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Let $A=\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]$. The only correct statement about the matrix A is

The shadow of a flag pole is 30 metres. If the altitude of the sun is at 30^o then the height of the flag pole is

Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution:

$\frac{3x}{2}-\frac{5y}{3}+2=0$

$\frac{x}{3}+\frac{y}{2}=2\frac{1}{6}$

The total surface area of a right circular cylinder of height 9m is 440 sq. meter.Find the radius of the cylinder. (Take π = 22/7)

Number of elements in each of the universal set, set A and set B are represented as n(U), n(A), n(B) respectively. The number of elements that are not in set A and not in set B is given by

The lower limit of the modal class of the following data is:

If the area of a rectangle is 24 m² and its perimeter is 20 m, the equation to find its length and breadth would be:

If sin(2α + 45^o) = cos(30^o - α), where, 0^o < α < 90^o, then the value of α in degrees is.

If fourth term of a G.P. is 3, the product of the first seven terms is

In a \Delta ABC, D and E are points on the sides AB and AC respectively such that DE||BC.
(i) If AD = 6cm, DB = 9 cm and AE = 8 cm, find AC.
(ii) If $\frac{AD}{DB}=\frac{3}{4}$ and AC = 15 cm, find AE.
(iii) If $\frac{AD}{DB}=\frac{2}{3}$ and AC = 18 cm, find AE.
(iv) If AD = 4, AE=8, DB =x-4, and EC = 3x - 19 find x
(v) If AD = 8 cm, AB=12 cm and AE = 12 cm, finde CE.
(vi) If ad = 4 CM, db = 4.5 cm and AE = 8 cm, find AC
(vii) If AD = 2 cm, AB = 6 cm and AC = 9cm, find AE.
(viii) If $\frac{AD}{BD}=\frac{4}{5}$ and 3C = 2.5 cm, find AE.
(ix) If AC=x, DB=x-2, AE=x+2 and EC=x-1, find the value of x.
(x) If AD= 8x -7. DB= 5x-3, AE=4x-3 and EC= (3x-1), find the value of x.
(xi) If AD= 4x-3, AE=8x -7, BC=3x-1 and CE=5x-3, find the value x.
(xii) If AD=2.5 cm, BD= =3.0 cm and AE=3.75 cm, find the length of AC.

What number should be subtracted from each of the numbers 11, 15, 23 and 35 so that the remainders are in proportion?

15 pastries and 12 biscuit packets have been donated for a school fete. These are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each. How many biscuit packets and how many pastries will each box contain?

An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel.

If the linear equation y = 7x - 4 is written in standard form, the standard form being ax +by +c =0, then what is the value of a, b and c?

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles, each of diameter 3 cm and height 4 cm. How many bottles are needed to empty the bowl?

For finding mean by assumed mean method

$\overline{x}$ = a + $\frac{(\sum f\times d)}{\sum f}$

Find the physical representation of a,d and f.

A ladder makes an angle of ${60}^{\circ }$ with the floor and its lower end is 20 m away from the wall. Find the length of the ladder.

Solution set of the inequality $lo{g}_{0.8}\left(lo{g}_6\frac{x^2+x}{x+4}\right)<0$

Find the mid-point of the line segment joining the points : (i) (-6, 7) and (3, 5) (ii) (5, -3) and (-1, 7)

Can I be an exponent for any variable

Question 58

A scooter travels 120 km in 3 hours and a train 120 km in 2 hours.
Find the ratio of their speeds.
[Hint: Speed = $\frac{\text{Distance travelled}}{\text{Time taken}}$

Find the value of c if the line y = 3x + c is a tangent to the circle $x^2+y^2=10$

If two circles with centers $C_{1}and{C}_{1}andradii{r}_{1}and{r}_2$ intersect in two distinct points, then

The distance between the points (-1, 5) and (2, 1) is ___ units.

Rahul bought a T.V with a marked price of Rs. 25000 .If the rate of sales tax is 9%, find the total amount paid by Rahul to buy the T.V

The GCD of two polynomials is $x{y}^2{z}^2$ and their LCM is $x{y}^3{z}^8$. If one of the polynomials is $x{y}^2{z}^2$, then the other one is .

1. 3

In the fig. AB, AC and PQ are tangents. given,PQ = 8 cm, AQ = 9 cm and PA = 7 cm, then find AC.

$△$ ABC is right angled at B and the perpendicular drawn to the opposite side bisects it at D. if $AD=DC=5cm,BD=$ ___ $cm$

State, true or false :
(i) Two similar polygons are necessarily congruent.
(ii) Two congruent polygons are necessarily similar.
(iii) All equiangular triangles are similar.
(iv) All isosceles triangles are similar.
(v) Two isosceles-right triangles are similar.
(vi) Two isosceles triangles are similar if an angle of one is congruent to the corresponding angle of the other.
(vii) The diagonals of a trapezium divide each other into proportional segments.

The solution for the equations $c_1$x + $b_1$y + $a_1$ = 0 and $c_2$x + $b_2$y + $a_2$ = 0 is

S1 :x = $\frac{(b_1{a}_2-b_2{a}_1)}{(c_1{b}_2-c_2{b}_1)}$

S2 : y =$\frac{(c_1{a}_2-c_2{a}_1)}{(a_1{b}_2-a_2{b}_1)}$

A train travels a distance of 340 km at a uniform speed. If the speed had been 3 km/h less, then it would have taken 2 hours more to cover the same distance. We need to find the speed of the train.

ABCD is a parallelogram and APQ is a straight line meeting BC at Pend DC produced at Q. prove that the rectangle obtained by BP and DQ is equal to the rectangle contained by AB and BC.

1. The manufacturer sold a TV to a wholesaler for Rs.7000. the wholesaler sold it to a trader at a profit of Rs.1000, find:H

1. The total VAT collected by the state government at the rate of 5%.

2. The amount that the customer pays for the TV>

From Delhi station, if we buy 2 tickets for station A and 3 tickets for station B. the total cost is Rs. 77. But if we buy 3 tickets for station A and 5 tickets for station B. the total cost is Rs. 124. What are the fares from Delhi to station A and to station B ?

The angles of a triangle in A.P. the smallest being half of the greatest. So what are the angles ?

In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
$[Use\pi =\frac{22}{7}]$

The first and the last term of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

In the given figure P(5, -3) and Q(3, y) are the points of trisection of the line segment joining A(7, -2) and B(1, -5). Then y equals

(a) 2 (b) 4 (c) -4 (d) $\frac{-5}{2}$

If one zero of the quadratic polynomial $k{x}^2+3x+k$ is 2 then the value of k is

(a) $\frac{5}{6}$ (b) $\frac{-5}{6}$ (c) $\frac{6}{5}$ (d) $\frac{-6}{5}$

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation is 45°. Find the height of tower PQ.