InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The cofficient of `x^(18)` in the product `(1 + x) (1 - x)^(1) (1 + x + x^(2))^(9)` isA. -84B. 84C. 126D. -126 |
| Answer» Correct Answer - B | |
| 2. |
The positive value of `lambda` for which the coefficient of `x^(2)` in the expression `x^(2) (sqrt(2) + (lambda)/(x^(2)))^(10)` is 720 isA. `sqrt(5)`B. 4C. `2sqrt(5)`D. `3 |
| Answer» Correct Answer - B | |
| 3. |
The coefficient of `t^4` in `((1-t^6)/(1-t))^3` (a) `18` (b) `12` (c) `9` (d) `15`A. 12B. 15C. 10D. 14 |
| Answer» Correct Answer - B | |
| 4. |
Number of rational terms in the expansion of `(sqrt2+4sqrt3)^100` is : (A) 25 (B) 26 (C) 27 (D) 28A. 25B. 26C. 27D. 28 |
| Answer» Correct Answer - B | |
| 5. |
In a triangle the sum of two sides is x and the product of the same is y. If `x^2 - c^2 = y` where c is the third side. Determine the ration of the in-radius and circum-radiusA. `(3y)/(2x(x+c))`B. `(3y)/(2c(x+c))`C. `(3y)/(4x(x+c))`D. `(3y)/(4c(x+c))` |
| Answer» Correct Answer - B | |
| 6. |
In a right - angled isosceles triangle , the ratio of the circumradius and inradius isA. `2(sqrt(2) +1):1`B. `(sqrT(2)+1):1`C. `2:1`D. `sqrt(2):1` |
| Answer» Correct Answer - B | |
| 7. |
The ratio of the area of a regular polygon of `n`sides inscribed in a circle to that of the polygon of same number of sidescircumscribing the same is 3:4. Then the value of `n`is6 (b)4 (c) 8(d) 12A. 1B. 8C. 12D. 6 |
| Answer» Correct Answer - D | |
| 8. |
In a triangle ABC a= 4 , b= 3 , `angle A =60 ^@` ,Then c is root of equation :-A. `c^2+3c-7=0`B. `c^2-3c-7=0`C. `c^2-3c+7=0`D. `c^2+3c+7=0` |
| Answer» Correct Answer - B | |
| 9. |
In a `DeltaABC`, `a=6, b=10,` area of `Delta=15sqrt3` sq units, if `/_ACB` is obtuse and `r` denotes the radius of inscribed circle then value of `r^2=`A. 4B. 5C. 6D. 3 |
| Answer» Correct Answer - D | |
| 10. |
In triangle ABC,a= 5,b=7 and sin A =3/4 how many such triangle are possibleA. 1B. 0C. 2D. Infinite |
| Answer» Correct Answer - B | |
| 11. |
Let `(1+x^2)^2(1+x)^n=A_0+A_1x+A_2x^2+…."if" A_0A_1A_2` are in A.P then the value of n isA. 2B. 3C. 5D. 7 |
| Answer» Correct Answer - A::B | |
| 12. |
If the angle A, B and C of a triangle ABC are in A.P and a:b=1: `sqrt(3)` If c=4 cm then the area (in sq. cm) of this triangle is :A. `5:9:13`B. `5:6:7`C. `4:5:6`D. `3:4:5` |
| Answer» Correct Answer - C | |
| 13. |
With the usual notation , in `Delta ABC` if `angle A+ angle B= 120^@` ,a=sqrt(3)+1 " and " b= sqrt(3)-1` then the ratio `angle A : angle B ` is :A. `7:1`B. `5:3`C. `9:7`D. `3:1` |
| Answer» Correct Answer - A | |
| 14. |
The anlges A,B and C of a triangle ABC are in A.P and a:b=1 `sqrt(3)`.If c=4 cm then the area (in sq. com of this triagle is :)A. `4 sqrt(3)`B. `2/(sqrt(3)`C. `2 sqrt(3)`D. `4/(sqrt(3)` |
| Answer» Correct Answer - C | |
| 15. |
Given `(1-2x+5x^2-10x^3)(1+x)^n=1+a_1x+a_2x^2+...` and that `a_1^2=2a_2` then `n=`A. 6B. 2C. 5D. 3 |
| Answer» Correct Answer - A | |
| 16. |
In `Delta ABC ` , a= 6 ,b=3 and cos (A-B) = 4/5 .Then are of triangle isA. 4 square - unitB. 6 square - unitC. 9 square unitD. 12 square - unit |
| Answer» Correct Answer - C | |
| 17. |
In the expansion of `((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^(1/2)))^10` the term which doers not contain xA. `""^(11)C_(4)-""^(10)C_3`B. `""^10C_7`C. `""^(10)C_(4)`D. `""^(11)C_(5)-""^(10)C_5` |
