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Question 112

Special balances can weigh something as 0.00000001 gram. Express this number in the standard form.

A path of uniform width 1.5 m runs around the outside of a rectangular field 18 m by 15 m. The area of the path is _____ $m^2$.

The cost of an article was rupee 15500.rupee 451 spend on its repairs. if it is sold for a profit of 15%, find the selling price of the article.

Find the product $-3y(xy+y^2)\text{and find its value for}x=4andy=5.$

The common difference for the arithmetic progression

$3+2\sqrt{2},3+4\sqrt{2},3+6\sqrt{2},3+8\sqrt{2}$ is

Are angles in a rhombus equal? Do diagonals bisect the angles of the rhombus?

Find the area of four walls of a room whose length 3.5 m, breadth 2.5 m and height 3 m.

There are $7$ periods in each working day of a school. In how many ways can one organize $6$ subjects such that each subject is allowed atleast one period?

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

Twelve persons are sitting in two rows containing six persons each. In row- 1 - A, B, C, D, E and F are sitting facing West but not necessarily in the same order. In row-2 - P, Q, R, S, T and U are sitting facing North but not necessarily in the same order. There is an equal distance between adjacent persons.
S sits third to the right of R, S doesn't sit at any extreme. R is not an immediate neighbour of U. Two persons sit between P and Q. T sits third to the left of U.
D sits to the left of C, F sits third to the right of D. C doesn't sit at any extreme end. One person sits between B and D. C is not an immediate neighbour of B and A.

What is the position of S with respect to R?

To draw a square inside a circle, the diameters must be _______ .

If 9^n×3^2×3^n-(27)^n÷3^3m×2^3=1/27,prove that m=1+n.

The set of positive and negative integers together with 0 is called

Find the total surface area of the cuboid with l = 4 m, b = 3 m and h = 1.5 m.

The given figure shows a sqaure, a regular pentagon and a regular hexagon put together. The measure of $\angle BAC$ is

A wire attached to a vertical pole is 37 m long and it is pulled from the pole for a distance of 12 m so that the wire becomes taut. Find the height of the pole.

Question 10

Find the values of the letters in the following and give reasons for the steps involved.

$12A$

$\underset{–}{+6AB}$

$\underset{–}{A09}$

Question 50

Solve the following:

$\frac{5x}{2x-1}=2$

Question 4

Construct a parallelogram OKAY where OK=5.5 cm and KA=4.2 cm.

A person invests Rs. 10,000 for two years at a certain rate of interest compounded yearly. At the end of one year this sum amounts to Rs. 11,200. Calculate

Prime factorization of 1400:

Suppose a 3-digit number is divisible by 3. Prove that is divisible by 9.

Volume of a right circular cone of radius ${}^{\prime }r{}^{\prime }$ and height ${}^{\prime }h{}^{\prime }$ = .

Question 84 (xii)

Simplify

$(pq-qr{)}^2+4p{q}^{2}r$

The angles in a rectangle are given by $(x+30{)}^{\circ }$ and $(y+50{)}^{\circ }$ respectively, find the value of $x+y$

If $a^2+b^2=10andab=3$; find :

(i) a -b (ii) a + b

A beam 5 m long and 40 cm wide contains 0.6 cubic metre of wood. How thick is the beam?

A quadrilateral is constructed using 2 congruent triangles. Two of its sides are 2 and 3 units. What are the possible values of the 3rd side?