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Choose the correct statement

Prove that the straight lines perpendicular to the same straight line are parallel to one another.

The base radii of two right circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes is

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder.

$p\left(x\right)=x^3-3x^2+5x-3,g\left(x\right)=x^2-2$

A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

Which of the following is the correct expanded form of 0.0504?

Factorise:
$4(a+b)-6(a+b{)}^2$

Prove that the line segment joining the mid-points of the diagonals of a trapezium is parallel to each of the parallel sides and is equal to half the difference of these sides. [4 MARKS]

What will be the product of $p^2-2pq$ and $q^2+5pq$?

ABCD is a parallelogram and $\angle A={75}^{\circ }.$ Find $\angle B$.

In the figure below, each curved line is an arc of a circle centered at a vertex of the triangle.

if x +y+ 4 =0 , then find the value of x³ + b³ - 12xy + 64

Find the radius of a sphere whose surface area is 154 cm².

The ratio (sinA + sinB): sin(A + B), when A = 60^o and B = 30^o is

What is the value of (a + b) (a – b)?

In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. What is the probability that in a given throw, the ball does not hit the boundary?

(a) $\frac{1}{4}$

(b) $\frac{1}{5}$

(c) $\frac{4}{5}$

(d) $\frac{3}{4}$

Question 17

The reciprocal of -1 is

(a) 1

(b) –1

(c) 0

(d) Not defined

An irrational number between 3 and 4 is .

With reference to the graph below, which of the following is true?

$\text{In the given figure, AD divides}\angle BAC\text{in the ratio 1:3 and AD=DB.Determine the value of x .}$

Find the radius of a sphere whose surface area is $154c{m}^2$

Choose the multiplication statement that gives the same result as $3\times 5$.

What will come in place of (?) in the following number series?

$\begin{array}{ccc}6& 18& 15\\ 3& 2& 5\\ 4& 3& 7\\ 8& 27& 9\end{array}$

Directions For The Following 4 (Four) (22-25) Items:

Read the following information carefully and answer the questions that follow.
There are six cities M, N, O, P, Q and R.
1. M is not a hill station.
2. N and Q are not historical places.
3. P is not an industrial city.
4. M and P are not historical cities.
5. M and N are not alike.

An amount of Rs. 5000 is invested for 1.5 years which will be compounded half yearly at a rate of 10%. Find the final amount (Approximately) after one and a half years?

The graph of --------------- is a straight line parallel to y axis.

A rectangular paper of width 10 cm is rolled along its width to form a cylinder. If the volume of such cylinder is 6160 cm³, then find the length of the rectangle.

p(x) is a polynomial satisfying $p(x+\frac{3}{2})=p\left(x\right)$, for all real values of 'x'. If p(5)=2010, what is the value of p(8)?

What is the planar shape observed when one end of a rod is fixed and the other end is rotated about the fixed end?

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If $\Delta MNP\sim \Delta RST$, then find the value of x.

Which of the following is a trinomial in x?

Raghu needs to make a cylindrical aluminum tube. What will be the area of the aluminum sheet required to make the tube, if the length and radius of the tube should be 1 $m$ and 3.5 $cm$ respectively [Top and bottom of the tube are of another material]?

($use\pi =\frac{22}{7}$)