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$\text{Factorise the following by splitting the}\text{middle term and find the roots.}2x^2+x–6=0$

Which of the following list of numbers forms an AP?

If t,s are the roots of a quadratic equation $p{x}^2+qx+s$, then what is value of (s)$\times$(t)?

ABCD is a parallelogram as shown with two sides 2 and 4.

Find the sum of the squares of the diagonals?

In the given figure, DE || BC and DE : BC = 3 : 5. Calculate the ratio of the areas of $\Delta ADE$ and the trapezium BCED.

If $\Delta ABC$ is an equilateral triangle such that $AD$ is perpendicular to $BC,$ then $A{D}^2$ = ___.

Insert three numbers between 1 and 256 so that the resulting sequence is a GP.

$\Delta ABC$ of dimesions $AB=4cm,BC=5cm$ and ∠B= 60^o is given.
A ray $BX$ is drawn from $B$ making an acute angle with $AB$.
5 points $B_1,B_2,B_3,B_4\&B_5$ are located on the ray such that $BB1=B1B2=B2B3=B3B4=B4B5$.
$B_4$ is joined to $A$ and a line parallel to $B_{4}A$ is drawn through $B_5$ to intersect the extended line $AB$ at $A^{\prime }$.
Another line is drawn through $A^{\prime }$ parallel to $AC$, intersecting the extended line $BC$ at $C^{\prime }$.
Find the ratio of the corresponding sides of $\Delta ABC$ and $\Delta A^{\prime }B{C}^{\prime }$.

If the sum of the squares of first n natural numbers exceeds their sum by 330, then find the value of n.

For what value of 'k' are the following points (7,-2), (5, 1), (3, k) collinear ?

The graph below shows the ages of presidents of a country at the time of inauguration or the start of their tenure.

Find the correct option(s) among the following.

From a window 'h' m high above the ground of a house on a street, the angle of elevation and depression of the top and foot of another house on the opposite side of the street are $\alpha$ and $\beta$ respectively.
The height of the opposite house is ___

Solve graphically each of the following systems of linear equations. Also, find the coordinates of the points where the lines meet the axis of x in each system:

(i) 2x + y = 6

x - 2y = -2

(ii) 2x - y = 2

4x - y = 8

(iii) x + 2y = 5

2x - 3y = -4

(iv) 2x + 3y = 8

x - 2y = -3

The area of a sector of a circle of radius 5 cm is $5\pi c{m}^2$. Find the angle contained by the sector.

From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp-post CD are observed to be ${30}^{\circ }$ and ${60}^{\circ }$ respectively. Find

(i) the horizontal distance between AB and CD,

(ii) the height of the lamp-post,

(iii) the difference between the heights of the building and the lamp-post.

A kite is flying at a height of 75 m from the level ground, attached to a string inclined at ${60}^{\circ }$ to the horizontal. Find the length of the string, assuming that there is no slack in it. [Take $\sqrt{3}$=1.732].

Solve the following quadratic equation by factorization.
$\frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5x};x\ne 0,-1,2$

Two concertric circles are of radii 6.5 cm and 2.5cm. Find the length of the chord of the larger circle which touches the smaller circle.

The mean of 20 numbers is zero.Of them,at the most,how many may be greater than zero?

(a) 0 (b) 1 (c) 10 (d) 19

ABC is a right-angled triangle right angled at A. A circle is inscribed in it the lengths of the two sides containing the right angle are 6 cm and 8 cm. Find the radius of the circle.

In a basket, the ratio between the number of oranges and the number of apples is 7 : 13. If 8 oranges and 11 apples are eaten, the ratio between the number of oranges and the number of apples becomes 1 : 2. Find the original number of oranges and the original number of apples in the basket.

Find the sum of first 20 terms of an A. P. whose first term is 3 and the last term is 57.

Which of the following coordinates lies on the line 2x-3y = 12?

The expression that should be subtracted from the polynomial f(x) = x⁴ + 2x³ -13x² - 12x + 21 so that the resulting polynomial is exactly divisible by g(x) = x² – 4x + 3 is

A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A first and then at B, with radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and so on. The total length of such a spiral made up of 13 consecutive semi circles is ___. Take $\pi =\frac{22}{7}$

There are 60 students in a class among which 30 are girls.In another class, there are 50 students out of which 25 are boys.If one student from each class is selected, what is the probability that both are boys ?

In the following figure, find the value of x.

ABCD is a rectangle whose sides AB has equation 3x-12y+5 =0. Find the slopes of the other sides of the rectangle

In the figure, AE & BC intersect each other at D. If ∠CDE = 90^o, AB = 5 cm, BD = 4 cm & CD = 9 cm. Find DE.

Step 5. Draw 2 arcs with centres A and B respectively with radius R. If the arcs intersect at H, value of $\angle HOA$ is __.
Note: Answer in degrees.

If a=2^p ×3^q × 5^r and b= p^{​​​​​​2} × q^{​​​​​​3} × r^{​​​​​​5} , where p,q and r are primes, find the value of p+q+r , given that a=b.

$Twopipesrunningtogethercanfillacisternin2\frac{8}{11}minutes.Ifonepipetakesoneminutemorethantheothertofillthecistern,findthesumofindividualtimeinwhicheachpipewillfillthecistern.$

How can I find that how many 3 digit numbers are there which leave a remainder 3 on division by 7?

Number of real roots of x(x+2)(x^{​​​​​​2} -1)-1=0 are?

Explain the location of roots with explain and with all conditions and cases to that applied

Determine the square root of $x^4-6x^3+19x^3-30x+25$

A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of Rs. 498.96. If the cost of whitewashing is Rs. 2 per square meter, find the volume of the air inside the dome.
$[Assume\pi =\frac{22}{7}]$

The value of p for which the quadratic equation $2p{x}^2+6x+5=0$ has real and distinct roots is :

On plotting the points O(0,0), A(3,0), B(3,4),C(0,4) and joining OA, AB, BC and CO, which of the following figure is obtained?

In the given figure, O is the centre of the circle and A, B, C

are points on it, then $\angle OAC+\angle ABC=$___.

Which of the following polynomials are trinomials?

(1) p(x) = $x+x^2+\pi$

(2)q(x)= $\sqrt{2}+x-x^2$

(3) r(x) = $x^3+x^2+1$

(4)t(y) = $y^4+y+5$

Construct a triangle ABC, with AB= 6 cm,AC=BC=9 cm.Find a point 4 cm from A and equidistant from B and C.

A conical pit is dug into the earth up to the depth of 12 m. It is then closed with a lid of diameter 7m which exactly fitted on it. Find the volume of petrol that can be filled in the conical pit.

A letter of the English alphabet is chosen at random. Determine the probability that the letter chosen is a consonant.