Q1. The equation of the circle, whose centre is the point of intersection of the lines 2x – 3y + 4 = 0 and 3x + 4x – 5 = 0 and passes through the origin, is
(a) |
17(x2 + y2) + 2x – 44y = 0 |
(b) |
17(x2 + y2) + 2x + 44y = 0
|
(c) |
17(x2 + y2) + 2x – 44y = 0 |
(d) |
None of these |
Q2. The equation of the circle which touches the axis of y at a distance + 4 from the origin and cuts off an intercept 6 from the axis of x is
(a) |
x2 + y2 – 10x – 8y + 16 = 0 |
(b) |
x2 + y2 + 10x – 8y + 16 = 0 |
(c) |
x2 + y2 – 10x + 8y + 16 = 0 |
(d) |
None of these |
Q3. A circle of radius 2 lies in the first quadrant and touches both the axes of coordinates. The equation of the circle with centre at (6, 5) and touching the above circle externally is
(a) |
x2 + y2 + 12x – 10y + 52 = 0 |
(b) |
x2 + y2 – 12x + 10y + 52 = 0 |
(c) |
x2 + y2 – 12x – 10y + 52 = 0 |
(d) |
None of these |
Q4. The equation of the circle which has two normals (x – 1) (y – 2) = 0 and a tangent 3x + 4y = 6 is
(a) |
x2 + y2 – 2x – 4y + 4 = 0 |
(b) |
x2 + y2 + 2x – 4y + 5 = 0 |
(c) |
x2 + y2 = 5 |
(d) |
(x + 3)2 + (y – 4)2 = 5 |
Q5. The coordinates of the middle point of the chord which the circle x
2 + y
2 + 4x – 2y – 3 = 0 cuts off on the line y = x + 2, are
Q6. The equation of tangent to the circle x
2 + y
2 = 25, which is inclined at an angle of 30° to the axis of x, is
Q7. The limiting points of the coaxal system determined by the circle x
2 + y
2 – 2x – 6y + 9 = 0 and x
2 + y
2 + 6x – 2y + 1 = 0 are
(a) |
 |
(b) |
 |
(c) |
 |
(d) |
None of these |
Q8.The number of common tangents to the circle x
2 + y
2 = 4 and x
2 + y
2 – 8x + 12 = 0 is
Q9.The equation of the circle passing through (1, 0) and (0, 1) and having smallest possible radius is
(a) |
x2 + y2 – x – y = 0 |
(b) |
x2 + y2 + x + y = 0 |
(c) |
x2 + y2 – 2x – y = 0 |
(d) |
x2 + y2 – x – 2y = 0 |
Q10.The radical axis of the circles, belonging to the coaxal system of circles whose limiting points are (1, 3) and (2, 6), is
(a) |
x – 3y – 15 = 0 |
(b) |
x + 3y – 15 = 0 |
(c) |
x – 3y + 15 = 0 |
(d) |
2x + 3y – 15 = 0 |
Q11. The equation of the circle, which touches the circle x
2 + y
2 – 6x + 6y + 17 = 0 externally and to which the lines x
2 – 3xy – 3x + 9y = 0 are normal, is
(a) |
x2 + y2 – 6x – 2y – 1 = 0 |
(b) |
x2 + y2 + 6x – 2y + 1 = 0 |
(c) |
x2 + y2 – 6x – 2y + 1 = 0 |
(d) |
None of these |
Q12.A line meets the coordinate axes in A and B, and a circle is circumscribing triangle AOB where O is the origin. If m, n are the distances of the tangents to this circle at the origin from the points A and B respectively, then the diameter of the circle is
(a) |
m(m + n) |
(b) |
n(m + n) |
(c) |
m – n |
(d) |
m + n
|
Q13. Four distinct points (2K, 3K) , (1, 0), (0, 1) and (0, 0) lie on a circle when
(a) |
all values of K are integral |
(b) |
0 < K < 1 |
(c) |
K < 0 |
(d) |
For two values of K |
Q14.The length of the tangent from any point on the circle 15x
2 + 15y
2 – 48x + 64y = 0 to the two circles
5x
2 + 5y
2 – 24x + 32y + 75 = 0 and 5x
2 + 5y
2 – 48x + 64y + 300 = 0 are in the ratio of
(a) |
1 : 2 |
(b) |
2 : 3 |
(c) |
3 : 4 |
(d) |
none of these |
Q15.The circles x
2 + y
2 + x + y = 0 and x
2 + y
2 + x – y = 0 intersect at an angle of
(a) |
p/6 |
(b) |
p/4 |
(c) |
p/3 |
(d) |
p/2 |
Q16. The difference of the tangents of the angles which the lines
x
2(sec
2q - sin
2q) – 2xy tan
q + y
2 sin
2q = 0 with the x – axis is
(a) |
2 tan q |
(b) |
2 |
(c) |
2 cot q |
(d) |
sin 2 q |
Q17. If the line y =
cuts the curve x3 + y3 + 3xy + 5x2 + 3y3 + 4x + 5y -1 = 0 at the points A, B, C then OA . OB. OC is
(a) |
 |
(b) |
 |
(c) |
 |
(d) |
None of these |
Q18.A variable line drawn through the point (1, 3) meets the x-axis at A and y-axis at B. If the rectangle OAPB is completed, where ‘O’ is the origin, then locus of ‘P’ is
(a) |
 |
(b) |
x + 3y = 1 |
(c) |
 |
(d) |
3x + y = 1 |
