Exam (elaborations) TS_INTER_JR_ M.P.C

TS JUNIOR INTER
SUB: MATHS-IB IMPORTANT QUESTIONS- 2022-23

I VERY SHORT QUESTIONS:
QUESTION NO-1
1. Find the value of x if the slope of the line passing through (2,5) and (x,3) is 2.
2. Find the distance between the parallel straight lines 3x  4 y  3  0 and 6 x  8 y  1  0

3. Find the value of p, if the straight lines 3 x  7 y  1  0 and 7 x  py  3  0 are mutually perpendicular.

4. Transform the equation into normal form. x  y  1  0
5. Find the equation of the straight line passing through (-4, 5) and cutting off equal nonzero intercepts
on the coordinate axes.
QUESTION NO-2

1. Find the angle which the straight line y  3 x  4 makes with the y-axis
2. (i) Find the value of ‘P’ if the lines 4 x  3 y  7  0, 2 x  py  2  0 and 6 x  5 y  1  0 are concurrent.
(ii) Find the value of P, if the straight lines x + p = 0, y + 2 = 0, 3x + 2y + 5 = 0 are concurrent.
3. Find the value of y, if the line joining (3, y) and (2,7) is parallel to the line joining the points (-1,4)
and (0,6)
4. Find the length of the perpendicular drawn from the point (-2, -3) to the straight line 5x–2y+4=0
5. Find the equation of the straight line perpendicular to the line 5x-3y+1=0 and passing through the
point (4, -3).
QUESTION NO-3
1. If (3, 2, -1), (4, 1, 1) and (6, 2, 5) are three vertices and (4, 2, 2) is the centroid of a tetrahedron, find
the fourth vertex
2. Find the coordinates of the vertex ‘C’ of ABC if its centroid is the origin and the vertices A, B are
(1, 1,1) and (-2,4,1) respectively.
3. Show that the points A (1, 2, 3), B(7, 0, 1), C (–2, 3, 4) are collinear.
4. Find the ratio in which XZ plane divides the lines joining A  2,3, 4  and B 1, 2,3
5. Find x, if the distance between (5, -1,7) and (x, 5, 1) is 9 units.
QUESTION NO-4
1. Find the equation of the plane passing through the point (1,1,1) and parallel to the plane
x + 2y + 3z – 7 =0.
2. Find the equation of the plane passing through the point (-2,1,3) and having (3, -5 ,4)as direction
ratios of its normal
3. Find the equation of the plane whose intercepts on X, Y, Z - axes are 1, 2,4 respectively.
4. Find the angle between the planes x + 2y + 2z – 5 = 0 and 3x + 3y + 2z – 8 = 0
5. Reduce the equation x  2 y  3 z  6  0 of the plane into the normal form.

, QUESTION NO-5

lim  2 x
1. Show that  x  1  3

x0  x 

lim 8 x  3x
2. Find
x   3 x  2x

1 x  3 1 x
lim 3
3. Compute
x0 x

4. find
x

lim
x2  x  x 
lim esin x  1
5. Evaluate
x0 x

QUESTION NO-6

e 3 x  e 3
1. Compute Lt
x0 x
cos x
2. Find lim
x
  
2 x 
 2

lim 11x3  3x  4
3. Find
x   13x 3  5 x 2  7

sin( x  a) tan 2 ( x  a)
4. Compute Lt
x  a2 
x a 2 2




ax 1
5. Compute Lt ( a  0, b  o, b  1)Compute
x0 b x  1


QUESTION NO-7
dy
1. If x  a cos3 t , y  a sin 3 t , then find
dx

2. If f  x   x e x sin x, then find f 1  x 
3 3 x
3. If f ( x )  7 x ( x  0), then find f 1 ( x)

4. If y  aenx  be nx then prove that y "  n2 y .

1 dy ay
5. If y  ea sin x
then prove that  .
dx 1  x2
QUESTION NO-8
dy
1. If y  log  sin  log x   , find .
dx