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# GATE GNST|| Aptitude & Maths Quiz 5

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Question 1

A first order differential equation can be written as

The general solution of the equation is

Question 2

If A is 4 × 5 real matrix and A × = B is a consistent system of equations. The highest possible rank of A is:

Question 3

If a + 1/a = 4, a

^{2}+ 1/a^{3}= 7, then what is the value of a^{3}+ 1/a^{2 }?Question 4

For the matrix eigen vector corresponding to eigen value −2 is ___________.

Question 5

Find the number of zeroes at the end of the product of the expression 2

^{2}× 5^{6}× 2^{10}× 5^{14}× 2^{18}× 5^{22}× 2^{26}× 5^{30}.Question 6

P, Q & R start a business with the investment ratio 5:6:8. At the end of the year their profit ratio is 5:3:12. If R worked for entire year then find the sum of time duration of P and Q for which they invested their money.

Question 7

How many solutions does the following system of linear equations have?

-x + 5y = -1

x - y = 2

x + 3y = 3

-x + 5y = -1

x - y = 2

x + 3y = 3

Question 8

In the figure EC and AD are the diameters of the circle. Find ∠EPD + ∠BPA.

Question 9

If x + y = 10 then maximum value of xy is

Question 10

For a given matrix, where, the inverse of matrix p is

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Feb 22ESE & GATE ME

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Krishn PratapMember since Aug 2020

Cleared GATE, Selected for JWM interview, Cleared RRB JE, Cleared SSC JE, MPPSC AE Mains Cleared