| Answer» Correct Answer - A::C::D | |
| 18. |
If the middle term of the expansion of `(x^3/3+3/x)^8` is `5670` then sum of all real values of `x` is equal to (A) `6` (B) `3` (C) `0` (D) `2`A. 6B. 80C. 4D. |
| Answer» Correct Answer - C | |
| 19. |
If in a triangle ABC, `2 (cos A)/(a)`+(cos B)/(b)+2(cos C)/c=(a)/(bc)+b/(ca)` then the value of the angle A isA. `pi/3`B. `pi/4`C. `pi/2`D. `pi/2` |
| Answer» Correct Answer - C | |
| 20. |
If `A=75^0,b=45^0,`then prove that `b+csqrt(2)=2a`A. aB. a+b+cC. 2aD. `1/2(a+b+c)` |
| Answer» Correct Answer - C | |
| 21. |
The perimeter of atriangle ABC is 6 times the arihmetic mean of the sines of its angles .If the side a is 1. the `angle A` isA. `30^@`B. `60 ^@`C. `90^@`D. `120^@` |
| Answer» Correct Answer - A | |
| 22. |
Let `/_ABC` is `(B+C)/11=(c+a)/12=(a+b)/12` (where `AB=c,BC=a` and `AC=b)` and `(cosA)/alpha= (cosB)/beta` =(cosC)/gamma` then possible ordered triplet of `(alpha, beta, gamma)` is (A) `(9, 17, 25)` (B) `(19, 7, 25)` (C) `(7, 19, 25)` (D) `(19, 25, 7)`A. (3,4,5)B. (19,7,25)C. (7,19,25)D. (5,12,13) |
| Answer» Correct Answer - C | |
| 23. |
The sum of the co-efficients of all the even powers of x in the expansion of `(2x^2 - 3x + 1)^11` is -A. `2.6^(10)`B. `3.6^(10)`C. `6 ^11`D. none |
| Answer» Correct Answer - B | |
| 24. |
If `Sigma_(r=1)^(10) r(r-1) ""^(10)C_r = k. 2^9`A. 10B. 45C. 90D. 100 |
| Answer» Correct Answer - B | |
| 25. |
The sum of coefficients in integral powers of x in the binominal expansion `(1 - 2 sqrt(x))^(50)` isA. `1/2(3^(50) -1)`B. `1/2(2^(50) + 1)`C. `1/2(3^(50)+1)`D. `1/2(3^(50))` |
| Answer» Correct Answer - C | |
| 26. |
If sin `theta ` and - cos `theta ` are the roots of the equation `ax^2-bx-c=0` where a, b and c the side of a triangle ABC , then cos B is equal to :-A. `1-(c )/(2a)`B. `1-(c )/(a)`C. `1+( c)/(2a)`D. `1+ (c )/(3a)` |
| Answer» Correct Answer - C | |
| 27. |
The term independent of x in the expansion of `((1)/(60) - (x^(8))/(81)).(2x^(2) - (3)/(x^(2)))^(6)` is equal toA. 36B. -108C. -72D. -36 |
| Answer» Correct Answer - D | |
| 28. |
The number of irrational terms in expansion `(7^(1/5)-3^(1/10))^60` is (A) `54` (B) `48` (C) `42` (D) `40`A. 55B. 49C. 48D. 54 |
| Answer» Correct Answer - D | |
| 29. |
Greatest term in the binomial expansion of `(a + 2x)^9` when `a=1 & x =1/3` is :A. `3^rd & 4 ^th`B. `4^th & 5 ^th`C. only `4^(th)`D. only `5 ^th ` |
| Answer» Correct Answer - B | |
| 30. |
If the constant term of the binomial expansion `(2x -1/x)^n` is `-160`, then n is equal to -A. 4B. 6C. 8D. 10 |
| Answer» Correct Answer - B | |
| 31. |
A ratio of the `5^(th) ` term from the beginning and from the end in the binomial expansion of `(""^(2^(1//3))+1/(2(3)^(1//3)))^10` is :A. `1:4(16)^(1//3)`B. `1:2(6)^(1//3)`C. `2(36)^(1//3):1`D. `4(36)^(1//3):1` |
| Answer» Correct Answer - D | |
| 32. |
If the coefficients of `x^(2)` and `x^(3)`are both zero, in the expansion of the expression `(1 + ax + bx^(2)) (1 - 3x)` in powers of x, then the ordered pair (a,b) is equal toA. -28315B. (-54,315)C. (-21 , 714)D. -24861 |
| Answer» Correct Answer - A | |
| 33. |
If some three consecutive coefficeints in the binomial expanison of `(x + 1)^(n)` in powers of x are in the ratio 2 : 15 : 70, then the average of these three coefficients isA. 964B. 625C. 227D. 232 |
| Answer» Correct Answer - D | |