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If coordinates of the triangle are A(-2,4), B(2,4) and C(-2,1), then the triangle is ______________.

1. 3

In the figure, the radius of the circle and the semi-circles is 7 cm.
Find the area of the shaded region.

Question 52

Three times a number is 200% increase in the number, then one-third of the same number is 200% decrease in the number.

Construct a triangle ABC, in which $\angle$B = ${60}^{\circ }$, $\angle$C = ${60}^{\circ }$ and AB + BC+ CA = 18 cm. What type of triangle is this? Find the length of each side by calculation. Verify the calculation from the construction.

Question 91

Solve the following.
$\left(i\right){100}^{-10}\left(ii\right)2^{-2}\times 2^{-3}\left(iii\right){\left(\frac{1}{2}\right)}^{-2}÷{\left(\frac{1}{2}\right)}^{-3}$

Three angles of a quadrilateral are in the ratio 2:3:7. The mean of these angles is 64 degrees .Find all the four angles.

Determine the ratio in which the line 2x+y=4 divides the line segment joining the points A(2,-2) and B(3,7)

The price of a T.V set inclusive of sales tax of 9% is Rs. 13407. If the sales tax is increased to 13%, How much more does the customer have to pay for the T.V?

1. 4

Question 4
State whether the following is true or false.
A pair of tangents can be constructed to a circle inclined at an angle of ${170}^{\circ }$.
[Thinking process :
If the angle between a pair of tangents is greater than ${180}^{\circ }$, then the pair of tangent can never be constructed to a circle.]

If a person is looking up at an object, then the angle made by man’s line of sight with his eye level is the angle of __.

If A(-1, 0), B(5, -2) and C(8, 2) are the vertices of a $△ABC$ then its centroid is

(a) (12, 0) (b) (6, 0) (c) (0, 6) (d) (4, 0)

Find the value of k for which each of the following systems of equations has no solution:

$kx+3y=3,12x+ky=6.$

If twice the son's age in years is added to the father's age, the sum is 70. But, if twice the father's age is added to the son's age, the sum is 95. Find the ages of father and son.

Find the value of k for which each of the following systems of linear equations has an infinite number of solutions:

$2x+3y=7,(k-1)x+(k+2)y=3k.$

Find the value of x and y in the below given pair of equation.

$\frac{2}{x}$ + $\frac{3}{y}$ = 13

$\frac{5}{x}$ - $\frac{4}{y}$ = -2

Which of the following sets are finite or infinite?

(i) The set of months of a year

(ii) {1, 2, 3, ....................}

(iii) {1, 2, 3, .................... 99, 100}

(iv) The set of positive integers greater than 100.

(v) The set of prime numbers less than 99.

In the given diagram, a circle is inscribed in a right angled triangle such that AF = 6 cm and EC = 15 cm. Find the difference between CD and BD :

Given $P=\left[\begin{array}{cc}p& 0\\ 0& 2\end{array}\right],Q=\left[\begin{array}{cc}0& -q\\ 1& 0\end{array}\right]\text{and}R=\left[\begin{array}{cc}2& -2\\ 2& 2\end{array}\right]$

If $QP=R^2$, Find the values of p and q.

If ${}^n{C}_0$ + 3${}^n{C}_1$ + $3^2$${}^n{C}_2$ + .................$3^n$${}^n{C}_n$ = $a^n$, then a =

6k=k^{​​​​​​2} -> how does this come to be k =0 or k=6??

A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4 cm. Select the statements that hold true.

$[Assume\pi =\frac{22}{7}]$

Solve the following systems of equations graphically:

2x + 3y + 5 = 0

3x - 2y - 12 = 0

Water is stored up to its brim in a right circular cylinder whose volume is $100c{m}^3$. How many bottles of $10c{m}^3$ are required to empty the cylinder?

Find the value of $sin\theta +cos\theta$ when $\theta ={45}^{\circ }$.

A shopkeeper prepares 396 gulabjamuns and 342 rasgullas. He packs them into containers. Each container consists of either gulab jamun or rasgulla, but have equal number of pieces. Find the number of pieces. Find the number of pieces he should put in each container so that numbers of containers are least.

If $x=\sqrt{a}\tan \alpha$ and $y=\sqrt{a}\sec \alpha$, then $y^2–x^2=$__

The total surface area of a right circular cone of radius 5 cm and slant height 9 cm is . (Take $\pi =\frac{22}{7})$

A man standing on the bank of a river observes that the angle off elevation of a tree on the opposite bank is 60^o. When he moves 50 m away from the bank, he finds the angle of elevation to be 30^o. Calculate:

sec^-1x + cosec^-1x =

Earth dug out of a circular tank of diameter 17.5 m, is spread around the tank uniformly within a width of 4 m to form an emankment of height 2 m. Calculate the depth of the circular tank.

If the angles of elevation of a tower from two points at a distance a and b (where, b>a) from its foot and lying on the same side are ${60}^{\circ }$ and ${30}^{\circ }$, then height of the tower is

In the given figure, the circles touch the lines at X , Y , Z , B , C and D.

If PQ = 8cm , QA = 9cm and PA = 7cm, then the length PX , AZ and QY respectively are :

Find the value of and , if ( + 2) & ( + 3) are both factors of the expression

2³ + ² + 7 –

If the degree of the polynomial $x^a$ + $x^2$ + $1$ is 2, what can be said about ${}^{\prime }{a}^{\prime }$?

A tangent PQ at a point P of the circle with radius 5cm meets a line through the centre O at a point Q so that OQ is 12cm. the length of PQ is

In the give right angled triangle ABC. Which is the side adjacent to the angle $\theta$?

What term should be substracted to $a^2+2ab$ to make it a perfect square?

Angles BAC of triangle ABC is obtuse and AB = AC. P is a point in BC such that PC = 12 cm. PQ and PR are perpendiculars to sides AB and AC respectively.

If PQ = 15 cm and PR = 9 cm; then the length of PB is ___ cm.

Which of the quadratic functions has the widest graph?

If $\theta +\varphi =\alpha$ and $sin\theta =ksin\varphi$, then show that $tan\theta =\frac{ksin\alpha }{1+kcos\alpha }$ and $tan\varphi =\frac{sin\alpha }{k+cos\alpha }$

Or

If $sinx=\frac{-1}{3}$ and x lies in quadrant IV, then find the value of

(i) $sin\frac{x}{2}$

(ii) $cos\frac{x}{2}$

(iii) $tan\frac{x}{2}$

The roots of the quadratic equation √3x² - 2√2x - 2√3 = 0 are: