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The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is

The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction. ​

In a $\Delta ABC$, BD and CE are the altitudes. Prove that $\Delta ADB$ and $\Delta AEC$ are similar. Is $\Delta CDB\sim \Delta BEC$ ? [4 MARKS]

What is the area of the square inscribed in a circle with a circumference of 18.84 cm?

If the sum of four consecutive terms of an AP is 20 and the sum of their squares is 120, then the numbers are .

Find the square root of 10 using geometric method.

x = 7, y = 3 is a solution for which of the following?

A container made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the metal sheet used, if it costs ₹ 5 per 100 $c{m}^2$. (Take $\pi$= 3·14)

The number of nodes present in 3d is: _____

Question 6
In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in Fig. 12.24. Find the area of the design.

Find the equation of the circle passing the point (1, 2) and touching the line 2x + y - 1 = 0 at the point (1, -1).

If the hypotenuse of a right-angled triangle is 13 and it's inradius is 5, then it's area = _____.

Determine which of the following polynomials have $(x+1)$ as a factor: [2 MARKS]
(i) $x^3+x^2+x+1$
(ii) $x^4+x^3+x^2+x+1$

P and Q are points on sides CA and CB respectively of Δ ABC right angled at C. Prove that ${AQ}^2$ + ${BP}^2$ = ${AB}^2$ + ${PQ}^2$ [4 MARKS]

For what value of k are the points A(k, 2 – 2k) ,B(–k + 1, 2k) and C(–4 – k, 6 – 2k) are collinear ? [4 MARKS]

The perfect square binomial obtained by adding a constant to the expression : x² – 18x is

If the roots of the equation, $x^2+3x-18=0$ are $-6,3$ then the roots of the equation $2(x^2+3x-18)=0$ are

The value of a for which the lines $x=1$, $y=2$ and $a^{2}x+2y-20=0$ are concurrent is:

The lines joining the points of intersection of curve $5x^2+12xy-8y^2+8x-4y+12=0$ and the line x - y = 2 to the origin, makes the angles with the axes

Question 1 (i)
In which of the following situations does the list of numbers involved make an arithmetic progression and why?
(i) The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

$\text{If in}△CAB\text{and}△FED,$

$\frac{AB}{EF}=\frac{BC}{FD}=\frac{AC}{ED}$,

$\text{then which of the following is true?}$

If $log\frac{x}{y}+log\frac{y}{x}=log(x+y)$, then which of the following equations is true?

A) $2$
B) $\frac{1}{2}$
C) $-\frac{1}{2}$
D) $-2$

Solve the following pair of linear equations by elimination method : 3x + 2y = 8 and 2x – y = 3. [2 MARKS]

If $D,E,F$ are respectively the mid points of the sides $BC,CA$ and $AB$ of $△ABC$ and the area of $△ABC$ is $24$ sq. cm, then the area of $△DEF$ is -

If the 10th term of an A.P. is 21 and the sum of its first ten terms is 120, find term. its nth term.

Find the area of a quadrant of a circle whose circumference is 44 cm.

Solve the following systems of equations graphically:

x - 2y = 5

2x + 3y = 10

Solve the following systems of equations:

$\frac{4}{x}+3y=14$

$\frac{3}{x}-4y=23$

In the following diagram, lines l,m and n are parallel to each other. Two transversals p and q intersect the parallel lines at points A,B,C and P,Q, R as shown. Prove that : $\frac{AB}{BC}=\frac{PQ}{QR}$

The sum of the $2^{rd}$ term and the $7^{th}$ term of an A. P. is 30. If its ${15}^{th}$ term is 1 less than twice of its $8^{th}$ term, find the A. P.

Which of the following statements are true?

In an AP given a=8,a_n=62,S_n=210,find n and d.

The fourth proportional to 5, 8, 15 is ___ .

There are three figures of areas $x^2,12x$ and $z$ respectively, as shown. Figures A and C are squares while B is a rectangle, with the length of one side is $x$. What should be the value of $z$ so that all the 3 figures can be arranged to form a square of side $(x+6)$?

In what ratio does the point (-4, 6) internally divide the line segment joining the points A(-6, 10) and B(3, -8).

In the figure shown below, $\frac{PS}{SQ}=\frac{PT}{TR}$ and $\angle PST=\angle PRQ.$ Then $△PQR$ is __ triangle.

If $x>1,y>1,z>1$ are in GP, then $\frac{1}{1+lnx},\frac{1}{1+lny},\frac{1}{1+lnz}$ are in