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Construct a triangle ABC in which BC is 3.5 cm, Angle B is ${75}^{\circ }$ and AB+AC=6.5cm

$\frac{cot({90}^o-\theta )sin({90}^o-\theta )}{sin\theta }+\frac{cot{40}^o}{tan{50}^o}-(co{s}^2{20}^o+co{s}^2{70}^o)$ = ?

(a) 0 (b) 1 (c) -1 (d) none of these

On a circular table cover of radius 42 cm, a design is formed by a girl leaving an equilateral triangle ABC in the middle, as shown in the figure. Find the covered area of the design.

[Use $\sqrt{3}=1.73and\pi =\frac{22}{7}$.]

$\frac{cosA}{cotA}+sinA=$

The sum up to $n$ terms of an AP with first term $a$, last term $l$ and common difference $d$ is

A manufacturer has 600 L of a 12% solution of acid. How many litres of 30% acid solution must be added to it, so that acid content in the resulting mixture will be more than 15% but less than 18%?

Malini Opens a recurring deposit account and deposits ₹ 600 per month for 5 years. The rate of interest is 8 %. Find the interest and maturity value she receives at the end of the maturity period

If HCF of657and 963 is expressible n the form of 657x+963(-15) find x.

Which of the following is not a measure of central tendency?

(a) Mean (b) Mode (c) Median (d) Range

Find the value of k for which the following system of equations has no solution: (20-25):

3x - 4y + 7 = 0

kx + 3y - 5 = 0

Find k for which the system2x+3y-5=0,4x+ky-10=0 has a an infinite number of solutions.

$\text{In the given figure BD = DC and}\angle CBD={30}^{\circ }\text{Find}\left(\angle BAC\right)$

If counted in pairs 1will remain. If counted in threes 2 will remain. If counted in fours 3 will remain. If counted in fives 4 will remain. If counted in sixes 5 will remain. If counted in sevens 0 will remain. Number is not more than 150. What is the number?

James buys a chair listed at Rs.1,500 and gets successive discounts of 20% and 10%. He spends Rs.20 on transportation and sells it at a profit of 20%. The selling price of the chair is

Find the ${12}^{th}$ term of the series $1^2.2+2^2.3+3^2.4+-------\infty$

(i) Find the equation of the line passing through (5, -3) and parallel to x - 3y = 4.

(ii) Find the equation of the line parallel to the line 3x + 2y = 8 and passing through the point (0, 1).

A man bought 20 shares of ₹ 50 at ₹ 5 discount, the rate of dividend being $13\frac{1}{2}$ The rate of interest obtained is:

A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumes.

If an equilateral triangle is drawn inside a circle such that the circle is the circum-circle of the triangle, find the relation between the length of the triangle and the radius of the circle.

What are the two consecutive even integers whose squares have sum 340?

Define perimeter of a circle.

A man goes 10 m due south and then 24 m due west. How far is he from the stating point ?

A toy is in the form of a cylinder with hemispherical ends. If the whole length of the toy is 90 cm and its diameter is 42 cm, find the cost of painting the toy at the rate of 70 paise per sq cm.

If $\frac{tan\theta }{sec\theta -1}$ - $\frac{tan\theta }{sec\theta +1}$ = k cot$\theta$ , then k =

Sachin wants to make a pet house for his dog with length, breadth and height of 3m, 2m and 1m respectively. What is the area of walls inside the pet house that has to be painted?

Find the mean.

$$\begin{array}{cccccc}{x}_i& 10& 14& 18& 21& 25\\ f_i& 10& 15& 7& 9& 9\end{array}$$

Steven Gerard, arguably one of the most consistent and skilled player in English premier league was given monthly ratings by a Football website. The ratings are given on monthly basis. The following are the ratings for the past 40 months.

$$\begin{array}{ccccccc}Rating& 6& 8& 8.5& 9& 7& 10\\ Numberofmonthswiththerating& 2& 8& 10& 7& 8& 5\end{array}$$

Calculate how his rating is deviating from his average performance in terms of mean deviation about mean.

If five times the fifth term of an A.P. is equal to 8 times its eighth term, show that its ${13}^{th}$ term is zero.

Extra tricky questions on trigonometry for my upcoming exams

Is it possible sir?

$(x+1),3xand(4x+2)$ are first three terms of an AP. Find its $5^{th}$ term.

(i).3u+4v=5

5u+6v=1

Solve this equation by elimination, cross multiplication, and substitution .

Shooters are required to shoot at a circular shaped target. The target is fixed onto a rectangular board with dimensions $44cm\times 21cm$. Assuming that all the bullets must hit the rectangular board, what is the probability that the bullets hit the circular target? (Given that the radius of the circle is 7 cm. )

\(\text{(D) In the given figure, O is the centre of the arc ABC which subtends an angle of} 130^\circ~ \text{at the centre.}\text{If AB is extended to P then}~\angle PBC = ___\)

tan² A sec²B - sec^{​​​​2}​​​​​​ A tan² B= tan² A- tan² B.

The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm form the quadratic equation to find the base of the triangle.

In completing square method should we add or subtract or consider signs in last step ?

The given figure shows a circle through the points A, B, C, and D. If $\angle BAC={67}^{\circ }$, find $\angle DBC+\angle DCB$

Given $15\cot A=8$, find $\sin A$ and $\cos A$

$\text{If}cot\theta =\frac{1}{\sqrt{3}},\text{find the value of}\frac{1-co{s}^2\theta }{2-si{n}^2\theta }$

(i) A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs 25 per metre.

(ii) The radius and height of a solid right-circular cone are in the ratio of 5 : 12. If its volume is 314 $c{m}^3,$ find its total surface area. $[Take\pi =\mathrm{3.14.}]$

Find the median for the following data

$$\begin{array}{ccccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ Frequency& 16& 20& 32& 48& 30& 14\end{array}$$

the sum of four consecutive terms of A.P is 2 .The sum of 3rd and 4th terms is 11. Find the terms

Find the area of the canvas required to make a conical tent 14m high and 96m in diameter. Given that:
1) canvas used in folds and stitchings is 20% of the curved surface area of the tent.

Tax imposed on a country’s imports from the rest of the world is called

By selling an item for Rs. 24, the shopkeeper earns the percent profit equal to cost price of the item. Find the cost price of the item.