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The solutions of the equation $(3|x|-3{)}^2=|x|+7$ which belongs to the domain of definition of the function $\sqrt{\left\{x(x-3)\right\}}$ are given by:

$\frac{1}{1+a{}^{\left(n-m\right)}}+\frac{1}{1+a{}^{\left(m-n\right)}}=?$

Find a point on y = 4 where ordinate and abscissa are the same.

From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid point of BC.

Prove that :

(i) $\Delta$ DCE $\cong \Delta$ LBE

(ii) AB = BL.

(iii) AL = 2DC

If f (x) is a cubic polynomial such that f (1)=1,f (2)=2,f (3)=3 and f (4)=16. Find the value of f (5).

In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and $\angle$ DCB = ${120}^o$. Calculate :

(i) $\angle$ DAB, (ii) $\angle$ DBA,

(iii) $\angle$ DBC, (iii) $\angle$ ADC.

Also, show that the $\Delta$ AOD is an equilateral triangle.

In the given figure, PQR is a triangle and S is any point in its interior. Then which of the following option is correct?

The pairs of linear equations which have the unique solution x = 2, y = –3 are

Question 1 (d)

Find the area of each of the following parallelograms:

It is required to paint a glass cylindrical chimney of height 20 m and base diameter 14 m. What is the area to be painted? [2 MARKS]

A sum of Rs. 44,200 is divided between John and Smith, 12 years and 14 years old respectively, in such a way that if their portions be invested at 10 percent per annum compound interest, they will receive equal amounts on reaching 16 years of age.

(i) What is the share of each out of Rs. 44,200 ?

(ii) What will each receive, when 16 years old ?

ABCD is a square and the diagonals intersect at O. If P is a point on AB such that AO=AP, prove that 3(angle POB)=(angle AOP).

The length of the line that marks out a circle and its region is the

An open metallic conical tank is 6m deep and its circular top has a diameter of 16m.find the cost of tin plating in its inner surface at the rate of ₹0.8 per 100cm².(take π=3.14)

If $lo{g}_{12}27=a$, then $lo{g}_{6}16=$

Mr. Raj deposited Rs 800 per month in a recurring account for a time period of 1 year at the rate of 10% per annum. What is the amount that he will receive at the time of maturity?

Two rectangular boxes have the same height and length, but different widths as shown in the figure.

The difference in the volumes of the boxes is 360 cm³. What is the height of the boxes?

The lateral surface area of a cube is 100 m². The volume of the cube is:

If the three sides of the triangle are 11m,15m, and 6m, what is the semiperimeter of the triangle?

If A = {1, 3, 6}, B = {4, 8} then A x A is

Let r1 and r2 be the remainders when the polynomials

p(x)= x3+x2-5kx-7 and q(x)=x3+kx2-12x+6

are divided by x+1 and x-2 respectively.

Find the value of k if 2r1-r2=10

Which of the following options the point P represents (3,2)?

A boy starts running from origin towards east for 4km and takes a left turn towards north and runs another 6km. If the east direction is towards the positive direction of the X-axis, what would be the position of that boy when represented on co-ordinate axes?

In the given figure, O is the centre of the circle. Find the value of $X$.

What do we understand by the term 'statistics'?

Which of the following is a binomial?

If the length of the hypotenuse in the given triangle is 1, what is the value of side AB?

Factorise: x⁷y + xy⁷

A circum-circle is drawn around a right triangle PQR. The height and the base of the triangle are 5 cm and 12 cm, respectively. What would be the area of the shaded region?

In a right triangle ABC, right-angled at B, the longest side is ___?

In the given figure, l || m and a transversal t cut them. If $\angle 1={120}^{\circ }$, find the measure of each of the remaining marked angles.

Factorise:
$5\sqrt{5}{x}^2+20x+3\sqrt{5}$

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
$\left(px\right)=x^3-6x^2+2x-4,g\left(x\right)=1-\frac{3}{2}x$

A ray stands on a line, then the sum of the two adjacent angles so formed is_______.

If $(2^3{)}^2=4^x,then{3}^x$ =

1. 140

D, E and F are the mid point of sides BC , CA,AB of a triangle ABC
1. BDEF is a parallelogram
2. $ar\left(DEF\right)=\frac{1}{4}ar\left(ABC\right)$
3. $\left(BDEF\right)=\frac{1}{2}ar\left(ABC\right)$