If $l subscript r end subscript superscript 2 end superscript plus m subscript r end subscript superscript 2 end superscript plus n subscript r end subscript superscript 2 end superscript equals 1$ where r = 1, 2, 3 and $I subscript 1 end subscript I subscript 2 end subscript plus m subscript 1 end subscript m subscript 2 end subscript plus n subscript 1 end subscript n subscript 2 end subscript$ = 0 …etc, then, $capital delta equals open vertical bar table row cell l subscript 1 end subscript blank m subscript 1 end subscript blank n subscript 1 end subscript end cell row cell I subscript 2 end subscript blank m subscript 2 end subscript blank n subscript 2 end subscript end cell row cell I subscript 3 end subscript blank m subscript 3 end subscript blank n subscript 3 end subscript end cell end table close vertical bar to the power of 2 end exponent$ is equal to

If I = $open square brackets table row cell 1 blank 0 end cell row cell 0 blank 1 end cell end table close square brackets$ , J = $open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets$ and B = $open square brackets table row cell c o s invisible function application theta end cell cell s i n invisible function application theta end cell row cell negative s i n invisible function application theta end cell cell c o s invisible function application theta end cell end table close square brackets$ , then B equals

If A^′ is the transpose of a square matrix A, then

If $open vertical bar table row cell stretchy sum from k equals 0 to n minus 2 of 1 end cell cell n left parenthesis n minus 1 right parenthesis end cell cell n to the power of 2 end exponent end cell row cell stretchy sum from k equals 1 to n of 1 end cell cell left parenthesis n plus 1 right parenthesis left parenthesis n minus 1 right parenthesis end cell cell n left parenthesis n plus 1 right parenthesis end cell row cell stretchy sum from k equals 1 to n minus 1 of 1 end cell cell n to the power of 2 end exponent plus 1 end cell cell n to the power of 2 end exponent end cell end table close vertical bar$ = 72, then n is equal to

The determinant $capital delta equals open vertical bar table row a b cell a alpha plus b end cell row b c cell b alpha plus c end cell row cell a alpha plus b end cell cell b alpha plus c end cell 0 end table close vertical bar$ is equal to zero if

Equation of the line passing though the point of intersection of the lines x + 2y – 3 = 0 and x
+ y –2 = 0 and also through the point (2, 1) is

For such questions, we should know different formulas to find equation of line.

Equation of the line passing though the point of intersection of the lines x + 2y – 3 = 0 and x
+ y –2 = 0 and also through the point (2, 1) is

For such questions, we should know different formulas to find equation of line.

The locus of the point which moves so that the square of its distance from the point (3, 0) is
equal to 7 is

Locus of a point means path traced by the given point while satisfying the given conditions. For such questions, we should know distance formula.

The locus of the point which moves so that the square of its distance from the point (3, 0) is
equal to 7 is

Locus of a point means path traced by the given point while satisfying the given conditions. For such questions, we should know distance formula.

The area of triangle with vertices at (–4, –1) , (1, 2), (4, –3)

Here, the area of a triangle cannot be negative. Hence only the numerical value is considered.

The area of triangle with vertices at (–4, –1) , (1, 2), (4, –3)

Here, the area of a triangle cannot be negative. Hence only the numerical value is considered.

An object is placed on the surface of a smooth inclined plane of inclination $theta$ . It takes time t to reach the bottom. If the same objective is allowed to slide down a rough inclined plane of same inclination $theta$ , it takes not to reach the bottom where n is a number greater than 1. The coefficient of friction $mu$ is given by

Two masses A and B each of mass M are fixed together by a massless spring. A force F acts on the mass B as shown in figure. At the instant shown the mass A has acceleration a. What is the acceleration of mass B?

A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force F is applied at one end of the rope, the force which the rope exerts on the block is:

A force-time graph for the motion of a body is shown in figure. Change in linear momentum between 0 and 8 s is:

Three blocks are connected on a horizontal frictionless table by two light strings, one between m₁and m₂, another between m₂ and m₃ . The tensions are T₁ between m₁ and m₂ and T₂ between m₂ and m₃. if m₁ = 1 kg, m₂ = 8 kg, m₃ = 27 kg and F = 36 N applied on m₃, then T₂ will be

A block of mass m is held at the top of an inclined rough plane of angle of inclination $theta$ . The coefficients of static and kinetic friction are $mu subscript 1 end subscript$ and $mu subscript 2 end subscript$ respectively. If the block is pushed down at the verge of slipping, assuming $theta$ < tan^-1 $mu subscript 1 end subscript$ , Its acceleration down the plane is :

Choose the wrong statement