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check whether 12ⁿ cannot end with the digit 0 or 5 for any natural number n

Find the largest number which divides 705 and 1053 leaving a reminder 9 in each case.

If the relation R on set A = {1, 2, 3 . . . . . . 13, 14} is defined as R = {(x, y):3x - y = 0}, find the range of R

If no. Of apples and mangoes are zeroes of polynomial3x²=8x-2k+1 and the no. Of apples is seven times tha no. Of mangoesthen find the zeroes and valie of k.

FInd the $n^{th}$ term of the series $(1{)}^3$ + ($1^3$ + $2^3$) + ($1^3$ + $2^3$ + $3^3$) + ------------------- n terms.

In a cage, there are rabbits and parrots and the number of heads are 28 and feet are 72. Find the number of parrots and rabbits.

An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45^o. The height of the tower is

Voluntary debt is a debt which is taken from the people by the government on

Find the ratio compounded of the reciprocal ratio of 15 : 28, the sub -duplicate ratio of 36 : 49 and the triplicate ratio of 5 :4.

The lateral surface area of a square pyramid comprises of equilateral triangles and the length of the base edge is $50cm$. What is its surface area?

A (4, 5), B (1, 1) & C (6, 1) are the vertices of a Δ ABC. L is the midpoint of AB and M is the midpoint of AC. What is the value of BC in terms of LM ?

In parallelogram PQRS, P(-3,2), Q(2,7) and S(1,9) are three vertices. Then the length of diagonal PR is

If the sides of a triangle are 3 cm, 4 cm and 6 cm long, determine whether the triangle is a right-angled triangle.

Two towers X and Y are standing at some distance apart. From the top of tower X, the angle of depression of the foot of tower Y is found to be ${30}^{\circ }$. From the top of tower Y, the angle of depression of the foot of tower X is found to be ${60}^{\circ }$. If the height of tower Y is ‘h’ m then the height of tower X in terms of ‘h’ is _____ m

A person observes the angle of elevation of the peak of a hill from a station to be $\alpha .$ He walks c metres along a slope inclined at the angle $\beta$ and finds the angle of elevation of the peak of the hill to be $\gamma$. Show that the height of the peak above the ground is $\frac{csin\alpha sin(\gamma -\beta )}{(sin\gamma -\alpha )}$

A circle of diameter 6 cm makes a sector of angle $P^{\circ }$, what will be the area of the sector?

Show that the points A(6, 1), B(8, 2), C(9, 4) and D(7, 3) are the vertices of a rhombus. Find its area.

The perimeter of a rhombus is $60cm.$ If one of its diagonals is $18cm$ long, find (i) the length of the other diagonal, and (ii) the area of the rhombus.

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5 cm. Find its capacity.

Four different paths connect opposite corners of a square as shown above. Which of the following statement(s) holds true?

In a circle of radius 10.5 cm, the minor arc is one-fifth of the major arc. Find the area of the sector corresponding to the major arc.

If the replacement set is the set of whole numbers, solve 7 - 3x $\ge$ -$\frac{1}{2}$

Find the sum of the following AP's.
(i) -37, -33, -29, .... to 12 terms
(ii) 115,112,110, ... to 11 terms.

Which of the following cannot be a factor of x⁵-ax³+bx²+200?

a)x³-8

b)x²-25

c)x+5

d)x+15

The length of a tangent from a point Q to a circle is 24 cm. The distance between Q and the center of the circle is 25 cm. The radius of the circle is _____ cm.

The sum of the first 14 terms of an AP is 1050 and its first term is 10. Find the ${20}^{th}$ term. ___

Riya has an account with a bank. Following are the entries from her pass-book:

$\begin{array}{ccccc}Date& Particulars& WithdrawalsRs.p.& DepositsRs.p.& BalanceRs.P.\\ 08-02-08& B/F& -& -& 8500.00\\ 18-02-08& Toself& 4000.00& -& -\\ 12-04-08& ByCash& -& 2238.00& -\\ 15-06-08& Toself& 5000.00& -& -\\ 08-07-08& Bycash& -& 6000.00& -\end{array}$

Compute the page of her pass book and therefore calculate the interest for six months, which is from the month of February to July 2008 at 4.5% per annum.

Simplify

4/7+3/5+7/10.

Which among the following represent the surface area of the right circular cylinder?

There are three figures of areas $x^2,12x$ and z respectively, as shown. Figures A and C are squares while B is a rectangle, with the length of one side $x$. What should be the value of $z$ so that all the 3 figures can be arranged to form a square of side $(x+6)$?

If a+b+c =0 , then the value of $\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}$

Assertion (A) In the given figure, If O is the centre of the circle and AC is the diameter with $\angle APB={120}^{\circ }$, then $\angle BQC={150}^{\circ }$.

Reason (R) In a cyclic quadrilateral, the sum of opposite angles is ${180}^{\circ }$.

The value of b and c for which the identity f(x+1) - f(x) = 8x + 3 is satisfied, where $f\left(x\right)=b{x}^2+cx+d$ are

If $M=\left[\begin{array}{c}0\\ 1\end{array}\right]$ and $N=\left[\begin{array}{c}1\\ 0\end{array}\right]$

Show that $3M+5N=\left[\begin{array}{c}5\\ 3\end{array}\right]$

The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.

The position of a point in a plane is expressed by a pair of two numbers called ________________

1. 8

On tossing three coins simultaneously, the probability of getting at least one head and tail is $\frac{x}{4}$.
The value of x is ___ .

The cost price of a Burger is Rs 80 and the Selling price of the Burger is Rs 100. How much will be the sales tax does the buyer pay for a burger? The sales tax on the burger is 8%.

If $\alpha$ and $\beta$ are the zeroes of the polynomial $f\left(x\right)=6x^2+x-7$ then evaluate the following:

(i)$\alpha -\beta$ (ii)${\alpha }^2+{\beta }^2$ (iii) ${\alpha }^2-{\beta }^2$ (iv) ${\alpha }^3-{\beta }^3$ (v) ${\alpha }^3+{\beta }^3$ (vi) ${\alpha }^4-{\beta }^4$

Find the discriminant of the quadratic equation $3x^2-5x+2=0$ and hence find the nature of the roots.