Dynamics

1 and 2 Mark Questions:

1.Explain the working of Landry Drier?
2.Explain Centrifuge, How does it work?
3.Difference between rotary and circular motion?
4.Difference between Inertial and non Inertial frames of references?
5.What is banking angle? What is the necessity for banking of roads?
6.What is the principle of launching a satellite into an orbit?

4 Mark Questions:

7.Difference between centripetal and centrifugal force?
8.Define Simple Harmonic Motion?Wat are the Characteristics?

Our Universe

1 and 2 Mark Questions:

1.What is Mass and Weight?

2.Define Weight of a Body?

3.Define Mass of a Body?

4.What is heliocentric theory?

5.State Hooks Law?

6.Write relation between ‘g’ and ‘G’?

7.What are the characteristic of Simple Harmonic Motion?

8.What is the acceleration due to Gravity?

4 Mark Questions:

9.State Newton’s Law of gravitation and derive F=gm₁m₂ / r² ?

10.State Hook’s Law and How to prove Hook’s Law in lab?

Kinematics

1 and 2 Mark Questions:

1) A body projected vertically with a velocity of 40 m/s. Find Maximum height reached by it?

2) A ball is thrown up attaining maximum height of 80m.Find its initial speed?

4 Mark Questions:

3) Show that Time of Ascent is equal to theTime of Descent?

Measurement Of Length

1 and 2 Mark Questions: 

1)What is the Principle of Screw Gauge? 

2) What is the Least Count of Screw gauge? 

3) Define pitch of screw?

4 Mark Questions: 

4) How do you determine the diameter of a wire using a screw gauge?

5 Mark Questions:

5) Draw a neat diagram of screw gauge and label its parts?

6) Draw a neat diagram of Positive and Negative error of Screw Gauge?

Polynomials

1 Mark and 2 Mark questions :

1) Find the value of 'm' in order that x⁴-2x³+3x²-mx+5 may be exactly divisible by (x-1)

2) Comment the roots of the quadratic equation 3x²-7x+2=0

3) Find the roots of the equation x²+x(c-b)+(c-a)(a-b)=0

4) If x³-3x²+4x+k is divisible by (x-2) find the value of k

5) Find the sum and product of the roots of the equation √3x² +9x+6√3 =0

6) State and prove the reminder Theorem.

7) Find the reminder, When x ⁴+4x³-5x²-6x+7 is divided by (x+3),(x-3)

8)  Find the Quadratic equation whose roots are i) 2 and 3 ii) 2+√3,2-√3

9) Find the value of k so that x³-3x²+4x+k is exactly divisible by x-2

10) find the middle term of(x/y + y/x)⁸

^{11) Find the Quadratic Equation in x ,Which when divided by (x-1),(x-2) and (x-3) leaves the reminder of 11 ,22 and 39 respectively..}

4 Mark Questions :

12) find the constant term in the expansion (3x-(5/x²))⁹

13) factorize the following i) x⁴+5³+5²-5x-6  ii) 3x⁴-10x³+5x²+10x-8

14) find the independent term of 'x' (6x-( (5/x²))¹²

15)find the values of 'b' and 'c' ,if divison of x²+bx+c by i)x-1 leaves the reminder zero ii) x+2 leaves the reminder 12

16) if f(x)=x²+5x+p and q(x)=x²+3x+q have common factor then i) find the common factor ii) show that (p-q)²=2(3p-5q)

 5 Mark Questions :

17) solve x²-4x+3=0 using the graph of y=x²

18) solve x²-x-2=0 using the graph of y=x²

19) solve x²-3x+2=0 using the graph of y=x²

20) Draw Graph for y=x²-5x+6 and solve x²-5x+6=0

21)  Draw Graph for y=x²+5x+6

Functions

1 Mark and 2 Mark questions :

Please note that  / stands for divison

1) If Function f: R-{2} -> R is defined as f(x)=(2x+1/x-2 )then prove that f(2x+1/x-2)= x

2) f: A->B and f have inverae function f^-1: B->A. then state the properties of f for which its inverse exist?

