Everyone thinks that maths is a very difficult chapter but if we understand it it will be very easy than any other subject. It’s very easy to understand and learn in whatever profession we are in maths will include in that. It’s very easy to learn maths, it is a very interesting subject. So here we are going to discuss **maths 1b 1st year question question paper**.

**Section A**

- Find the p value as you draw the lines x + p = 0, y + 2 = 0 and 3x + 2y + 5 = 0 together.
- If the straight line is 3x-4y+10=0 then find the length of the perpendicular drawn from the point (3, 4)
- (1, 2, 3) (7, 0, 1) and (-2, 3, 4) show that these points are collinear
- Find the direction cosines of the normal to the plane x+2y+2z-4=0
- Compute: Lim esinx-1

X___0 - Find f(x) if f(x)=xtan-1x
- Prove that yn=n2y if y=aenx
- Find yand dy for the function y=5×2+6x+6 at x=2 when x=0.001
- On an internal 1 define strictly increasing function and strictly decreasing function
**Section B**- A(2, 3) and B(-3, 4) are two given points. Find the equation of locus of P so that the area of a triangle PAB is 8.5
- Find the original equation of the curve when the axes are rotated through an angel 450, the
**transformed equation**of a curve is 17×2-16xy+17y2=225 - In the straight line 3x+4y-1=0 then find the image of the point (1, 2)
- From the first principle find the derivative of Sin2x
- At a point ‘l’ find the length of subtangent, subnormal on the curve x=a(Cost+tSint), y=a(sint-tcost)
- When the length of the edge is 10cm and the volume of a cube is increasing at a rate of 9cm3/sec. How fast is the surface area increasing
**Section C**- If p and q are the length of the perpendiculars from the origin to the straight lines xsec+y cosec=a and xcos-ysin=acos2, prove that 4p2+q2=a2
- If the equation S=ax2+2hxy+by2 +2gx+2fy+c=0represents a pair of parallel straight lines, then show that a) h2=ab b)af2=bg2 c) the distance between the parallel lines=2g
- Show that the lines joining the origin to the points of intersection of the curve x2-xy+y2+3x+3y-2=0 and the stringent line x-y-2=0 are mutually perpendicular

18. 3l+m+5n=0 and 6mn-2nl+5lm=0 are the given equations find the angle between the lines whose direction cosines - Show that dy=1 if y=tan-1

dx 1+x2 - In the 4th quadrant find the angle between the curves 2y2-9x=0, 3×2+4y=0
- Find the value of x, so that the volume of the the box is greatest, from a rectangular sheet a dimension of 30cmx80cm four equal squares of a side xcm are removed at the corners, and the sides are turned up as to form an open rectangular box

**Conclusion: **

These are the 1st year maths 1b question paper which is very important for higher studies. This will be very helpful in all kinds of careers. It’s very easy. Mathematics is very easy to understand and learn. **1st year maths** 1b is very helpful for all competitive exams.