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key points of chapter triangles and the theorems

Which of the following graph represents the quadratic polynomial $-x^2+5x-6$?

The area of a square field is 6050 $m^2$. The length of its diagonal is

(a) 135 m (b) 120 m (c) 112 m (d) 110 m

$\frac{1}{(1+sin\theta )}+\frac{1}{1-sin\theta }=2se{c}^2\theta$

Question 6
The expenditure of a family of different heads in a month is given below.

$\begin{array}{ccccccc}\text{Head}& \text{Food}& \text{Education}& \text{Clothing}& \text{House}& \text{Others}& \text{Savings}\\ & & & & \text{rent}& & \\ \text{Expenditure (Rs.)}& 4000& 2500& 1000& 3500& 2500& 1500\end{array}$

Draw a bar graph to represent the data above.

Point P divides the line segment joining the points A (8, 0) and B (16, -8) in the ration 3:5. Find its co-ordinates of point P.

Also, find the equation of the line through P and parallel to 3x + 5y = 7.

The wheels of the locomotive of a train are 2.1 m in radius. They make 75 reveloutions in one minute. Find the speed of the train in km per hour.

In the adjoining figure, AB = 10 cm, BC =15 cm and AD : DC = 2 : 3, then $\angle$ABC is equal to -

The 3rd and 5th terms of an AP are -12 and minus 112 then find its common difference.

The remainder when $x^{101}+101$ is divided by x+1 is:

1/1.3.5+1/3.5.7+......find sum of n term

In the given figure, a square is cut as shown in the first figure and rearranged to form a big square as shown in the second figure. Then the area of each quadrilateral pieces is ____.

Factorize $\sqrt{3}$ $x^2$ + 5x + 2$\sqrt{3}$ = 0 into the form (ax+b)(cx+d)=0.

Fiind the next term in the given series.

PMT, OOQ, NQN, MSK, ?

a) LWI b) LVH c) LVI d) LUH

Answer:

A storage tank in form of a cube has water up to its brim. The amount of water in the tank is 4096 m³. After some time, it is found that the depth of water present is 12 m. Find the volume of water used.

Find the area and perimeter of a sector with a central angle of ${60}^{\circ }$ in a circle of radius $7cm$.

Middle term split

x^{​​​​​​2}+2√2x-6

$(cosecA+sinA)(cosecA-sinA)=co{t}^{2}A+co{s}^A$

A coin was tossed 10 times, out of which 7 times, heads turned up. Based on the given data, what is the experimental probability of getting heads in the next toss?

The sum of a non-zero number and its reciprocal is $\frac{41}{20}$. Find that number.

What no.is to be added to the polynomial x² -5x+4 so that 5is zero of the polynomial? ^{​​​​​​}

A straight line passes through points P (-2, 5) and Q (6, -3). It intersects the coordinate axes at points A and B. M is the midpoint of the segment AB. Find:

Prepare trading and profit and loss account for the year ended 31st March, 2016 and a balance sheet as on that date from the following trial balance.

$\begin{array}{cccc}\text{Name of Accounts}& \text{Amt(Rs)}& \text{Name of Accounts}& \text{Amt (Rs)}\\ \text{Stock on 1st April, 2015}& 16,000& \text{Sales Less Returns}& \text{1,10,000}\\ \text{Purchases Less Returns}& 38,000& \text{Sundry Creditors}& 15,000\\ \text{SP Kumar}& 1,500& \text{Capital}& 33,900\\ \text{Wages}& 7,700& \text{Mortgage and Interest to Date}& 7,800\\ \text{Carriage Inwards}& 1,300& \text{Rent Outstanding}& 500\\ \text{Carriage Outwards}& 750& & \\ \text{Salaries}& 20,000& & \\ \text{Advertisements}& 4,500& & \\ \text{Trade Expenses}& 2,400& & \\ \text{Rent}& 6,000& & \\ \text{Establishment}& 2,700& & \\ \text{Stable Expenses}& 1,050& & \\ \text{Mortgage Interest}& 300& & \\ \text{Sundry Debtors}& 20,000& & \\ \text{Cash in Hand}& 1,250& & \\ \text{Machinery}& 43,750& & \\ & \overline{\underset{–}{\underset{–}{1,67,200}}}& & \overline{\underset{–}{\underset{–}{1,67,200}}}\end{array}$

Additional Adjustments:

(i) Closing stock was Rs. 23,000.

(ii) Provision for doubtful debts be created on sundry debtors $5\%$ and a provision for discount on sundry debtors at $2\%$.

(iii) Salary of Rs. 1,500 paid to SP Kumar an employee of the firm, stands debited to his personal account and it is to be corrected.

(iv) A stationery bill for Rs. 100 remains unpaid and unrecorded.

(v) Write-off one third of advertisement expenses.

(vi) Sundry creditors include Rs. 5,000 loan taken from Mr. Sudhir on 1st September, 2015 bearing interest $12\%$ per annum.

Find the HCF of 592 & 252 and Express it as a linear combination of them.

From a solid sphere of radius 2 m a sphere of radius 1 m is removed. The new centre of mass from $C_1$ is

In what ratio does the point (a, 6) divide the join of (-4, 3) and (2, 8) ? Also, find the value of a.

A cylindrical container with a diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions $22cm\times 14cm\times 10.5cm$. Find the rise in the level of the water when the solid is sub-merged.

Which among the following would be obtained on simplifying the expression $(A^{T}BA{)}^T$.

Define random experiment.

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?

If the line (3x+14y+7)+k(5x+7y+6)=0 is parallel to y-axis then the value of k is

In an auditorium. seats were arranged in rows and columus. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats increased by 300. Find :

(i) the number of rows in the original arrangement.

(ii) the number of seats in the auditorium after re-arrangement.

From the top of a tower 100 m high, a man observes two cars on the opposite of the tower with angles of depression ${30}^{\circ }and{45}^{\circ }$ respectively. Find the distance between the cars.
$Use[\sqrt{3}=1.73]$

What value/s can x take in the expression k(x - 10) (x + 10) =0 where k is any real number.

$x\in \left\{realnumbers\right\}and-1<3-2x\le 7,$ evaluate x and represent it on a number line.

If one root of the cubic equation $x^3-30x+133=0is\frac{7+3\sqrt{3}i}{2}$. Find the real root of the cubic equation.

If I draw two circles of radius 3 cm and 5 cm with a common centre and draw a line AB such that it is a common chord to both circles. CD = 4.46 cm. Find the distance of the chords from the centre and the length AC.

If x = a cos θ and y = b sin θ then b²x² + a²y² is equal to

Given an A.P. few of whose terms are x, y, 2, 4, 6, 8,.......... What must be the values of x and y?

ABCD is a square of side 10 cm. The area of the shaded region will be

Manu has a 5 years recurring deposit account and deposits Rs. 240 per month. If he receives Rs. 17,694 at the time of maturity, find the rate of interest.

The L.C.M. of two numbers is 48. The numbers are in the ratio 2:3. Then sum of the numbers is:

Show that the line joining the points (2,-3) and (-5, 1) is parallel to the line joining the points (7,-1) and (0, 3) and perpendicular to the line joining (4, 5) and (0,-2).