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On simplification, $(cosec\theta +cot\theta )\times (1-cos\theta )=$

Does the values of trigonometric ratios of an angle vary with length of the sides of the triangles ,if the angles remain same justify the answer.

Gregor J. Mendel is the Father of Genetics. He conducted various experiments by mating pea plants of varying characteristics. He then calculated the number of variants produced by mating and finally calculated the probability of transmission of a particular character. This approach is a:

Solve the following systems of equations:

x+y=5xy

3x+2y=13xy,

In $\Delta$ABC, if DE divides AB and AC in the same ratio, then which of the following options is true?

The nature of roots of $\frac{x-1}{x-1}=\frac{x+4}{2x+2}$ is/are ____.

Show that 5n cannot end with the digit 2

A man is known to speak the truth $3$ out of $4$ times. He throws a die and reports that it is a six. The probability that it is actually a six is:

To find the sum of the first 24 terms of an AP whose $n^{th}$ term is given by $a_n=3+2n$, what is the best approach to solve this question?

Question 120

A birthday cake has two tiers as shown in the figure below. Find the volume of the cake.

What function does the underlined connector perform in the sentence?
The team celebrated the birthday of the young intern. Moreover, it was his last day at the office.

Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and $\angle$BOD = ${160}^{\circ }$, then find the measure of $\angle$BPD.

If $\Delta$ ABC is a right triangle such that $\angle C={90}^o,\angle A={45}^o$ and BC = 7 units. Find $\angle B$, AB and AC.

(i) $\frac{2}{3}(co{s}^4{30}^o-si{n}^4{45}^o)-3(si{n}^2{60}^o-se{c}^2{45}^o)+\frac{1}{4}co{t}^2{30}^o$

(ii) $4(si{n}^4{30}^o+co{s}^4{60}^o)-\frac{2}{3}(si{n}^2{60}^o-co{s}^2{45}^o)+\frac{1}{2}ta{n}^2{60}^o$

(iii) $\frac{sin{50}^o}{cos{40}^o}+\frac{cosec{40}^o}{sec{50}^o}-4cos{50}^{o}cosec{40}^o$

(iv) $tan{35}^{o}tan{40}^{o}tan{45}^{o}tan{50}^{o}tan{55}^o$

(v) $cosec({65}^o+\theta )-sec({25}^o-\theta )-tan({55}^o-\theta )+cot({35}^o+\theta )$

(vi) $tan{7}^{o}tan{23}^{o}tan{60}^{o}tan{67}^{o}tan{83}^o$

(vii) $\frac{2sin{68}^o}{cos{22}^o}-\frac{2cot{15}^o}{5tan{75}^o}-\frac{3tan{45}^{o}tan{20}^{o}tan{40}^{o}tan{50}^{o}tan{70}^o}{5}$
(viii)$\frac{3cos{55}^o}{7sin{35}^o}-\frac{4\left(cos{70}^{o}cosec{20}^o\right)}{7\left(tan{5}^{o}tan{25}^{o}tan{45}^{o}tan{65}^{o}tan{85}^o\right)}$
(ix) $\frac{sin{18}^o}{cos{72}^o}+\sqrt{3}\left\{tan{10}^{o}tan{30}^{o}tan{40}^{o}tan{50}^{o}tan{80}^o\right\}$
(x) $\frac{cos{58}^o}{sin{32}^o}+\frac{sin{22}^o}{cos{68}^o}-\frac{cos{38}^{o}cosec{52}^o}{tan{18}^{o}tan{35}^{o}tan{60}^{o}tan{72}^{o}tan{55}^o}$

AP and AQ are the two tangents drawn to a circle with centre O, these tangents are inclined to each other at an angle ${60}^0$. Find $\angle APQ$ in the given figure.

In $△ABC,$ sides opposite to angles $A,B,C$ are denoted by $a,b,c$ respectively. Then the value of $(b-c)\sin A+(c-a)\sin B+(a-b)\sin C=$

P(x) =2x⁴-6x³+2x²-x+2

G(x)=x+2

Find remainder by long division.

A fruit seller buys fruits from a wholesaler for Rs 1000 and paid sales tax at 10%. He then sells it to the consumer for Rs 1500 and charges the same sales tax. What is the VAT paid by the shopkeeper?

TSA of hollow hemisphere of outer radius R and inner radius r is _______.

For a pair of linear equations

$a_{1}x+b_1+c_1=0$ and $a_{2}x+b_2+c_2=0$

$a_1=12,b_1=2,c_1=6$ and $a_2=24,b_2=4,c_2=7$.

Find the number of solutions the pair of equations will have.

If one zero of 2x² - 3x + k is reciprocal to the other, then the value of k is :

Given that BC and BC' lie on the same ray BY. The ratio of $\frac{BC}{C{C}^{\prime }}$ is 3:5.
What will the ratio of corresponding sides be if triangles ABC and A'BC' are similar?

Question 92 (xii)

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

$\frac{x^2}{25}-625$

If A is a square matrix of order n and A=kB, where k is a scalar, then |A|=

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients :

$2\sqrt{3}{x}^2-5x+\sqrt{3}$

The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is: