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If the LCM of two polynomials is $(x-1{)}^2(x-2{)}^2$ and their HCF is $(x-1)(x-2)$, then the product of the polynomials is:

The line 4 – 3y + 12 = 0 meets the y-axis at A. Write down the coordinates of A.

Determine the equation of the line passing through A and perpendicular to 4 – 3y + 12 = 0.

Tangents from a point P are drawn onto a circle with angle between them as ${120}^{\circ }$ . The tangents from P meet the circle at A and B. If a line is drawn from point P through the center of the circle O, the value of $\angle$POA is

The length of minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6:05 am and 6 : 40 am.

Priya withdrew Rs 2,500 at the end of each month. The partnership deed provides for charging the interest on drawings 12$\%$ p.a. Calculate interest on Priya’s drawings for the year ending 31st December, 2017

Directions:- Study the following information carefully to answer the question given below.

Twelve persons are sitting in two rows containing six people, each in such a way that there is an equal distance between adjacent persons. In row 1 - A, B, C, D, E and F are seated and all of them are facing South but not necessarily in the same order. In row 2 - P, Q, R, S, T and V are seated and all of them are facing West but not necessarily in the same order. D sits third to the right of B. Either D or B sits at one of the extreme ends of the line. The one who is adjacent to B sits second to the right of T. Two persons sit between Q and V. Neither Q nor V sits at the extreme end of the line. The immediate neighbour of Q is eighth left of A. C and E are immediate neighbours of each other. R sits second to the left of T. E is fourth to the left of the immediate neighbour of S.

Who amongst the following sits at extreme ends of the rows?

If $A$ and $B$ are two sets such that $n\left(A\right)=3$ and $n\left(B\right)=5,$ then $n(A\times B)=$ .

In Fig. 7.142, if $AB\perp BC,DE\perp BC$ and $DE\perp AC$, prove that $\Delta CED\sim \Delta ABC$.

Which type of ogive curve would be best suitable to determine the median?

For less than type ogive type L , for more than type ogive type M

$$\begin{array}{cc}Time& TotalNumberofQuestions\\ <10& 2\\ <20& 5\\ <30& 10\\ <40& 15\\ <50& 17\\ <60& 25\end{array}$$

The radii of the circular bases of a frustum of a right cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.

While boarding an aeroplane, a passenger got hurt, The pilot showing promptness and concern, made arrangements to hospitalise the injured and so the plane started late by 30 minutes. To reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hour. Find the original speed of the plane.
Do you appreciate the values shown by the pilot, namely promptness in providing help to the injured and his efforts to reach in time?

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

A right cylinder and a right circular cone have the same radius and same volumes.The ratio of the height of the cylinder to that of the cone is

Find the 10th term from the end of the A.P. 8,10,12,...,126.

In the frollowing determine whetehr the given quadratic equations have real roots
$\left(i\right)16x^2=24x+1\left(ii\right)x^2+x+2=0\left(iii\right)\sqrt{3}{x}^2+10x-8\sqrt{3}=0\left(iv\right)3x^2-2x+2=0\left(v\right)2x^2-2\sqrt{3}x+3=0\left(vi\right)3a^2{x}^2+8abx+4b^2=0,a\ne 0\left(vii\right)3x^2+1\sqrt{3}x-5=0\left(viii\right)x^2-2x+1=0\left(ix\right)2x^2+5\sqrt{3}x+6=0\left(x\right)\sqrt{2}{x}^2+7x+5\sqrt{2}=0\left(xi\right)2x^2-2\sqrt{2}x+1=0\left(xii\right)3x^2-5x+2=0$

Solve for x and y:

$0.4x+0.3y=1.7,0.7x-0.2y=\mathrm{0.8.}$

Find the values of $a\&b$ such that it satisfies following linear equations:
$\frac{4}{a+b}+\frac{2}{a-b}=5\frac{1}{a+b}+\frac{1}{a-b}=3$

If matrix
$P=\left(\begin{array}{ccc}0& 1& -1\\ 4& -3& 4\\ 3& -3& 4\end{array}\right]=Q+R$, where Q is symmetric matrix and R is skew symmetric matrix. Then find matrix Q and R.

