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The rank of A =A=[0    1     3      1     1      0        1         1   3        1        0        21    1     2         0]A=\begin{bmatrix}0 \ \ \ \ 1 \ \ \ \ \ -3 \ \ \ \ \ \ -1\\ \ \ \ \ \\ \ 1 \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ 1 \\ \\ \ \ \ 3 \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ 2 \\\\ 1 \ \ \ \ 1 \ \ \ \ \ -2 \ \ \ \ \ \ \ \ \ 0 \end{bmatrix} is

The system of the linear equations is consistent if coefficient and the augmented matrix have
The eigen values of a skew symmetric matrix are

If A=[1  42  3]A = \begin{bmatrix} 1 \ \ 4 \\ 2 \ \ 3 \end{bmatrix}, Find A24A5I? A^2 - 4A - 5I?

Ltx01sinx1x=Lt_{x→0}\frac{1}{sinx}-\frac{1}{x}=

Ltx0x+2x2+53Lt_{x→0}\frac{x+2}{\sqrt{x^2+5-3}}=

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

x=asin1t,y=acos.1tx=\sqrt{a^{sin^{-1}t}} , y=\sqrt{a^{cos^{-.1}t}}dy/dx=?

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

y=3x2y=\sqrt{3x-2}എന്ന curve ന്റെ equation എന്ത് ? ഈ tangent 4x - 2y + 5 = 0 എന്ന രേഖക്ക് സമാന്തരമാണ്

WFB, TGD, QHG , ________
6/ 09/ 2022 മുതൽ 8 മാസം 7 ദിവസം പൂർത്തിയാകുന്ന തിയ്യതി
E = 5 PEN = 35 എങ്കിൽ PAGE = _________ ?
In which among the given samples, does 6.022 x 10^23 molecules contain ?
The main constituent of LPG is:
How many grams of sodium hydroxide present in 250 ml. of 0.5 M NaOH solution?
Which among the following metal is refined by distillation?
The energy possessed by a stretched bow is:
Fog is an example for colloidal system of
Which one of the following product is formed at cathode during electrolysis of aqueous sodium chloride solution?

A body fell down from rest and is falling down with an acceleration 10 m/s2. When it was hitting the ground, its displacement was 20 m. The velocity with which it hits the ground is:

There are 3 shells in the atom of element X. 6 electrons are present in its outermost shell. In which group is the element included ?
Which of the following will never give a real image?
Which of the following deals with inertia of a body ?
Which among the following is used as fungicide?
The number of electron pairs shared in the formation of nitrogen molecule is___________________
Which among the following is an alkyne?
In which of the following situation is friction an advantage ?
Which among the following is not a property of ionic compound?

Which of the following is the correct figure regarding the hanging of two iron nails from the pole of a magnet?

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A strong electrolyte is one which _________
The mass number of an atom is 31. The M shell of this atom contains 5 electrons. How many neutrons does this atom have?

The figure shows a person travelling from A to B and then to C. If so the displacement is:

image.png
Molar volume of 17 g ammonia is
Which of the following component is most suitable for rectification?
In an electric circuit the current is 0.5 A when a potential difference of 6 V is applied. When a potential difference of 12V is applied across the same circuit, the current will be :
Which of the following is the correct way regarding the expressing of temperature?
Which of the following method is to be used to separate oxygen from air ?
Which compound is used to decrease the rate of decomposition of hydrogen peroxide ?
What should be the position of an object in front of a concave mirror to get a real image having the same size as that of the object ?

The figure shows a wave generated in 0.2 s. Its speed is:

Screenshot 2025-08-19 132802.png

Find out the most suitable one regarding the pressure exerted by a liquid.
The eye ball of a person is small in size. The power of the eye lens is normal he is having the problem of:
On rubbing a glass rod with silk, the glass acquires positive charge. This is because:
Which of the following is the basis of working of an inductor ?
The most suitable substance that can be used as core of an electromagnet is :
A solution which contains the maximum possible amount of solute at any given temperature is known as
An object of height 2 cm is kept in front of a convex lens. The height of the image formed on a screen is 6 cm. If so the magnification is: