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$\Delta ABC\sim \Delta PQR$ and ar $\Delta ABC$ = $4ar\Delta PQR$. If BC = 12 cm, find QR.

The mid point of 2 co-ordinates (x,y) and (a,b) is

M and N are points on the sides PQ and PR respectively of a $\Delta PQR$. For each of the following cases, whether MN || QR:
(i) PM = 4 cm, QM = 4.5 cm, PN = 4 cm, NR = 4.5 cm
(ii) PQ =1.28 cm, PR = 2.56 cm, PM = 0.16 cm, PN = 0.32 cm

Which of the given equations are quadratic?

In the given figure, there are two circles with the centres O and O' touching each other internally at P. Tangents TQ and TP are drawn to the larger circle and tangents TP and TR are drawn to the smaller circle . Find TQ : TR

If the sum of n terms of an A.P in $nP+\frac{1}{2}n(n-1)Q$, where P and Q are constants, find the common difference.

When was the opening ceremony of the 2012 London Summer Olympics held?

In the given figure , PA and PB are tangents of a circle with centre O. If the radius of the circle is r ,

then OP $\times$ OQ = _____.

Match the following events with corresponding probability on tossing two coins simultaneously.

If sin $\theta$ = x, write the value of cot $\theta$.

A well with inner radius 4 m is dug 14 m deep. Earth taken out of it has been spread evenly all around a width of 3 m it to form an embankment. Find the height of the embankment.

If the sixth term of an AP is zero then show that its 33rd term is three times its 15th term.

Find the distance between the points :

(i) A(9, 3) and B (15, 11) (ii) A (7, -4) and B(-5, 1)

(iii) A(-6, -4) and B(9, -12) (iv) A (1, -3 ) and B (4, -6)

(v) P (a+b, a-b) and Q (a-b, a+b)

(vi) P (a sin α, a cos α) and Q (a cos α, - a sin α)

Show that : $\frac{1+sinA}{cosA}+\frac{cosA}{1+sinA}=\frac{2}{cosA}$

If $D\ne 0$ and at least one of $D_1,D_2,D_3$ is not 0 then according to Cramer's rule the system of linear equations will have

In the given figure, ∠ABC = ${90}^{\circ }$ and BM is a median, AB = 8cm and BC = 6 cm. Then, length BM is equal to -

(TanA +cosec B)^2-(cot B-sec A)^2=2tanAcotB(cosecA+secB)

The inner radius of a hollow iron sphere is $9cm$. If the iron is $1cm$ thick, find the volume of iron used in the sphere.

A fraction becomes $\frac{4}{5}$ when 1 is added to each numerator and denominator. However, if we subtract 5 from each then it becomes $\frac{1}{2}$. Find the fraction.

1. 102.66

If a, b and c are in A.P. and also in G.P., show that : a = b = c .

From each corner of a square of side 4cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in the figure. Find the area of the remaining portion of the square. [2 MARKS]

In what ratio is the line joining A(0, 3) and B(4,-1) divided by the x-axis? Write the coordinates of the point where AB intersects the x-axis.

A card is drawn from a deck of 52 cards. What is the probability of not getting an ace?

If length of three sides of a trapezium other than base are equal to $5cm$, then the base length of the trapezium when the area is maximum is

Find the value of x, y in the pair of equation given below, where $x\ne 0\&y\ne 0$.
$\frac{2}{x}+\frac{3}{y}=13$
$\frac{5}{x}-\frac{4}{y}=-2$

In the graph of y = p(x) below for some polynomial p(x), the number of zeroes is

$\begin{array}{cc}ColumnA& ColumnB\\ 1.\text{Area}& a.67m\\ 2.\text{Perimeter}& b.Rs.6/m^2\\ 3.\text{Cost per}{m}^2& c.100m^2\\ & d.Rs.6m^2\\ & e.100/m^2\end{array}$

Which of the following options show the correct match of parameters in column A with possible values in column B?

The expansion for the identity ${(a–b)}^2$ is .

In $\Delta$ABC, if a triangle is formed by joining the midpoints of the sides, the area of the triangle is___ times the area of $\Delta$ ABC.

In $\Delta$ ABC, the bisector AX of $\angle$A intersects BC at X. XL $\perp$ AB and XM $\perp$ AC are drawn. Is XL = XM?

Convert the given class intervals in exclusive form.

In Fig., a circle inscribed in triangle ABC touches its sides AB,BC and AC at points D,E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.

Find the sum of the integers which are divisible by 5 or 7 and lie between 1 and 100.

Which of the following is/are the types of common tangents?

What is the equation of polar of the point (1, 2) with respect to the circle $x^2+y^2+8x+2y+1=0$

A(6,4), B(8,4), C(10,6) and D(2,8) are the vertices of quadrilateral ABCD. Then the point of intersection of its diagonals is

Two buildings on a plane ground are 30 m apart. From the top of the smaller building, one sees the base of the other building at an angle of depression of ${60}^{\circ }$ and its top at an elevation of ${35}^{\circ }.$ The height of the bigger building is

$\left[\begin{array}{c}Tan{60}^{\circ }=1.7\\ Tan{35}^{\circ }=0.7\end{array}\right]$

Let CD $\&$ AB be the smaller and taller building respectively.

DE = AC = 30 m