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2x³+bx²-cx+d leaves the same remainder, when divided by x+1 (or)x-2(or)2x-1. Find b and c.

Find the least number which when divided by 12 leaves a remainder of 7 ,when divided by 15 leaves a remainder of 10 and when divided by 16 leaves a remainder of 11.

(ANS given :235)

if d is the H.C.F of 45 and 27, find x and y satisfying d= 27x +45y.

What is the triplicate ratio of 9:4?

The following table gives the marks obtained by the students of a class in English.
$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ 30& 2\\ 40& 5\\ 50& 14\\ 60& 21\\ 70& 23\\ 80& 8\\ 90& 7\\ 100& 1\end{array}$

Which of the following is true ?

Solve the given inequation and graph the solution on the number line.

$2y-3<y+1\le 4y+7,y\in R$

A cheque which is crossed by two parallel lines on the top left side is called a

If $10y=7x-4$ and $12x+18y=1$; find the values of $4x+6y$ and $8y-x$.

How much money will be required to buy 400 shares id nominal value is Rs 12.50 per share at a premium of Rs 1?

In the given figure, AB and AC are tangents to the circle with centre O such that BAC = 40o. Then, BOC is equal to

1. 21

In the figure, PC is the tangent to the circle. A and B are 2 points on the circle. If $\angle$BPC = ${60}^0$ and $\angle$APB = ${55}^0$, then find $\angle$ABP .

A point P divides the line segment joining the points A (3, -5) and B (-4, 8) such that $\frac{AP}{PB}=\frac{k}{1}.$ If P lies on the line x + y = 0, then find the value of k.

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:
Lifetimes (in hours): 0-20 20-40 40-60 60-80 80-100 100-120
No. of components: 10 35 52 61 38 29
Determine the modal lifetimes of the components.

A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs.44 per litre which the container can hold.

Water flows at the rate of 15 km/hr through a pipe of diameter 14 cm into a cuboidal pond which is 50m long and 44m wide. In what time will the level of water in the pond rise by 21 cm?

Find the area and perimeter of an isosceles right triangle, each of whose equal sides measures 10 cm. [Take $\sqrt{2}$ = 1.41.]

Which point on x- axis is equidistant from (5, 9) and (-4 , 6) ?

A train travel a distance of $480km$ at a uniform speed. If the speed had been $8km/hr$ less, then it would have taken $3$ hours more to cover the same distance. Formulate the quadratic equation in terms of the speed of the train.

Cot theta - tan theta?

The following table gives the marks obtained by the students of a class in an exam out of 50.

$\begin{array}{cc}Marks& No.ofStudents\\ Below10& 5\\ Below20& 10\\ Below30& 23\\ Below40& 31\\ Below50& 40\end{array}$

(i) Convert the cumulative frequency distribution into a regular frequency distribution.

(ii) Find the mean.

X and Y can do a piece of work in 72 days. Y and Z can do it in 120 days. X and Z can do it in 90 days. How many days does it take if all the three can work together?

Prove that $(tan\theta +cot\theta {)}^2=$ _____________

Two men or 4 women or 8children can do a job in 10 days . In how many days 1man ,1women and 2 children can do the same job?

If the product of the zeroes of $7x^2-13x-k$ is $\frac{6}{7}$ find the value of k

A square lawn is bounded on three sides by a path 4 m wide. If the area of the path is $\frac{7}{8}$ that of the lawn, find the dimensions of the lawn.

If one of the roots of the equation 2$x^2$ + ax + 6 = 0 is 3, then find the value of a

In the following figure, O is centre of the circle, $\angle AOB={60}^{\circ }$ and $\angle BDC={100}^{\circ }$, Find $\angle OBC$

If x = 1 is a root of equation x² - Kx + 5 = 0 then value of K is

In the given figure, the circle touches the sides AB, BC, CD and DA of a quadrilateral ABCD at the points P, Q, R, S respectively. If AB = 11 cm, BC =x cm, CR = 4 cm and AS = 6 cm, the value of x is

___ cm.

Check whether x^ - 6√x + 2 = 0 is a quadratic equation or not

Is there a polynomial without having zeros of the polynomial?

$\frac{\sin ({90}^{\circ }-\theta )\cos ({90}^{\circ }-\theta )}{\cot ({90}^{\circ }-\theta )}+{\sin }^2\theta =$___

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph verify the result by using the formula.

Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels 5 km/hr faster than the second train. If after 2 hours, they are 50 km apart, find the speed of each train.

If sec4A = cosec (A – 20^o), where 4A is an acute angle.

Find the value of A.

Given that AB = AC and $\angle$BOC = ${140}^{\circ }$ where O is the center of the circle. $\angle$ABC =?

The letter that will show lateral inversion-

The locus of the middle points of those chords of the circle $x^2+y^2=4$ which subtend a right angle at the origin is

In the given figure, AB is the diameter of a circle with centre O & OA = 7 cm. Find the area of shaded region.

Find the equation of line ⏊ to 4 + 3y = 5 & passing through the point where the line 5 – 6y = 30 cuts the – axis.

If in a $\Delta$ ABC, perimeter is 12 units, b = 3 units, c = 5 units then find $sin\left(\frac{A}{2}\right)$.

Find the surface area (in cm sq.) of a container with radius 4 cm and height 10 cm, The container is open from the top.