If the radii of the circular ends of a bucket 28 cm high, are 28 cm and 7 cm, find its capacity and total surface area.

In the given figure, $△ABC$ is right-angled at A. Find the area of the shaded region if AB = 6 cm, BC = 10 cm and O is the centre of the incircle of $△ABC$. [Take $\pi$ = 3.14 ]

Find the sum of the first 15 terms of each of the following sequences having nth term as
(i) $a_n=3+4n$ (ii) $b_n=5+2n$ (iii) $x_n=6-n$ (iv) $y_n=9-5n$

Show that the roots of the equation $x^2+px-q^2=0$ are real for all real values of p and q

If $f:R\to R$ is a twice differentiable function such that $f"\left(x\right)>0$ for all $xϵR$, and $f\left(\frac{1}{2}\right)=\frac{1}{2}$, f(1) = 1, then,

Find the missing variable from a, d, n and $a_n$, where a is the first term, d is the common difference and $a_n$ is the $n^{th}$ term of AP.
(i) a= 7, d = 3, n = 8
(ii) a = -18, n= 10, $a_n$=0
(iii)d = -3, n = 18, $a_n$=−5

Given the linear equation 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is

(i) intersecting lines (ii) Parallel lines (iii) coincident lines

A part of monthly expenses of a family is constant and the remaining vary with the number of members in the family. For a family of 4 persons. the total monthly expenses are Rs. 10.400: whereas for a family of 7 persons. the total monthly expenses are Rs. 15,800. Find the constant expenses per month and the monthly expenses on each member of a family.

Let the constant monthly expenses be Rs. x and for each member of the family the monthly expenses be Ra. y.

$\therefore x+4y=10,400$ and $x+7y=15,800$.

Question 123

A student used the proportion $\frac{n}{100}=\frac{5}{32}$ to find 5 % of 32. What did the student do wrong ?

Ashok and Sandeep invested Rs 18000 each in buying shares of two different companies, Ashok buys 7.5%. Rs 100 share at a discount of 20%, whereas Sandeep buys Rs 50 share at a premium of 20%. If both receive equal dividend at the end of the year, then the rate of dividend received by Sandeep is ___

In the figure, the $\angle ABC=30°$. If $CB=18m$ , then AC = ________.

In the given figure, RS is the diameter of the circle. NM is parallel to RS and $\angle MRS={29}^o$. Calculate $\angle RNM$

If $\alpha ,\beta$ are roots of the equation $x^2+lx+m=0,$ write an equation whose roots are $-\frac{1}{\alpha }and-\frac{1}{\beta }.$

The length of the tangent from a point A to a circle, of radius 3 cm, is 4 cm. Find the distance of A from the center of the circle.

A Bangle of inner radius 2.1 cm and thickness 0.7 cm and height 0.5 cm. Find the volume of material used for bangle.(approx)

If d is the HCF of 45 and 27, find x and y satisfying d=27x+45y

In a hostel, 60% of the students read Hindi newspaper 40% read English newspaper and 20% read both read both Hindi and English newspapers. A student is selected at random
Find the probability that he/she reads neither Hindi nor English newspapers.

If he/she reads Hindi newspaper, find teh probability that she reads English newspaper.

IF he/she reads Hindi newspaper, find the probability that she reads English newspaper.

Question 1 (iv)
Without actually performing the long division, state whether $\frac{15}{1600}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

The angle of elevation of the top of tower from two points at distance of $\sqrt{3}$ and $\sqrt{48}$ from base of the tower and in the same straight line with it is complementary. then height of tower is

A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. find the volume and the curved surface area of the solid so formed.

Find the sum of n terms of the series (4- 1/n)+(4- 2/n ) + (4 - 3/n ) +.....

If P (-5, -3), Q (-4, -6) , R (2, -3) and S (1, 2) are the vertices of a quadrilateral PQRS, find its area.

If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when $\frac{AP}{BP}=\frac{3}{4}.$