3) Let f:R->R; g: R->R defined f(x)=1+2x ; g(x)=3-2x find fog(3)?

4) If f(x)=2x+3 , then find the value of f(x+h)-f(x) / f(x)  (h ≠ 0)

5)  If function f;R-{1} -> R is defined as f(x)=(x+1/x-1) ; then prove that f(x) + f(1/x) =0 (x ≠ 0)

6)  If f(x)=(1-x/1+x) find f(0),f(1),f(2) and f(3)

7)  If f(x) = x+2 ; g(x)= x²-x-2 then find g(1)+g(2)+g(3)

                                                             f(-4)+f(-2)+f(2)

8) If f={(1,3)(2,5)(3,7)} ; g={(3,7)(5,9)(7,10)} find gof

9) Define one-one function show that f(x)=3x-2 x ∈N is one to one

10) If f: R-{3} -> R is defined by f(x)=(x+3/x-3) show that f(3x+3/x-1) =x for x ≠ 1

11) Define the following 1) one to one function 2) Onto function 3) constant function 4) Bijection function

4 Mark Questions :

12 ) Let f,g,h be the functions defined as following f(x)=x+2;g(x)=3x-1; h(x)=2x then show that h0(g0f)=(h0g)0f
13)  If f:R->R define as f(x)=2x+3 ,show that f^-1 is a function and find f^-1(4)
14) let f be given by f(x) =x+2 and  f has the domain { x: 2 ≤ x ≤ 5} find f^-1 and its domain and range
15) Given f(x)=1+2x ; g(x)=3-2x ∀x ∈R find f0g(x),gof(x) ; gof(3);fog(3)
16) Let f,g,h are the functions defined by f(x)=x ;g(x)=1-x and h(x)=x+1 find 1) (h0g) 0f 2) h0(gof) then waht you observe from 1 and 2
17) let f(x)=x-1;g(x)=x²-2 ; h(x) =x³-3 then prove that f0(g0h) = (f0g)0h
18) if f(x)=x+2 ; g(x)=x ;h(x)=x² then shoe that (h0g)0f=h0(g0f)

Statements and sets Important Questions

1 Mark and 2 Mark Questions

1) Define Conjunction and write its Truth Table?

2) Define Disjunction and write its Truth Table?

3) Define Implication and write its Truth Table?

4) Define Bi Implication and write its Truth Table?

5) Write Converse,inverse and Contra positive of the conditional statement

     i) "If Triangle is an equilateral triangle, Then it is an Isosceles Triangle"

     ii) " In a triangle ABC if AB=AC then  ∠B = ∠C

6) Define Tautology and give Examples?

7) define contradiction and give example?

8) show that [P ∧(~q)] ∧[(~p)∨q] is a contradiction?

9) Prove that A ∩ B' = A-B

10) If A and B are disjoint set and n(A)=4 ,n(AUB)=10 then find n(A∩B) ?

11) Show that ~[p => q]≡ p ∧ (~q)

12) prove that A ∩ B= ∅implies B ∩ A' =B

13) If A and B are Two sets then show that A'-B' = B-A

14) Let A={ All primes less than 20 }; B={ All whole numbers less than 10} then find A∩ B and AUB.

15) Show that A ∩ B= A-B' =B-A'.

4 Mark Question

16) Prove that A-(B ∩ C) =(A-B) U (A-C) for any three sets of A,B and C?
17) Show that A-(BUC)=(A-B)  ∩ (A-C) for any three sets of A,B and C?
18) Prove that for any three sets A,B,C AU(B ∩ C)=(A U B) ∩ (AUC) ?
19) Prove that for any three sets A,B,C A∩(B U C)=(A ∩ B) U (A∩C) ?
20) using element wise ,Prove that (A ∩ B)' =A' U B' ?