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The point (-2, 0) on reflection in a line is mapped to (2, 0) and the point (5, -6) on reflection in the same line is mapped to (-5, -6).

(i) State the name of the mirror line and write its equation.

(ii) State the co-ordinates of the image of (-8, -5) in the mirror line.

The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1

Pintu takes 6 days more than those of Nishu to complete a certain work .If they work together they finish it in 4 days. How many days would it take to complete the work if they work alone.

If $3\tan \theta +\cot \theta =5cosec\theta$, then $\theta =$ __ (in degrees) [$0^{\circ }<\theta <{90}^{\circ }$]

In the given figure, ABC is a right-angled triangle, right angle is at B. Find lengths AB and BC and hence AC.

Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1m and base radius 3.5cm? (Take π=22/7) [3 MARKS]

Which of the following numbers can never be an outcome for the single roll of an unbiased die?

How many terms are identical in two arithmetic progressions: 2, 4, 6, 8, ..... up to 100 terms and 3, 6, 9, ....up to 80 terms?

How many terms of an A.P. 7 , 14 , 21 ....... are needed to give sum 5740.

The value of the observation having greatest frequency is called____.

If the roots of the cubic equation $a{x}^3+b{x}^2+cx+d=0$ are in G.P., then ___.

Find the unknown length x of the following figure.

The equation of a line passing through the intersection of lines x = 0 and y = 0 and through the point (2, 2) is ________.

Question 7
If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of k is
(a) $-\frac{5}{4}$
(b) $\frac{1}{2}$
(c) $\frac{15}{4}$
(d) $\frac{3}{2}$

A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... The total length of such a spiral made up of thirteen consecutive semicircles is ___ ( Round off to the nearest 10)

Two solid cones A and B are placed in a cylindrical tube as shown in the figure below. The ratio of their capacities is 2:1. Find the volume of the remaining portion of the cylinder.

In an equilateral triangle ABC, find the value of sin ${30}^{\circ }$ and cos ${30}^{\circ }$

If discriminant of a quadratic equation < 0, how many distinct real roots does it have?

Given below is a combination figure of square ABCD of side 26cm and four circles. Find the area of the shaded region.

A regular die numbered 1 - 6 is rolled 50 times and the observations are taken in a table :

$\begin{array}{cc}\text{Score}& \text{Frequency}\\ 1& 15\\ 2& 9\\ 3& 8\\ 4& 5\\ 5& 6\\ 6& 8\end{array}$

Calculate the Median.

If the points (1,2), (0,0) and (a,b) are collinear, then the area of the triangle formed by these points is ____.

1. 27

Komal has a recurring deposit account in a post office of Rs 500 per month at the rate of 9% per annum for 4 years. Find the maturity value.

Let $f\left(x\right)=a{x}^2+bx+c$. Then, match the following.
$\begin{array}{cc}\text{a. Sum of roots of f(x) = 0}& 1.–\frac{b}{a}\\ \text{b. Product of roots of f(x) = 0}& 2.\frac{c}{a}\\ \text{c. Roots of f(x) = 0 are real and distinct}& 3.b^2–4ac=0\\ \text{d. Roots of f(x) = 0 are real and identical.}& 4.b^2–4ac>0\end{array}$

$\Delta ABC$ and $\Delta DBC$ lie on the same side of BC, as shown in the figure. From a point P on BC, PQ || AB and PR || BD are drawn, meeting AC at Q and CD at R respectively. Prove that QR || AD.

In the figure given below, AC is a transverse common tangent to two circles with centres P and Q and of radii 6 cm and 3 cm respectively.

Given that AB = 8 cm, calculate PQ.

How many of the following are matched correctly?

$\begin{array}{cc}\text{Degree measurement}& \text{Radian measurement}\\ \text{(A)}{180}^{\circ }& \text{(1)}\pi \\ \text{(B)}{60}^{\circ }& \text{(2)}\frac{\pi }{6}\\ \text{(C)}{0}^{\circ }& \text{(3)}0\\ \text{(D)}{120}^{\circ }& \text{(4)}2\frac{\pi }{6}\\ \text{(E)}{360}^{\circ }& \text{(5)}2\pi \\ \text{(F)}{30}^{\circ }& \text{(6)}\frac{\pi }{3}\\ \text{(G)}{90}^{\circ }& \text{(7)}\frac{\pi }{2}\\ \text{(H)}{45}^{\circ }& \text{(8)}\frac{\pi }{4}\\ \text{(I)}{270}^{\circ }& \text{(9)}3\pi \end{array}$
___

The ratio of $\frac{BC}{C{C}^{\prime }}$ is 3:5. What will the ratio of corresponding sides be if triangles ABC and A'BC' are similar? Given that BC and BC' lie
on the same ray BY.

In the equation ax+by+c=0, if y= $\frac{(cx+d)}{b}$ then x =

Calculate the area of the shaded region in the figure given in $c{m}^2.$

A person on tour has Rs.10800 for his expenses. If he extends his tour by 4 days, he has to cut down his daily expenses by Rs.90. Find the original duration of the tour.

Find the coordinates of the points of trisection of the line segment joining the points A(7, -2) and B(1, -5).

If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.

The radius of a wheel is 0.25 m. How many revolutions will it make in covering 11 km ?

(a) 2800 (b) 4000 (c) 5500 (d) 7000

Prove the following trigonometric identities:

$\frac{1}{secA-1}+\frac{1}{secA+1}=2cosecAcotA$

Which of the following are quadratic equations?
$\left(i\right)x^2+6x-4=0$
($ii)\sqrt{3x^2}-2x+\frac{1}{2}=0$
$\left(iii\right)x^2+\frac{1}{x^2}=5$
$\left(iv\right)x-\frac{3}{x}=x^2$
$\left(v\right)2x^2-\sqrt{3x}+9=0$
$\left(vi\right)x^2-2x-\sqrt{x}-5=0$
$\left(vii\right)3x^2-5x+9=x^2-7x+3$
$\left(viii\right)x+\frac{1}{x}=1$
$\left(ix\right)x^2-3x=0$
$\left(x\right){(x+\frac{1}{x})}^2=3(x+\frac{1}{x})+4$
$\left(xi\right)(2x+1)(3x+2)=6(x-1)(x-2)$
$\left(xii\right)x+\frac{1}{x}=x^2,x\ne 0$
$\left(xiii\right)16x^2-3=(2x+5)(5x-3)$
$\left(xiv\right)(x+2{)}^3=x^3-4$
$\left(xv\right)x(x+1)+8=(x÷2)(x-2)$

From a solid right circular cylinder of height $2.4cm$ and radius $0.7cm$ a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.

Sum of the first 14 terms of an AP is 1505 and its first term is 10. Find its 25th term.

Find the 8th term from the end of the AP = 7 , 10, 13, ..., 184.

If the sum of the zeros of the quadratic polynomial $k{x}^2-3x+5$ is 1, write the value of k.

A card is drawn from a well-shuffled deck of playing cards. Find the probability of getting a black card which is not a face card and ace?

The distance between the tops of two trees 20 m and 28 m high is 17 m. The horizontal distance between the trees is