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The expression $a^3+b^3+c^3-3abc$ can be expressed as a product of two expressions. What is the product?

Find the roots of the quadratic equation $\sqrt{2}{x}^2+7x+5\sqrt{2}$ = 0 using factorization method.

Question 177(iv)

Find it
${\left(\frac{-6}{7}\right)}^{x-7}=1$

If 16 cotA=12, find sinA+cosA÷sinA-cosA

If -2 is a zero of the polynomial $3x^2+4x+2k$ then find the value of k.

The value of $\sum _{r=1}^{n}log\left(\frac{a^r}{b^{r-1}}\right)$ is

The shape of a gulli in the gulli-danda game is a combination of

(a) a cone and a cylinder

(b) two cylinders

(c) two cones and a cylinder

(d) two cylinders and a cone

In the given figure, OABC is a square of side 7 cm. If COPB is a quadrant of a circle with centre C find the area of the shaded region.

The angles of a triangle are in A.P. The greatest angle is twice the least. Find all the angles.

A cylinder with base radius 8 cm and height 2 cm is melted to form a cone of height 6 cm. Calculate the radius of the base of the cone.

An arithmetic sequence has its $5^{th}$ term equal to 22 and its ${15}^{th}$ term equal to 62. Find the ${100}^{th}$ term

The areas of two similar triangles are 12 $c{m}^2$ and 48 $c{m}^2$. If the height of the smaller one is 2.1 cm, then the corresponding height of the bigger one is

If the line $(3x+14y+7)+k(5x+7y+6)=0$ is parallel to the y-axis, then the value of $k$ is

Question 9

$\frac{1}{5}÷\frac{4}{5}$ is equal to

(a) $\frac{4}{5}$
(b) $\frac{1}{5}$
(c) $\frac{5}{4}$
(d) $\frac{1}{4}$

Attempt this question on graph paper.

(a) Plot A (3, 2) and B (5, 4) on graph paper.

(b) Reflect A and B in the x-axis to A' and B' respectively. Plot these points also on the same graph paper.

(c) Write down :

(i) the geometrical name of the figure ABB' A';

(ii) the measure of angle ABB';

(iii) the image A" of A, when A is reflected in the origin.

(iv) the single transformation that maps A' to A".

Pavan filled water in a cylindrical vessel of radius 7 cm and height 14 cm. Then he gently dropped a spherical ball of radius 0.7 cm. Find the height the water will be raised to when the spherical ball is dropped into it?

Raju wants to see Avengers Infinity war on the 1st day of release i.e., after 20 days. The money required is Rs. 500 and at the end of 20 days he was unable to make 500. Money he saved per day is (Assume he saved the same amount every day)

Evaluate 1 – 2$sin\theta$ $cos\theta$, if $sin\theta$ = $cos\theta$.

Using factor theorem the factors of $y^3-2y^2-y+2$ is

Which of the following trigonometric functions have the same value?

The mean of 5 consecutive natural numbers is 10. What is the largest of the five?

a circular field has a circumference of 480 km. Three cyclists Abishek, Varun and Gautham start together and can cycle at speeds of 10 km/hr, 12 km/hr, 15 km/hr respectively, round the circular field.After how many hours will they meet again at the starting point?

Why 6/15 has a terminating expansion and 64/455 has a non terminating expansion

A man bought 750 share, each face of value of ₹10, of a certan business concern and during the first year, receives ₹675 as dividend on his shares. Find the rate of dividend.

If aabb is a 4 digit number and also a perfect square then the value of a+b is?

In a particular year , shopkeeper purchased goods worth ₹ 4,00,000 and paid a total tax of ₹ 40000. During the same year, he sold all the goods purchased as below :
(i) goods worth ₹ 25,000 at 5% tax,
(ii) goods worth ₹ 3,60,000 at 12% tax and
(iii) goods worth ₹ 15000 which are exempted from tax.
Calculate the tax liability (under VAT) for the year under consideration.

Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle drawn. Draw two tangents PA and PB to the given circle and measure the length of each tangent.

Describe the locus for questions 1 to 13 given below:

The locus of a point in space, which is always at a distance of 4 cm from a fixed point.

A person wanted to distribute 96 apples and 112 oranges among poor children in an orphanage. He packed all the fruits in boxes in such a way that each box contains fruits of the same variety, and also every box contains an equal number of fruits.
(i) Find the minimum number of boxes in which all the fruits can be packed?
(ii) Which concept have you used to find it?
(iii) Which value of this person has been reflected in above situation?

From an external point $T,$ two tangents $TP$ and $TQ$ are drawn to a circle having it's center at O. Prove that $\angle PTQ=2\angle OPQ$

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:

(i) Equidistant from A and B.

(ii) Always 4 cm from the line AB.

(iii) Mark two points X and Y, which are 4 cm from AB and equidistant from A and B, Name the figure AXBY.

Find the values of A and B for which the following pair of linear equations infinitely many solutions:

2x+3y=7

(a+b)x+(2a-b)y=21

The ‘Shilling Series’ was popular in which country?

Solve for X and Y using elimination method

X/3 + Y/4 = 11

5X/6 - Y/3 + 7 = 8

A tent is of the shape shown in the given figure. The area of the floor under the tent is 64π m². (Use = π = ²²/₇)

If 1 square metre of canvas costs Rs 5, then what is the cost of the canvas required for making the tent?

If zeros of f(x)= ax³+3bx²+3cx+d are in arrithmatic progression , prover that 2b³-3abc+a²d=0

A circular disc of radius 6 cm is divided into three sectors with central angles 90^o, 120^oand 150^o. The ratio of the areas of the three sectors is

State Sin45°+ Sin45° = Sin 90° as true or false and give reason for the same.

If the first term of a G.P. is 1 and the sum of the third and fifth term is 20, find its common ratio.

Degree of the polynomial of 4x⁴+0x³+0x raise to 5+5x+7

Find the common difference of the given AP.

5, 8, 11, 14, ...

Volume of a sphere is directly proportional to the __ of its radius.

Find the total number of outcomes in a toss of n coins :
N = 1
___
N = 2
___
N = 3
___ = ?

In the given figure, AB is the diameter and DC is perpendicular to AB such that AC = 9 units and CB = 4 units. Calculate the length of perpendicular DC.

5 defective glasses are accidentally mixed with 20 good ones. The good and the defective ones look the same from the outside. If a glass is picked at random, what is the probability that the glass picked is non-defective?