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Which of the following is parallel to the line of equation x=a?

Question 60

State whether the following statement is True or False.

The model of a ship shown is of height 3.5 cm. The actual height of the ship is 210 cm if the scale chosen is 1 : 60.

In the given quadrilateral, $QS$ is the bisector of $\angle S$ and $\angle Q$. $PS=5cm$ and $PQ=8cm$. Fin the measure of $SR$.

If the coordinates of two points are P(-2,3) and Q(-3,5), then (abscissa of P) - (abscissa of Q) is

how can root 256 is equal to 16

In a $\Delta ABC$, the internal bisector of $\angle A$ meets opposite side BC at D. Through vertex C, line CE is drawn parallel to DA which meets BA produced at point E. Which of the following is/are true?

A juice vendor makes juice in a cylindrical jug of radius 10 cm and height 45 cm. If he serves juice in small cylindrical glasses of radius 3 cm and height 5 cm each, how many glasses of juice can he fill from the jug at a time if the jug is full?

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

(i) the rate of interest per annum

(ii) the amount at the end of the second year

Which of the following figures are similar figures?

In the figure, a square PQRS is given in which RY = SX. Which of the following result can be deduced from the given information?

Simplify $\left(\frac{2+\sqrt{5}}{2-\sqrt{5}}\right)+\left(\frac{2-\sqrt{5}}{2+\sqrt{5}}\right)$

In the given right angle triangle, if $Sin\theta =\frac{3}{5}$, then find the value of $3tan\alpha$.

The diameters of two cones are equal.If their slant heights are in the ratio 5:4,the ratio of their curved surface areas, is

${\left(\frac{1}{5}\right)}^0$ is equal to

Factorise
$x-8x{y}^3$

Verify whether the line 3x + 4y = 7 passes through the point (1,1)

In the given figure, PQ = QR, $\angle RQP={68}^{\circ }$, PC and CQ are tangents to the circle with center O. Calculate the values of:

$\left(i\right)\angle QOP$

$\left(ii\right)\angle QCP$ [4 MARKS]

Following data gives the number of children in 40 families:
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2,4,3,2, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.
Represent it in the form of a frequency distribution, taking classes 0-2,2-4, etc.

Mr. Thomas invested an amount of Rs. 13,900 divided into two different schemes A and B at the simple interest rate of $14\%$ p.a. and $11\%$ p.a. respectively. If the total amount of simple interest earned in 2 years is Rs.3508, what was the amount invested in scheme B?

Construct the histogram for the following grouped frequency distribution.

Question 103

State whether the statement is True or False.

$a÷(-1)=-a$

The distance between the points A(a cos ${20}^{\circ }$ + b sin${20}^{\circ }$, 0) and B(0, a sin${20}^{\circ }$ - b cos${20}^{\circ }$) is:

$\frac{tan{55}^{\circ }}{cot{35}^{\circ }}\times sin{30}^{\circ }=A$

The value of 2A is___

Condition for a$x^2$ + bx+ c = 0 to be a quadratic equation is

Question 92 (v)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$28a{y}^2-175a{x}^2$

Question 64

Describe two method to compare $\frac{13}{17}$ and 0.82. which do you think is easier and why?

The mean of 31 results in 60 .If the mean of the first 16 is 58 and that of the last 16 is 62 what is the 16th result?How can I do this sum?

If (x,y) are the coordinates of any point P, then if (x,y)=(y,x), which of following options must hold true?

What does the underlined preposition indicate?

Prajot drove his car $\underset{–}{\text{into}}$ a tree.

The construction of a triangle ABC, given that BC = 3 cm, ∠B = 45° is possible when difference of AB and AC is equal to:

If one angle of a triangle are equal and the third angle is greater than each of those angles by 30°.determine all the angles of the triangle

From given points name abcissab and ordinates

(2,5) (-7,-6) (4,-5) (-7,9) (0,0) and (3,-6)

Prove: $\sin 3a=3\sin a-4{\sin }^{3}a$, when $a={30}^{\circ }$

Mark the correct option choosing the correct coordinates.
A. X-coordiate In a right angled triangle ABC, right angled at B, the ratio of AB to AC is
$1:\sqrt{2}$, then $\frac{4tanA}{1+ta{n}^{2}A}$
y-coordinate In a right angled triangle ABC, right angled at B, $\angle ACB=\theta$, AB=2 cm and BC=1 cm, then $2(si{n}^2\theta +co{s}^2\theta )$.

B. x-coordinate If$sinB=\frac{1}{2}$, then value of $3cosB-4co{s}^{3}B$.
y-coordinate the value of $ta{n}^2\theta +\frac{1}{ta{n}^2{\theta }^{\prime }}$
if $tan\theta +\frac{1}{tan\theta }=\sqrt{2}$

C. x-coordinate The value of
$(\frac{-1}{tanA}-\frac{sinA}{1+cosA})$, if $cosecA=1$,
y-coordinate If $cos\theta =\frac{3}{5}$, then -$(cot\theta +cosec\theta )$

Find the expression whose expanded form is $(x–y)(x^2+xy+y^2$).

Find the mean.

$$\begin{array}{cccccc}Observation& 3& 6& 7& 9& 10\\ frequency& 8& 10& 15& 9& 8\end{array}$$

An exterior angle of a triangle is ${105}^{\circ }$ and its two interior opposite angles are equal. Each of these equal angles is

Prove that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle. [4 MARKS]

The volume of water in a cuboidal container of dimensions 50 cm, 20 cm and 30 cm will be

In a right triangle, the hypotenuse is $6m$ more than twice the shortest side. If the third side is $2m$ less than the hypotenuse. Then the length of the hypotenuse is