**Ques.** The rationalising factor of a^{1/3} + a^{–1/3} is

(a) a^{1/3} + a^{–1/3}

(b) a^{2/3} + a^{–2/3}

(c) a^{2/3} – a^{–2/3}

(d) a^{2/3} + a^{–2/3} – 1

Ans:- (d)

**Ques. **A uniform rod *BC* of length 6 *cm * and weight 2 *kg* can turn freely about the fixed point *B*. The rod is attached to the point *A* by a string *AC* of length 8* cm.* The points *A* and *B* are in a horizontal line at a distance 10 *cm*. The tension in the string is

(a) 3/5 *kg -wt*

(b) 1/5 *kg-wt*

(c) 2/5 *kg-wt*

(d) None of these

Ans:- (a)

**Ques.** In a certain test a_{i} students gave wrong answers to at least i questions where i = 1, 2, 3, … k. No student gave more than k wrong answers. The total numbers of wrong answers given is

(a)a_{1} + 2a_{2} + 3a_{3} + … + ka_{k}

(b) a_{1} + a_{2} + a_{3} + … + a_{k}

(c) Zero

(d) None of these

Ans:- (b)

**Related:** chemistry nomenclature quiz

**Ques.** Two candidates attempt to solve the equation x2 + px + q = 0. One starts with a wrong value of *p* and finds the roots to be 2 and 6 and the other starts with a wrong value of *q* and find the roots to be 2 and – 9. The roots of the original equation are

(a) 2, 3

(b) 3, 4

(c) –2, – 3

(d) – 3, – 4

Ans:- (d)

**Ques.** The upper ¾ th portion of a vertical pole subtends an angle tan^{–1} (3/5) at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is

(a) 20 m

(b) 40 m

(c) 60 m

(d) 80 m

Ans:- (b)

**Ques.** x^{2} = xy is a relation which is

(a) Symmetric

(b) Reflexive

(c) Transitive

(d) None of these

Ans:- (b)

**Ques.** If the portion of the line lx + my = 1 falling inside the circle x^{2} + y^{2} = a^{2} subtends an angle of 45^{o} at the origin, then

(a) 4[a^{2} (l^{2} + m^{2}) – 1] = a^{2} (l^{2} + m^{2})

(b) 4[a^{2} (l^{2} + m^{2}) – 1] = a^{2} (l^{2} + m^{2}) – 2

(c) 4[a^{2} (l^{2} + m^{2}) – 1] = [a^{2} (l^{2} + m^{2}) – 2]^{2}

(d) None of these

Ans:- (c)

**Ques.** The lines ax + by + c = 0, where 3a + 2b + 4c = 0 are concurrent at the point

(a) (1/2, 3/4)

(b) (1, 3)

(c) (3, 1)

(d) (3/4, 1/2)

Ans:- (d)

**Ques.** A ball is thrown vertically upwards from the ground with velocity 15 *m*/*s* and rebounds from the ground with one-third of its striking velocity. The ratio of its greatest heights before and after striking the ground is equal to

(a) 4 : 1

(b) 9 : 1

(c) 5 : 1

(d) 3 : 1

Ans:- (b)

**Ques.** Which of the following, in case of a discrete data, is not equal to the median

(a) 50th percentile

(b) 5th decile

(c) 2nd quartile

(d) Lower quartile

Ans:- (d)

**Ques.** If 3x = 2y –1 and 2x + 3y + 1 = 0 are two lines of regression, then the coefficient of correlation will be

(a) 0

(b) – 1

(c) 1

(d) None of these

Ans:- (a)

**Ques.** In any group the number of improper subgroups is

(a) 2

(b) 3

(c) Depends on the given group

(d) 1

Ans:- (a)

**Ques.** Binary equivalent of decimal number 0.3125 is

(a) 0101

(b) .1010

(c) .0101

(d) .1101

Ans:- (c)

Related: thermodynamics questions and answers

**Ques. **In a triangle *R * and *r* are the circumradius and inradius respectively. The harmonic mean of the exradii of the triangle is

(a) *R* + 3*r*

(b) *R* + 2*r**
*(c)

*R*+

*r*

(d) 3

*r*

*Ans. (d)*