Mathematics Test Series IIT JEE

Mathematics test Series 3 Q1. The domain of the function ( ) A) B) C) D)

(

)

√

[1,2] [2,3] [1,3] [1,2]

Sol: B) Q2. If A, B and C are three sets such that A B=A C And A B= A C, then A) B=C B) A B= C) A=B D) A=C Sol: A) B=C Q3. If

( )

( ), then

is equal to

A) -1 B) 1 C) -2 D) 2 Sol: A) Q4. The value of a for which one root of the quadratic equation ( A) -2/3 B) 1/3

)

(

)

is twice as large as the other is

C) -1/3 D) 2/3 E) Sol: D) 2/3 Q5. If a, b, c are positive integers such that a> b > c and |

|

Then 3a +7b +10c equals A) 10 B) 11 C) 12 D) 13 Sol: D) Assertion – reason Type Q6.Statement -1: The sum of divisors of is (

)(

)(

Statement -2: The number of divisors of P1,P2,………Pr are distinct primes and ( )( )…….( +1)

)(

)(

)

where are natural numbers is

A) STATEMENT -1 is true, STATEMENT -2 is true; STATEMENT -2 is a correct explanation for STATEMENT -1 B) STATEMENT -1 is true, STATEMENT -2 is true; STATEMENT -2 is NOT a correct explanation for STATEMENT -1

C) STATEMENT -1 is True, STATEMENT -2 is False D) STATEMENT -1 is False, STATEMENT -2 is False Sol: B) Q7. Statement :1If n is an odd prime , then greatest integer contained in (

√ )

is divisible by 20 n.

Statement :2 If p is a prime and 1

then ( ) is divisible by p.

A) STATEMENT -1 is true, STATEMENT -2 is true; STATEMENT -2 is a correct explanation for STATEMENT -1 B) STATEMENT -1 is true, STATEMENT -2 is true; STATEMENT -2 is NOT a correct explanation for STATEMENT -1 C) STATEMENT -1 is True, STATEMENT -2 is False D) STATEMENT -1 is False, STATEMENT -2 is False Sol: A) Q8. If a1, a2…….., a3 are in A.P. with common difference d series is A) Sec a1 – sec an B) Cosec a1 – cosec an C) Cot a1- cot an D) Tan a1 – tan an Sol: C) Q9. Let f(x) = {

, then

then sum of the

A) f is discontinuous for every real x B) f is continuous on R C) f is continuous at the points where x is rational D) f is continuous at the points where x is irrational Sol: A) Q10. The number of times the function y= sin -1 (

) doesn’t exist for

A) all values of x for which |x|1 D) none of these Sol: B) Q11. The curve that passes through the point (2,3) and has the property that the segment of any tangent to it lying between the coordinate axes is bisected by the point of contact , is given by : A) B) C) D) ( ) ( ) Sol: B) Q12. ( )

∫

A) Polynomial of degree 3 in cot x B) Polynomial of degree 4 in cot x C) Polynomial of degree 4 in sin x D) Polynomial of degree 4 in tan x

Sol: A) ) Q13. The area of the region bounded by the parabola ( the tangent to the parabola at the point (2,3) and the x-axis is A) 9 B) 12 C) 3 D) 6 Sol: A) Q14. The solution for

∫√

√

of the equation

is

A) 2 B) -√ C)

√

D) 2√ Sol: B) Q15. The curves given by

represents

A) Family of circles with centre on y-axis B) Family of parabola passing through origin C) Family of circles with centre on x-axis D) Family of hyperbola Sol: C)

(

),

Q16. If the sum of the slopes of the lines given by four times their product , then the value of c is

is

A) 2 B) -1 C) 1 D) -2 Sol:A) Q17. Locus of centroid of the triangle whose vertices are (a cost, a sint), (b sin t, -b cos t) and (1,0), where t is a parameter is A) ( B) ( C) ( D) (

) ) ) )

( ) ( ) ( ) ( )

Sol: A) Q18. If the chord along the line of the circle subtends an angle of 300 in the major segment of the circle cut off by the chord then A) 3 B) 6 C) 9 D) 36 Sol: B) Q19. A circle is drawn on a normal chord of the parabola passes through its vertex . radius of the circle is A) √

and

B) √ C) 3√ D) 6√ Sol: C) Q20. The vertices of triangle are A(1,0,0), B(0,2,0), C(0,0,3). If the orthocenter and circumcentre of the triangles are a,b, -111, the a+b is equal to A) 5 B) 10 C) 15 D) 25 Sol: C) Q21. The two lines will be perpendicular , if and only if A) aa’+bb’+cc’=0 B) (a+a’)(b+b’)(c+c’)=0 C) aa’+cc’+1=0 D) aa’+bb’+c’+1=0 Sol:C) Q22. If A.M., G.M. and H.M. in any series are equal then A) the distribution is symmetric B) all the values are same C) the distribution is unimodal D) none of these Sol: B)

Q23. A and B are two students. Their probabilities of solving a problem correctly are ¼ and 1/5 respectively. If the probability of their making a common error is 1/40, and they obtain the answer, then the probability of their answer is correct is A) 1/12 B) 1/20 C) 10/13 D) 13/200 Sol: C) Q24. The acute angle of a rhombus whose side is a mean proportional between its diagonals is A) 150 B) 200 C) 300 D) 800 Sol: C) Q25. Four persons are selected from a group of 4men, 2 women and 3 children. The probability that exactly two of them are men is A) 9/11 B) 10/23 C) 11/24 D) 10/21 Sol: D)