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In the following question, there is a sentence which is divided into four parts. Choose the fragment that carries an error (if any). Ignore punctuation errors if any.

As sooner did he / return from school, / he was told to / go to the shop.

The median of observations 17, 18, 20, 22, x+2, x+4, 31, 35, 37 is found to be 24. If the observations have been arranged in ascending order, the value of x will be

PA and PB are tangents from P to the circle with center O. At point M which lies on circle, a tangent is drawn cutting PA at K and PB at N. Prove that KN = AK + BN. [2 MARKS]

In the given circle O is the centre of the circle. The measure of (x + y) is equal to

A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively 6 cm and 4 cm. Find the height of water in the cylinder.

Solve the following pair of linear equations:

$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$

$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$

(Where $x>0,y>0)$

Let a be a rational number and b be an irrational number. Is ab necessarily an irrational number?justify your answer with an example.

If $(x-2)(x+a)(x-b)$ is the factorised form of the polynomial $(x^3-2x^2-9x+18),$ then find the values of $a$ and $b.$

In a right ∆, the ratio of the side opposite and the largest side of the triangle is angle $\theta$, the ratio is known as

What is the area of this triangle? [2 MARKS]

Factorize:

$2a^2+2\sqrt{6}ab+3b^2$

Construct the equilateral triangle whose altitude is 6 cm. Find the side of the triangle.

If x = 1, y = 2 is a solution of the equation 3x + 2y = k, the value of k is ___.

If $x+a$ is a common factor of expressions $f\left(x\right)=x^2+px+q$ and $g\left(x\right)=x^2+mx+n$, then 'a' is equal to:

Question 75

In the following question, state whether the given statement is true (T) or false (F).
Every multiple of a number is greater than or equal to the number.

The radius of a spherical vessel whose volume is 2483.712 cm³ i

A pond is in shape of trapezium. A bridge is to be constructed such that the bridge is perpendicular to the parallel sides. It is given that the area of a pond is 1080 $m^2$ and the lengths of its parallel sides are 55.6 m and 34.4 m. Find the length of the bridge.

In the given figure, PQR is a triangle and S is any point in its interior. Then which of the following options is correct?

2.2 $d{m}^3$ of lead is to be drawn into a cylindrical wire 0.50 cm in diameter. The length of the wire is

(a) 110 m (b) 112 m (c) 98 m (d) 124 m

Find the area of the quadrilateral shown below:

Given: Area $\left(\Delta ADC\right)=16c{m}^2$

The area of the given polygon is ${\text{cm}}^2$.

Three angles of a quadrilateral measure ${37}^{\circ }$, ${130}^{\circ }$ and ${53}^{\circ }$. Find the measure of the fourth angle.

Have you made choices that are acceptable and less 'risky' or have you followed the beaten track? Why?

If two equal chords AB and CD of a circle when produced, intersect at point P, then PB =

Question 119

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the ratio between the height and radius of the cylinder.

If $p$ =$\frac{7-\sqrt{11}}{7+\sqrt{11}}$ and $q$ =$\frac{7+\sqrt{11}}{7-\sqrt{11}}$,then find the value of $(p+q{)}^2$.