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There is hollow cube. Its external edge is 5 cm long and its internal edge is 3 cm long. What is its surface area in $c{m}^2$ ?

If (x + 1) is a factor of 2x³ + ax² + 2bx + 1, then find the values of a and b given that 2a - 3b = 4.

Two observers one at P and the other at Q were 500m apart when they observed the flash of an enemy gun at R. If ∠RPQ = 45^o and ∠RQP = 30^o, find out how far P was from the enemy gun.

In the given figure, AB is the chord to the circle having centre at O. If AC = CB and $\angle AOC={50}^{\circ }$, then $\angle CAO$ is equal to.

$(cosec\theta +\cot \theta )\times (1-\cos \theta )=$ _____

In a group of 70 people, 37 like coffee, 52 like tea and each person like at least one of the two drinks. The number of persons liking both coffee and tea is:

Solve the pair of equations using method of substitution.
2x+3y = 13 , 4x-y = 5 [2 MARKS]

If $sin\theta +cosec\theta =2,thensi{n}^6\theta +cose{c}^6\theta$ is equal to

What are the values of a, b and c for the equation $y=0.5x+\sqrt{7}$ when written in the standard form: $ax+by+c=0$ ?

If one zero of the polynomial $3x^2-8x+2k+1$ is seven times the other, then the value of $k$ is ___.

$\begin{array}{cc}{x}_i& f_i\\ 4& 10\\ 8& 11\\ 12& 9\\ 16& 13\end{array}$
Find $\sum f_i{x}_i$ from the given table.

A bag contains 8 red, 2 black and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is not black?
(a) $\frac{8}{15}$ (b) $\frac{2}{15}$ (c) $\frac{13}{15}$ (d) $\frac{1}{3}$

A boy is standing on the ground and flying a kite with $100m$ of string at an elevation of ${30}^{\circ }$. Another boy is standing on the roof of a $10m$ high building and is flying his kite at an elevation of ${45}^{\circ }$. Both the boys are on opposite sides of both the kites. Find the length of the string that the second boy must have so that the two kites meet.

Question1 (ii)
Answer the following and justify
What will the quotient and remainder be on division of $a{x}^2+bx+c$ by $p{x}^3+q{x}^2+rx+s,p\ne 0$?

In $△ABC$, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Then $AD\times DC$ = ?

Ankur Jewellery Ltd. issued 50,00,000, $8\%$ Debentures of Rs 100 each at a discount of $6\%$ on April 1 , 2012 redeemable at premium of $4\%$ by draw of lots as under:

20,00,000 Debentures on March 31,2015

10,00,000 Debentures on March 31,2016

20,00,000 Debentures on March 31,2017

Compute the amount of discount to be written off in each year till debentures are paid. Also prepare discount /loss on issue of debentures account.

Prove the following trigonometric identities:

$ta{n}^2\theta -si{n}^2\theta =ta{n}^2\theta si{n}^2\theta$

Question 3 (ii)
Express $0.4\overline{7}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$.

The zero of the quadratic polynomial $x^2+(a+1)x+b$ are $2$ and $-3$, then

a) $a=–7,b=–1$
b) $a=5,b=–1$
c) $a=2,b=–6$
c) $a=0,b=–6$

The mean of the following distribution is ____.
$$\begin{array}{ccccc}{x}_i& \text{10}& \text{13}& \text{16}& \text{19}\\ f_i& \text{2}& \text{5}& \text{7}& \text{6}\end{array}$$

There are 300 shelves in a gym. Each shelf has 2 lockers. The gym just opened today. Ram and Arjun are its first 2 customers. It is given that Ram is allotted one locker in the ${235}^{th}$ shelf. What is the probability that Arjun also is allotted a locker in the ${235}^{th}$ shelf?

Krishna and Goutham are holding the ends of an elastic thread at a point O. Krishna starts moving towards the east at a speed of 8ms^-1 and Goutham, towards North at a speed of 15ms^-1. If the maximum length the elastic could attain was 170m, how long could they move till the elastic breaks (in seconds)? Both started moving at the same time.

Solve the problem

2(ax-by)+a+4b=0

2(bx+ay)+b-4a=0

The sum of the digits of a two digit number is 7. If the digits are reversed, the number formed is 9 less than the original number.Find the original number.

Write with each and every step.

D and E are respectively the points on the sides AB and AC of a triangle ABC ,such that AE =5cm AC=7.5 cm and DE =4.2cm and DE//BC ,find the length of BC.

In a right triangle $\Delta$ ABC, right angled at B, BD is a perpendicular dropped onto the hypotenuse AC.

If AC = 2AB, find the area of $\Delta$ ABD, given, area of $\Delta$ ABC = 5 sq units.

In each of the following systems of equations determine whether the system has a unique solution, no solution or ininitely many solutions. In case there is a unique solution, find it (1-4)

x- 3y = 3

3x - 9y = 2

Which of the following is/are random experiment(s)?

If-4 is a root of the equation $x^2+2x+4p=0$, find the value of k for which the quadratic $x^2+k(2x+k+2)+p=0$ are equal.

How many terms are there in the $AP=18,15\frac{1}{2},13,...,-47?$

Question 4

In the following question, out of the four options, only one is correct. Write the correct answer:

The value fo $\frac{1}{4^{-2}}$ is
(a) 16
(b) 8
(c) $\frac{1}{8}$
(d) $\frac{1}{8}$

Solve for x and y:

$6x+5y=7x+3y+1=2(x+6y-1)$

In the given figure, $\angle ABC=\angle AED={90}^{\circ }$, AB = 12 cm, AC = 15 cm and DE = 3 cm. The area of $\Delta ABC$ and $\Delta AED$ are ___ and ___ respectively.

At $\theta ={90}^{\circ }$ which of the two trigonometric ratios are not defined?

A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs. 25 per square metre (Use $\pi =3.14$).

If the price of a book is reduced by Rs.5, a person can buy 4 more books for Rs.600. Find the original price of the book.

A cylindrical tank full of water is emptied by a pipe at the rate of 225 litres per minute. How much time will it take to empty half the tank, if the diameter of its base is 3m and its height is 3.5 m?