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The volume of a cube is 2744 $c{m}^3$. Its surface area is

(a) 196 $c{m}^2$ (b) 1176 $c{m}^2$ (c) 784 $c{m}^2$ (d) 588 $c{m}^2$

Read each sentence to find if there is any grammatical error in it. If there is any error, it will be only in one part of the sentence. The number or alphabet of that part is your answer.

Question 5

Study the pattern:
$\begin{array}{ccc}1\times 8+1=9;& 12\times 8+2=98;& 123\times 8+3=987\\ 1234\times 8+4=9876;& 12345\times 8+5=98765& \end{array}$

Write the next two steps. Can you say how the pattern works?

Construct a triangle ABC in which BC is 6 cm, angle B is ${70}^{\circ }$ and AB+AC=14cm by using the method of perpendicular bisector.

8 + 88 + 888 + .............n terms = ____

The length, breadth and height of a room are 8 m 25 cm, 6 m 75 an d 4 m 50 cm, respectively. Determine the longest rod which can measure the three dimensions of the room exactly.

A 5 m wide cloth is used to make a conical tent of base diamter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs.25 per metre.

Solve the following systems of equations:

$x-y+z=4$

$x-2y-2z=9$

$2x+y+3z=1$

The sum of a two-digit number and the number formed by reversing the order of digits is $66.$ If the two digits differ by $2,$ find the number. How many such numbers are there?

Find the length of circumradius of a right-angled triangle whose adjacent sides are 3cm and 4cm?

On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are ${45}^{\circ }and{60}^{\circ }$. If the height of the tower is 150 m, find the distance between the objects.

Use Euclid's division algorithm to find the HCF of:
$867$ and $255$

Show that any positive odd integer is of the form 6q + 1 or, 6q + 3 or, 6q + 5, where q is some integer.

There is a building with window at a height of 12 m. You want to use a ladder to go up to the window, and you decide to keep the ladder 5 m away from the building to have a good slant. How long should the ladder be?

Find the discriminant of the following quadratic equations $x^2$ – x + 1 = 0

If $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{6}=2.449,$ find the value of $\frac{2+\sqrt{3}}{2-\sqrt{3}}+\frac{2-\sqrt{3}}{2+\sqrt{3}}+\frac{\sqrt{3}-1}{\sqrt{3}+1}$ .

This question is from AMTI 2016 .So, solve this problem as fast as you can.

If a, b, c are positive real numbers.Then find the minimum value of

(a+3c/a+2b+c) + (4b/a+b+2c) - (8c/a+b+3c)

Solve the following:

(i)cos 225°+sin165°

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are $\frac{7}{5}$ of the corresponding sides of the first triangle.

Which of the following is not an example of Barter system?

If-5 is a root of the quadratic equation $2x^2+px-15=0$ and the quadratic equation $p(x^2+x)+k=0$ has equal roots, find the value of k.

Find the cumulative frequency for the class interval 65-70$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 50-55& 5\\ 55-60& 20\\ 60-65& 10\\ 65-70& 10\\ 70-75& 9\\ 75-80& 6\\ 80-85& 6\\ 85-90& 8\end{array}$

In the given figure, a circle is inscribed in a right-angled triangle such that $AF=6\text{cm}$ and $EC=15\text{cm}$. The perimeter of the triangle is:

In $\Delta ABC,AB=10cm,\angle A={40}^{\circ },\angle B={80}^{\circ }.$ The area of triangle ABC will be equal to

$\left[\begin{array}{c}tan{40}^{\circ }=0.83\\ tan{80}^{\circ }=5.6\end{array}\right]$

Question 95

Solve the following:

Hamid has three boxes of different fruits. Box A weighs 2 $\frac{1}{2}$ kg more than box B and Box C weighs 10 $\frac{1}{4}$ more than box B. The total weight of the three boxes is 48$\frac{3}{4}kg$. How many kilograms does box A weigh?

If f(x) = $4x^3-6x^2+5x-1$ and $\alpha ,\beta$ and $\gamma$ are its zeros, then $\alpha \beta \gamma$ =

Question 8
The product of a non – zero rational and an irrational number is

A) Always irrational
B) Always rational
C) Rational or irrational
D) One

$7^{\text{th}}$ term of the sequence
$\sqrt{2},\sqrt{10},5\sqrt{2},.........$ is ___.

When divided by x-3 the polynomials x³-px²+x+6 and 2x³-x²-(p+3)x-6 leave the same remainder .Find the value of 'p'.

Passing through the points (-1, 1) and (2, -4)

One card is drawn from a pack of 52 cards. Then, the probability of getting a red coloured king is ___.

ABCD is a cyclic quadrilateral. If $\angle BCD={100}^{\circ }$ and $\angle ABD={70}^{\circ },$ then find $\angle ADB.$

Equation of the line passing through (4,-5) cutting of equal intercepts, but of the opposite sign, from the axes.

The co-ordinates of the points which divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is _____.

The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. Let’s say x toys were produced on a day, what is the cost of production of each toy?

Find the common difference for the arithmetic progression $3+2\sqrt{2},3+4\sqrt{2},3+6\sqrt{2},3+8\sqrt{2}$.

Identify the linear polynomials among the following.

1. $\frac{1}{x-1}$

2. $\sqrt{x}+2$

3. $\sqrt{3}x+5$

4. $y+\sqrt{2}$

What is the ratio that relates the opposite side of an angle to the hypotenuse in a right-angled triangle?

A carton consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Jimmy, a trader accepts shirts only which are good. But, Sujatha, another trader will reject shirts which have only major defects. One shirt is drawn randomly. Find the probability that the shirt selected is (i) Acceptable to Jimmy (ii) Acceptable to Sujatha

Where does the centre of circumcircle of an obtuse triangle lie?

Find the number of terms in the G.P 6,12, 24 ... 1536.

Find the point where the graph of the function sgn (x) breaks or becomes discontinuous. ( sgn is the signum function )

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