if cos(ɑ + β) = 0 , then sin (ɑ - β) can be reduced to

The length of the shadow of a pole is √3 times its height. The elevation of the sum must be

Two chimneys 18m and 13m high stand upright in the ground. If their feet are 12m apart, then the distance between their tops is

In a farm there are hens and cow. If the heads are counted there are 200 and if the legs are counted there are 580. How many hens are there?

A vessel contains a liquid in which there is 5 part milk and 3 part water. What part of the mixture should be taken out and replaced with water so that the ratio of a milk and water may become 1 : 1?

A bottle is full of pure alcohol. One third of it is taken out and then equal amount of water is poured into the bottle to fill it. This operation is done four times. Find the final ratio of alcohol and water in the bottle?

A jar has 40 L milk. From the jar, 8 L of milk was taken out and replaced by an equal quantity of water. If 8 L of the newly formed mixture is taken out of the jar, what is the final quantity of milk left in the jar?

Jar A contains ‘X’ L of pure milk only. A 27 L mixture of milk and water in the respective ratio of 4 : 5, is added into it. If the new mixture thus formed in jar A contains 70% milk, what is the value of X?

A vessel of 160 L is filled with milk and water. 70% of milk and 30% of water is taken out of the vessel. It is found that the vessel is vacated by 55%. Find the quantity of milk and water in this mixture.

300 g of sugar solution has 40% of sugar in it. How much sugar should be added to make it 50% in the solution?

In a mixture of 150 L, the ratio of milk to water is 2 : 1. What amount of water must be further added to the mixture so as to make the ratio of the milk to water 1 : 2 respectively?

A milkman bought 15 L of milk and mixed 3 L of water in it. If the price per kg of the mixture becomes ₹ 22, what is the cost price of the milk per litre?

A vessel contains liquids P and Q in the ratio 5 : 3. If 16 L of the mixture is removed and replaced by same quantity of liquid Q and the ratio becomes 3:5 What is the quantity that the vessel hold ?

R ആരമുള്ള ഒരു ഗോളത്തിന് ഉള്ളിൽ ആലേഖനം ചെയ്യാൻ പറ്റുന്ന പരമാവധി വ്യാപ്തമുള്ള സിലിണ്ടാറിൻ്റെ ഉയരം എത്ര?

i. [a, b] യിൽ f continuous ആണ്. ii . (a , b ) യിൽ f differentiable ആണ്. iii . f(a) - f(b) = (b - a)f'(c ) എന്ന സമവാക്യം സമവാക്യം സാധൂകരിക്കുന്ന c എന്ന പോയിന്റ് (a, b) യിൽ ഉണ്ട് . iv. f(a) = f(b) = 0 v. f'(a)=0 എന്ന സമവാക്യം സാധൂകരിക്കുന്ന c എന്ന പോയിന്റ് (a, b) യിൽ ഉണ്ട്. അഞ്ചു വ്യവസ്ഥകളിൽ Rolle's theorem ത്തിനോട് ബന്ധപ്പെട്ട വ്യവസ്ഥകൾ ഏതൊക്കെ

i. [a, b] യിൽ f continuous ആണ്. ii . (a , b ) യിൽ f differentiable ആണ്. iii . f(a) - f(b) = (ബി - a)f'(c ) എന്ന സമവാക്യം സമവാക്യം സാധൂകരിക്കുന്ന c എന്ന പോയിന്റ് (a, b) യിൽ ഉണ്ട് . iv. f(a) = f(b) = 0 v. f'(a)=0 എന്ന സമവാക്യം സാധൂകരിക്കുന്ന c എന്ന പോയിന്റ് (a, b) യിൽ ഉണ്ട്. അഞ്ചു വ്യവസ്ഥകളിൽ Rolle's theorem ത്തിനോട് ബന്ധപ്പെട്ട വ്യവസ്ഥകൾ ഏതൊക്കെ