Q19.ABC is a right angled isosceles triangle, right angled at A(2, 1). If the equation of side BC is 2x + y = 3, then the combined equation of lines AB and AC is
(a) |
3x2 – 3y2 + 8xy + 20x + 10y + 25 = 0 |
(b) |
3x2 – 3y2 + 8xy – 20x – 10y + 25 = 0 |
(c) |
3x2 – 3y2 + 8xy + 10x + 15y + 20 = 0 |
(d) |
None of these |
Q20. If the line y = x is one of the angle bisector of the pair of lines ax
2 + 2hxy + by
2 = 0, then
(a) |
a + b = 0 |
(b) |
h = 0 |
(c) |
a – b = 0 |
(d) |
None of these |
Q21. If the sum of the slopes of the lines given by x
2 – 2cxy – 7y
2 = 0 is four times their product, then c has the value:
(a) |
1 |
(b) |
– 1 |
(c) |
2 |
(d) |
– 2 |
Q22. If one of the lines given by 6x
2 – xy + 4cy
2 = 0 is 3x + 4y = 0, then c equals:
(a) |
1 |
(b) |
– 1 |
(c) |
3 |
(d) |
– 3 |
Q23. If the pair of straight lines x
2 – 2pxy – y
2 = 0 and x
2 – 2qxy – y
2 = 0 be such that each pair bisects the angle between the other pair, then
(a) |
p = q |
(b) |
p = – q |
(c) |
pq = 1 |
(d) |
pq = – 1 |
Q24. The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is
Q25. Let L
1 be a straight line passing through the origin and L
2 be the straight line x + y = 1. If the intercepts made by the circle x
2 + y
2 – x + 3y = 0 on L
1 and L
2 are equal, then which of the following equations can represents L
1?
(a) |
x + y = 0 |
(b) |
x – y = 0 |
(c) |
x + 7y = 0 |
(d) |
x – 7y = 0 |
Q26.The number of numbers are there between 100 and 1000 in which all the digits are distinct is
(a) |
648 |
(b) |
548 |
(c) |
448 |
(d) |
none of these |
Q27.The number of arrangements of the letters of the word ‘CALCUTTA’ is
(a) |
5040 |
(b) |
2550 |
(c) |
40320 |
(d) |
10080 |
Q28. How many different words can be formed with the letters of the word “PATLIPUTRA” without changing the position of the vowels and consonants?
(a) |
2160 |
(b) |
180 |
(c) |
720 |
(d) |
none of these |
Q29. How many different words ending and beginning with a consonant can be formed with the letters of the word ‘EQUATION’?
(a) |
720 |
(b) |
4320 |
(c) |
1440 |
(d) |
none of these |
Q30.The number of 4 digit numbers divisible by 5 which can be formed by using the digits 0, 2, 3, 4, 5 is
(a) |
36 |
(b) |
42 |
(c) |
48 |
(d) |
none of these |
Q31.The number of ways in which 5 biscuits can be distributed among two children is
(a) |
32 |
(b) |
31 |
(c) |
30 |
(d) |
none of these |
Q32.How many five-letter words containing 3 vowels and 2 consonants can be formed using the letters of the word “EQUATION” so that the two consonants occur together?
(a) |
1380 |
(b) |
1420 |
(c) |
1440 |
(d) |
none |
Q33.If the letters of the word ‘RACHIT’ are arranged in all possible ways and these words are written out as in a dictionary, then the rank of this word is
(a) |
365 |
(b) |
702 |
(c) |
481 |
(d) |
none of these |
Q34.On the occasion of Dipawali festival each student of a class sends greeting cards to the others. If there are 20 students in the class, then the total number of greeting cards exchanged by the students is
(a) |
20C2 |
(b) |
2 . 20C2 |
(c) |
2 . 20P2 |
(d) |
none of these |
Q35.The sum of the digits in the unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time is
(a) |
18 |
(b) |
108 |
(c) |
432 |
(d) |
144 |
Q36.How many six digits numbers can be formed in decimal system in which every succeeding digit is greater than its preceding digit
(a) |
9P6 |
(b) |
10P6 |
(c) |
9P3 |
(d) |
none of these |
Q37.How many ways are there to arrange the letters in the work GARDEN with the vowels in alphabetical order?
(a) |
120 |
(b) |
240 |
(c) |
360 |
(d) |
480 |
Q38.A five-digit numbers divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done is
(a) |
216 |
(b) |
240 |
(c) |
600 |
(d) |
3125 |
Q39.How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?
(a) |
16 |
(b) |
36 |
(c) |
60 |
(d) |
180 |
Q40.The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is
(a) |
40 |
(b) |
60 |
(c) |
80 |
(d) |
100 |
Vriti Edustore
