Read the following short write-up and answer the questions at the end of it The name ‘silica’ covers an entire group of minerals, which have the general formula $S i O subscript 2 end subscript comma$ the most common of which is quartz. Quartz is a framework silicate with $S i O subscript 4 end subscript$ tetrahedra arranged in spirals. The spirals can turn in a clockwise or anti-clockwise direction $–$ a feature that results in there being two mirror images, optically active, varieties of quartz The following pictures represent various silicate anions. Their formulae are respectively

A particle is moved from (0, 0) to (a, a) under a force $stack F with rightwards arrow on top equals open parentheses 3 stack i with tilde on top plus 4 stack j with rightwards arrow on top close parentheses blank$ from two paths. Path 1 is OP and path 2 is OQP. Let $W subscript 1 end subscript$ and $W subscript 2 end subscript$ be the work done by this force in these two paths. Then:
S

In the figure shown all the surfaces are frictionless, and mass of the block, m = 1 kg. The block and wedge are held initially at rest. Now wedge is given a horizontal acceleration of 10 $m divided by s to the power of 2 end exponent$ by applying a force on the wedge, so that the block does not slip on the wedge. Then work done by the normal force in ground frame on the block in $square root of 3 blank$ seconds is:

With what minimum velocity $V subscript 0 end subscript$ should block be projected from left end A towards end B such that it reaches the other end B of conveyer belt moving with constant velocity v? Friction coefficient between block and belt is $mu$ .

A bob is suspended from a crane by a cable of length $l equals 5 blank$ m. The crane and load are moving at a constant speed $V subscript 0 end subscript$ . The crane is stopped by a bumper and the bob on the cable swings out an angle of $60 to the power of ring operator end exponent$ . The initial speed $v subscript 0 end subscript text is end text text end text text - end text open parentheses g equals 9.8 m divided by s to the power of 2 end exponent close parentheses$

If $A plus B plus C equals 270 to the power of ring operator end exponent$ then $c o s invisible function application 2 A plus c o s invisible function application 2 B plus c o s invisible function application 2 C equals$

If $A plus B plus C equals 270 to the power of ring operator end exponent$ then $s i n invisible function application 2 A plus s i n invisible function application 2 B plus s i n invisible function application 2 C equals$

If $s i n invisible function application left parenthesis y plus z minus x right parenthesis comma s i n invisible function application left parenthesis z plus x y right parenthesis comma s i n invisible function application left parenthesis x plus y minus z right parenthesis$ are in A.P. then $t a n invisible function application x comma t a n invisible function application y$ and $t a n invisible function application z$ are in

Maths-

In any $straight triangle A B C fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis over denominator 4 b squared c squared end fraction equals$

s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.

In any $straight triangle A B C fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis over denominator 4 b squared c squared end fraction equals$

Maths-General

s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.

In $straight triangle A B C sum a cubed Sin space left parenthesis B minus C right parenthesis equals$

If $A plus B plus C equals 90 to the power of ring operator end exponent$ then $s i n to the power of 2 end exponent invisible function application A plus s i n to the power of 2 end exponent invisible function application B plus s i n to the power of 2 end exponent invisible function application C equals$

If $A plus B plus C equals 0 to the power of ring operator end exponent$ then $c o s to the power of 2 end exponent invisible function application A plus c o s to the power of 2 end exponent invisible function application B plus c o s to the power of 2 end exponent invisible function application C equals$

Maths-

In $straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals$

The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.

In $straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals$

Maths-General

The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.

Maths-

The perimeter of a Δ ABC is 6 times the A.M of the sines of its angles if the side "a" is 1, then the angle A is

The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.

The perimeter of a Δ ABC is 6 times the A.M of the sines of its angles if the side "a" is 1, then the angle A is

Maths-General

The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.

The resistance of a resistance thermometer has values $2.71$ and $3.70$ ohm at $1 0º C$ and $10 0º C$ The temperature at which the resistance is $3.26$ ohm is