$x=\sqrt{a^{sin^{-1}t}} , y=\sqrt{a^{cos^{-.1}t}}$ dy/dx=?

f(x)= |x - 1| + sin x continuous ആയിട്ടുള്ള എല്ലാ പോയിന്റുകളും കണ്ടുപിടിക്കുക

$Lt_{x→0}\frac{x+2}{\sqrt{x^2+5-3}}$ =

$Lt_{x→0}\frac{1}{sinx}-\frac{1}{x}=$

If $A = \begin{bmatrix} 1 \ \ 4 \\ 2 \ \ 3 \end{bmatrix}$ , Find $A^2 - 4A - 5I?$

The eigen values of a skew symmetric matrix are

The system of the linear equations is consistent if coefficient and the augmented matrix have

The rank of A = $A=\begin{bmatrix}0 \ \ \ \ 1 \ \ \ \ \ -3 \ \ \ \ \ \ -1\\ \ \ \ \ \\ \ 1 \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ 1 \\ \\ \ \ \ 3 \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ 2 \\\\ 1 \ \ \ \ 1 \ \ \ \ \ -2 \ \ \ \ \ \ \ \ \ 0 \end{bmatrix}$ is

24 സെ.മി ഉയരവും 6 സെ.മി ബേസ് റേഡിയസുമുള്ള ഒരു കോൺ ഉരുക്കി ഒരു ഗോളത്തിന്ടെ രൂപത്തിൽ പുനർ രൂപകൽപന ചെയ്തിരിക്കുന്നു. എങ്കിൽ ആ ഗോളത്തിന്ടെ ആരം എത്രയാണ് ?

If A is an orthogonal matrix, then the |A| is

108 കി.മി./മണിക്കൂർ വേഗത ______________ നു സമാനമാണ്

If A is a symmetric matrix, then adj A is

If A is a n-square matrix, then.

$\frac{0.003 \times 0.45}{0.009}=$

യഥാക്രമം 10, 15, 24 മിനിറ്റ് ഇടവേളകളിൽ മൂന്നു മണികൾ മുഴങ്ങുന്നു. രാവിലെ 8 മണിക്ക് മൂന്നു മണികളും ഒരുമിച്ച് മുഴങ്ങാൻ തുടങ്ങും . അവ രണ്ടും ഒരുമിച്ച് മുഴങ്ങുന്നത് എത്ര മണിക്കാണ് ?

Find the reminder when $3^{101}$ is divided by 7?

reproductive property ഇല്ലാത്ത distribution താഴെ പറയുന്നവയിൽ ഏതാണ്

Among how many people may 429 kg of rice and also 715 kg of wheat be equally divided?

The students in a class can be divided into groups of 2, 3, 5 and 6. What is the least number of children this class can have?

Find the volume of a cube whose surface area is 96 cm³.

The dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88m². Find the dimensions?

Let $x^2+y^2-2a (x+y)+a^2=0$ be an equation of a circle. Then

There are three cycles to distributed among five children. If no child gets more than one cycle, then this can be done in how many ways?

If the sum of the roots of $(p + 1) \times x ^ 2 + (2p + 3)x + (3p + 4) = 0$ is -1 , then the product of the roots is

The roots of the equation $2 (a ^ 2 + b ^ 2) \times x ^ 2 + 2(a + b) \times x + 1 = 0$ are

Let f be a function from Z to Z. such that f(x) = x + 3 Find the inverse of f?

Let fand g be the functions from R to R such that $f(x)=2x$ and $g(x) = x ^ 2$ What is fg ?

The relation "division" on the set of positive integers is

How many reflexive relations there in a set of n + 1 elements?

The primary goal of the action plan phase in Action Research is

Which among the following is the exact situation where the maxim 'Simple to Complex is implied?

Which statement is NOT TRUE as per Piaget?

Which among the following typically demands 'predictive validity?"

Which level of thinking is aligned with 'the expectation for a student to articulate the underlying concept and process in mathematical induction"?

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