Question 1 :
Number of 4 digit positive integer if the product of their digits is divisible by 3 is:
Question 2 :
In a plane there are two families of lines y = x + r, y = - x + r. where r ∈ {0, 1, 2, 3, 4}. The number of squares of diagonals of the length 2 formed by the lines is -
Question 3 :
The no. of 5 digit nos. using 0, 1, 2, 3, 4 with repetition allowed which are divisible by 4.
Question 4 :
All the five digit numbers that can be formed using the digits $1, 2, 3, 4, 5$, without repetition, are arranged in the decreasing order of magnitude. The rank of the number $34215$ is
Question 5 :
$In\quad how\quad many\quad ways\quad can\quad 5\quad keys\quad be\quad put\quad in\quad a\quad ring\quad \quad $
Question 6 :
If there are three objects, then the number of permutations of these objects taken two at a time is 8.<br/>
Question 7 :
How many five letter words, with meaning or without meaning, can be formed by using the letters $A,B,C$ such that letter $A$ cannot be repeated but $B$ and $C$ can be used any number of times
Question 8 :
<font>Let S be the set of all functions from the set A to the set A. If n(a) = k, then n(S) is</font></p>
Question 9 :
In how many ways 3 letters can be posted in 4 letter-boxes, if all the letters are not posted in the same letter-box?
Question 10 :
<font>In how many ways can 5 boys and 5 girls sit in a circle so that no boys sit together</font></p>
Question 11 :
<sup>n</sup>C<sub>r</sub> + 2 <sup>n</sup>C<sub>r − 1</sub> + <sup>n</sup>C<sub>r − 2</sub> is equal to
Question 12 :
A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is drawn without replacement. The probability that both the tickets will show even number, is
Question 13 :
A carton contains 12 green and 8 blue bulbs .2 bulbs are drawn at random. Find the probability that they are of same colour.
Question 14 :
An anti-aircraft gun take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are {tex} 0.4,0.3 , 0.2 {/tex}and {tex}0.1{/tex}, respectively. The probability that the gun hits the plane is
Question 16 :
A five digits number is formed by writing the digits 1, 2, 3, 4, 5 in a random order without repetitions. Then the probability that the number is divisible by 4, is
Question 17 :
The probability that in a year of the 22nd century chosen at random there will be 53 Sundays, is
Question 18 :
The equation of the hyperbola whose foci are (6, 4) and (-4, 4) and eccentricity 2 is-
Question 19 :
The coordinates of the extremities of the latus rectum of the parabola {tex} 5 y ^ { 2 } = 4 x {/tex} are
Question 20 :
AB is a chord of the parabola y<sup>2</sup> = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-
Question 21 :
The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x-y+1=0 is
Question 22 :
The centre of the circle passing through the point (0, 1) and touching the curve y = x<sup>2</sup> at (2, 4) is
Question 23 :
ABCDIs a square whose side isa. If AB and AD are axes of coordinates, the equation of the circle circumscribing the square will be
Question 24 :
If the lines joining the foci of the ellipse $\frac{x^{2}}{a^{2}\text{\ \ }} + \frac{y^{2}}{b^{2}}\ = \ 1$, where a > b and an extremity of its minor axis are inclined at an angle 60<sup>∘</sup>, then the eccentricity of the ellipse is
Question 25 :
If y = 2x + k is a tangent to the curve x<sup>2</sup> = 4y, then k is equal to
