array}{ccc}4& 6& -1\\ 3& 0& 2\\ 1& -2& 5\end{array}\right],B=\left[\begin{array}{cc}2& 4\\ 0& 1\\ -1& 2\end{array}\right]$ and C = [3 1 2]. The expression which is not defined is

Find such a point whose ordinate is twice the abscissa and it also passes through the line 7x - 3y = 8.

If -5 is a root of the quadratic equation $2x^2+px-15=0$, and the quadratic equation $p{x}^2+px+k=0$ has equal roots, find the value of $k$.

Prove that (2, -2), (-2, 1) and (5, 2) are the vertices of a right angled triangle. Find the area of the triangle and the length of the hypotenuse.

Taylor purchased a rectangular plot of area $634m^2$. The length of the plot is 2 m more than thrice its breadth. Find the length and breadth (approximate values).

What is the common difference of an AP in which $a_{18}-a_{14}=32?$
(a) 8 (b) -8 (c) 4 (d) -4

PQ is a tangent to a circle with centre O at the point P. If $\Delta$ OPQ is an isosceles triangle, then $\angle$ OQP is equal to

(a) ${30}^o$ (b) ${45}^o$ (c) ${60}^o$ (d) ${90}^o$

Using vertical line test, determine which of the following curves represent a function?

Construct a $\Delta ABC$ with BC = 7 cm, $\angle B={60}^{\circ }$ and AB = 6 cm. Construct another triangle whose sides are $\frac{3}{4}$ times the corresponding sides of $\Delta ABC.$

The volume of a hemisphere is $2425\frac{1}{2}c{m}^3.$ Find its curved surface area.

The are small metal pieces each 1 cm long. ‘L’ number of metal pieces are put together to form a long thin rod. What is the length of the rod in cm?

18, 25, 32, 39, 46, ?. Find the number in place of question mark.

Graph of the quadratic equation ax² + bx + c = 0 , with a > 0, D > 0 is

$A=\left[\begin{array}{ccc}1& 0& 0\\ 0& -5& 0\\ 0& 0& 9\end{array}\right]$ is a ________.

Which among the following is the largest ?

Mia goes for shopping to buy a dress which costs Rs.1809. The rate of sales tax is $8\%$. She tells the shopkeeper to reduce the price to such an extent that she has to pay Rs.1809, inclusive of sales tax. Find the reduction needed in the price of the dress.

Places A and B are 100km apart on the highway. One car starts from A and another from B at the same time. If the car travel in same direction at a different speed, they meet in 5hrs. If they travel towards each other, they meet in 1hr. What are the speeds of the two cars?

The distance between the point (1, 2) and a point on the line x+y = 6 is 3 units. The coordinates of the point is

The capacity of a closed cylindrical vessel of height 1 m is 15.4 l. How many square metres of the metal sheet would be needed to make it?

John goes to a shop to buy a bicycle quoted at Rs 1000. The rate of sales tax is 12% on it. He asks the shopkeeper for a rebate on the price of the bicycle to such an extent that he has to pay Rs 1008, inclusive of sales tax. Find the rebate percentage on the price of the bicycle.

Given two squares with same centre and sides being parallel to the corresponding sides of the each other. If length of the side of the bigger square is X and the length of the smaller square is Y, find the length of the line joining AB.

Check whether 6^n can end with the digit 0 for any natural number n

Find the height of a building, when it is found that on walking towards it 40 m in a horizontal line through its base the angular elevation of its top changes from ${30}^{\circ }to{45}^{\circ }$.

If we take a circle and a sphere of the same radius, then the surface area of the sphere is ___ times the area of the circle.

In the given figure, XY is a diameter of the circle, PQ is a tangent to the circle at Y. Given that $\angle$AXB = ${50}^0$ and $\angle$ABX = ${70}^0$, calculate $\angle$APY.s

If 2y = 5x+7, then what is the value of c with respect to the standard form ax+by+c = 0

If for a triangle $ABC$,
$\left|\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right|=0$
then ${\sin }^{3}A+{\sin }^{3}B+{\sin }^{3}C=$

ABDE is a trapezium.​​​​​​ with $AE\parallel BD$ and $ED\perp BD$, and AC is drawn parallel to the side DE

Find the values of $\text{cot}\theta \text{and}\text{cosec}\theta$ respectively, from the figure above.

The minute hand of a clock is 10 cm long. The area of the face of the clock described by the minute hand between 8 A.M and 8.25 A.M is

The lowest form of the rational expression $\frac{3x+21}{5x+35}$ is __________________

The $4^{th}$ and the $9^{th}$ term of a G. P. are 8 and 256 respectively. Find the G. P.

Find the frequency of 40 in the following given set of data.
10, 40, 80, 90, 60, 40, 30, 40, 20, 40, 80, 70, 40

1. 5

$si{n}^2{30}^o$ + 4 $co{t}^2{45}^o$ - $se{c}^2{60}^o$ = ?

(a) 0 (b) $\frac{1}{2}$ (c) 4 (d) 1

In the given figure, length of BC is: