Physics-
General
Easy

Question

Statement–I : A parachute descends slowly whereas a stone dropped from same height falls rapidly
Statement–II : The viscous force of air on parachute is larger than that of on a falling stone

  1. Statement–I is true, Statement–II is true ; Statement–II is correct explanation for Statement–I    
  2. Statement–I is true, Statement–II is true ; Statement–II is NOT a correct explanation for Statement–I    
  3. Statement–I is true, Statement–II is false    
  4. Statement–I is false, Statement–II is true    

The correct answer is: Statement–I is true, Statement–II is true ; Statement–II is correct explanation for Statement–I

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In ABC ,AD is median, point F lies on AD such that fraction numerator A F over denominator F D end fraction equals fraction numerator 1 over denominator 5 end fraction, and A B & C Fintersect at E and BF and AC intersect at G.
If stack a with minus on top comma stack b with minus on top comma stack c with minus on topare position vectors of points A, B, C respectively such that stack a with minus on top comma stack b with minus on top comma stack c with minus on topare non-coplanar and if mid-point of AG lambda stack a with minus on top plus mu stack b with minus on top plus v stack c with minus on top, then the value of lambda plus mu plus v is

In ABC ,AD is median, point F lies on AD such that fraction numerator A F over denominator F D end fraction equals fraction numerator 1 over denominator 5 end fraction, and A B & C Fintersect at E and BF and AC intersect at G.
If stack a with minus on top comma stack b with minus on top comma stack c with minus on topare position vectors of points A, B, C respectively such that stack a with minus on top comma stack b with minus on top comma stack c with minus on topare non-coplanar and if mid-point of AG lambda stack a with minus on top plus mu stack b with minus on top plus v stack c with minus on top, then the value of lambda plus mu plus v is

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Statement-1: line L subscript 1 end subscriptis stack r with minus on top equals 20 left parenthesis i plus j minus k right parenthesis plus lambda left parenthesis i minus j right parenthesisline L subscript 2 end subscriptis stack r with minus on top equals 4 left parenthesis 4 i plus 3 j right parenthesis plus mu left parenthesis i plus j plus k right parenthesis line L is parallel to z-axis and intersects L subscript 1 end subscript and L subscript 2 end subscriptin the point A and B then AB=8
Statement-2 : stack r with minus on top equals stack a subscript 1 end subscript with bar on top plus lambda stack m subscript 1 end subscript with bar on top text  and  end text stack r with minus on top equals stack a subscript 2 end subscript with bar on top plus lambda stack m subscript 2 end subscript with bar on topare two skew lines then there exists a unique line L parallel to m subscript 3 end subscriptsuch that line L intersects the given skew lines where stack m subscript 1 end subscript with bar on top comma stack m subscript 2 end subscript with bar on top comma stack m subscript 3 end subscript with bar on topare pair wise linearly independent

Statement-1: line L subscript 1 end subscriptis stack r with minus on top equals 20 left parenthesis i plus j minus k right parenthesis plus lambda left parenthesis i minus j right parenthesisline L subscript 2 end subscriptis stack r with minus on top equals 4 left parenthesis 4 i plus 3 j right parenthesis plus mu left parenthesis i plus j plus k right parenthesis line L is parallel to z-axis and intersects L subscript 1 end subscript and L subscript 2 end subscriptin the point A and B then AB=8
Statement-2 : stack r with minus on top equals stack a subscript 1 end subscript with bar on top plus lambda stack m subscript 1 end subscript with bar on top text  and  end text stack r with minus on top equals stack a subscript 2 end subscript with bar on top plus lambda stack m subscript 2 end subscript with bar on topare two skew lines then there exists a unique line L parallel to m subscript 3 end subscriptsuch that line L intersects the given skew lines where stack m subscript 1 end subscript with bar on top comma stack m subscript 2 end subscript with bar on top comma stack m subscript 3 end subscript with bar on topare pair wise linearly independent

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Assertion (A) : If stack a with minus on top equals 2 i plus stack k with minus on top comma stack b with minus on top equals 3 j plus 4 k text end textand stack c with minus on top equals 8 i minus 3 jare coplanar then stack c with minus on top equals 4 stack a with minus on top minus stack b with minus on top
Reason (R) : A set of vectors a1, a2, a3.an is said to be linearly dependent if for some relation of the form l subscript 1 end subscript a subscript 1 end subscript plus l subscript 2 end subscript stack a with minus on top subscript 2 end subscript plus l horizontal ellipsis horizontal ellipsis. plus 1 subscript n end subscript stack a with minus on top subscript n end subscript equals stack 0 with bar on topimplies at least one of the scalars li (i = 1,2.n) is not zero

Assertion (A) : If stack a with minus on top equals 2 i plus stack k with minus on top comma stack b with minus on top equals 3 j plus 4 k text end textand stack c with minus on top equals 8 i minus 3 jare coplanar then stack c with minus on top equals 4 stack a with minus on top minus stack b with minus on top
Reason (R) : A set of vectors a1, a2, a3.an is said to be linearly dependent if for some relation of the form l subscript 1 end subscript a subscript 1 end subscript plus l subscript 2 end subscript stack a with minus on top subscript 2 end subscript plus l horizontal ellipsis horizontal ellipsis. plus 1 subscript n end subscript stack a with minus on top subscript n end subscript equals stack 0 with bar on topimplies at least one of the scalars li (i = 1,2.n) is not zero

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Let stack a with rightwards arrow on top equals stack i with hat on top plus stack j with hat on top plus 2 stack k with hat on top text end textand stack b with rightwards arrow on top equals 2 stack i with hat on top minus stack j with hat on top minus stack k with hat on top. Then the point of intersection of the
lines stack r with rightwards arrow on top cross times stack a with rightwards arrow on top equals stack b with rightwards arrow on top cross times stack a with rightwards arrow on top and stack r with rightwards arrow on top cross times stack b with rightwards arrow on top equals stack a with rightwards arrow on top cross times stack b with rightwards arrow on topis

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lines stack r with rightwards arrow on top cross times stack a with rightwards arrow on top equals stack b with rightwards arrow on top cross times stack a with rightwards arrow on top and stack r with rightwards arrow on top cross times stack b with rightwards arrow on top equals stack a with rightwards arrow on top cross times stack b with rightwards arrow on topis

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If stack a with minus on topand stack b with minus on topare two unit vectors and ϕis the angle between them, then fraction numerator 1 over denominator 2 end fraction vertical line stack a with minus on top minus stack b with minus on top vertical lineis equal to

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Statement-1:The area of the triangle formed by the points A(20,22) ;B(21,24) and C(22,23) is the same as the area of the triangle formed by the point P(0,0) ;Q(1,2) and R(2,1) . Because
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The functions s i n to the power of 1 end exponent invisible function application x comma c o s to the power of 1 end exponent invisible function application x comma t a n to the power of 1 end exponent invisible function application x comma c o t to the power of 1 end exponent invisible function application x comma c o s e c to the power of 1 end exponent invisible function application x and s e c to the power of 1 end exponent invisible function application x are called inverse circular or inverse trigonometric functions which are defined as follows
s i n to the power of 1 end exponent invisible function application x text  1  end text x 1 pi divided by 2 s i n to the power of 1 end exponent invisible function application x pi divided by 2
c o s to the power of 1 end exponent cross times 1 cross times 10 c o s to the power of 1 end exponent cross times pi
t a n to the power of 1 end exponent invisible function application x cross times R pi divided by 2 less than t a n to the power of 1 end exponent invisible function application x less than pi divided by 2
c o s e c to the power of 1 end exponent invisible function application x vertical line x vertical line 1 pi divided by 2 c o s e c to the power of 1 end exponent invisible function application x 0
s e c to the power of 1 end exponent invisible function application x vertical line x vertical line 10 s e c to the power of 1 end exponent invisible function application x pi pi divided by 2
c o t to the power of 1 end exponent invisible function application x x R 0 less than c o t to the power of 1 end exponent invisible function application x less than pi
Number of solutions of t a n to the power of 1 end exponent invisible function application vertical line x vertical line c o s to the power of 1 end exponent invisible function application x equals 0 is/are

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s i n to the power of 1 end exponent invisible function application x text  1  end text x 1 pi divided by 2 s i n to the power of 1 end exponent invisible function application x pi divided by 2
c o s to the power of 1 end exponent cross times 1 cross times 10 c o s to the power of 1 end exponent cross times pi
t a n to the power of 1 end exponent invisible function application x cross times R pi divided by 2 less than t a n to the power of 1 end exponent invisible function application x less than pi divided by 2
c o s e c to the power of 1 end exponent invisible function application x vertical line x vertical line 1 pi divided by 2 c o s e c to the power of 1 end exponent invisible function application x 0
s e c to the power of 1 end exponent invisible function application x vertical line x vertical line 10 s e c to the power of 1 end exponent invisible function application x pi pi divided by 2
c o t to the power of 1 end exponent invisible function application x x R 0 less than c o t to the power of 1 end exponent invisible function application x less than pi
Number of solutions of t a n to the power of 1 end exponent invisible function application vertical line x vertical line c o s to the power of 1 end exponent invisible function application x equals 0 is/are

Maths-General
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Given : cos invisible function application xcos invisible function application open parentheses fraction numerator pi over denominator 3 end fraction plus x close parentheses cos invisible function application open parentheses fraction numerator pi over denominator 3 end fraction minus x close parentheses equals fraction numerator 1 over denominator 4 end fraction comma x element of open square brackets 0 , 6 pi close square brackets
Sum of all solutions is

Given : cos invisible function application xcos invisible function application open parentheses fraction numerator pi over denominator 3 end fraction plus x close parentheses cos invisible function application open parentheses fraction numerator pi over denominator 3 end fraction minus x close parentheses equals fraction numerator 1 over denominator 4 end fraction comma x element of open square brackets 0 , 6 pi close square brackets
Sum of all solutions is

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This section contains 3 multiple choice questions numbered 14 to 16 .Each question has 4 choices (A), (B),(c) , and (D), out of which ONE or MORE may be correct
If fraction numerator 3 plus i 2 s i n invisible function application theta over denominator 1 minus i 2 s i n invisible function application theta end fractionis real , then

This section contains 3 multiple choice questions numbered 14 to 16 .Each question has 4 choices (A), (B),(c) , and (D), out of which ONE or MORE may be correct
If fraction numerator 3 plus i 2 s i n invisible function application theta over denominator 1 minus i 2 s i n invisible function application theta end fractionis real , then

Maths-General
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A charge q is placed at the center of the open end of cylindrical vessel. The flux of the electric field through surface of the vessel is

A charge q is placed at the center of the open end of cylindrical vessel. The flux of the electric field through surface of the vessel is

Physics-General
parallel

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