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$\text{If}cosA+co{s}^{2}A=1,\text{prove that}si{n}^{12}\theta +3si{n}^{10}\theta +3si{n}^8\theta +si{n}^6\theta +2si{n}^4\theta +2si{n}^2\theta -2=1$

Prove that:

$\frac{1+cos\theta -si{n}^2\theta }{sin\theta (1+cos\theta )}=cot\theta$

Solve the following equations by using formula

(1) a² − 2a − 4 = 0

(2) x² − 8x + 1 = 0

(3) m² − 2m − 2 = 0

(4) k² − 6k = 1

(5) 2y² + 6y = 3

(6) 8r² = r + 2

(7) p = 5 − 2p²

(8) 2z² + 7z = 4 = 0

(9) 3b² + 2b = 2

(10) a² = 4a + 6

Find the LCM and HCF of the following integers by applying the prime factorisation method.

Two persons divided hundred rupees between them and one got ten rupees more than the other. How much did each get?

The area(in $\text{sq.units}$) bounded by the curve $y=(x+1)(x+2)(x-1)$ and $x-$axis, lying between the ordinates $x=-2$ and $x=1,$ is:

Which of the following cannot be the probability of an event?

If $\left[\begin{array}{cc}{x}^2-2x+1& x-2\\ 1-x^2+3x& 1-x^2\end{array}\right]=A{x}^2+Bx+C,$ where $A,B$ and $C$ are matrices, then $B+C$ equals to

The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm, and the other dimensions are as shown.

Find the total surface area of the solid.

Show that one and only one out of n,n+2,n+3,n+4 is divisible by 3, where n is a positive integer

The minimum number of parameters required to prove similarity between two triangles is ____.

Find the sum of

(i) all integers between $100$ and $550$, which are divisible by $9$.
(ii) all integers between $100$ and $550$ which are not divisible by $9$.
(iii) all integers between $1$ and $500$ which are multiples of $2$ as well as of $5$.
(iv) all integers from $1$ to $500$ which are multiplies $2$ as well as of $5$.
(v) all integers from $1$ to $500$ which are multiples of $2$ or $5$.

In a box, there are $3$ blue, $4$ red, and $5$ green balls. What is the probability of picking up four balls such that there are $2$ red balls and $1$ ball each of blue and green?

Construct a transverse common tangent to two circles of radii 4 cm and 3 cm whose centres are 9 cm apart.

In the given figure BD = DC and $\angle CBD={30}^{\circ }$, Find $\angle BAC$

What comes next in the Arithmetic progression: 800, 1000, 1200, 1400, ...?

A boat goes 35 km upstream and 42 km downstream in 11 hours. In 14 hours, it can go 43 km upstream and 59 km down-stream. To determine the speed of the stream and that of the boat in still water , express the information in the form of equations of the type ax + by + c = 0

Find the sum of the roots of the equation $x^2–8x+2=0$.

Zeroes of quadratic polynomials are given on the left. Match them with the respective quadratic polynomials.

A tax burden which can be shifted to another person and the impact and the incidence of tax lies on a different person is called

A rectangle having the longer side as 9 cm makes an angle of ${30}^{\circ }$ with the diagonal. The length of the other side and the area of the rectangle will be equal to

Given: 15 cot A = 8, find sin A and sec A.

Half the perimeter of a rectangular garden, whose length is 4 m more than it's breadth, is 16 m, then the dimensions of the garden are .

The weekly wages (in $Rs.$) of $30$ workers in a factory are.

$830,835,890,810,835,836,869,845,898,890,820,860,832,$ $833,855,845,804,808,812,840,885,835,835,836,$ $878,840,868,890,806,840$

Using tally marks make a frequency table with intervals as $800-810,810-820$ and so on.

Show that any number of the form 6raise to x,XEN can never end with digit zero .

What is the probability of a sure event?

D, E, F are the mid points of the sides BC, CA and AB respectively of $△$ ABC. Then $△$ DEF is congruent to triangle –

Question 47

Additional expenses made after buying an article are included in the cost price and are known as Value Added Tax.