TU FoHSS | Mathematics
If $A={1,2,3,4}$ and $B={3,4,5}$, then $n(A\cup B)$ is
Answer: 5
Model set 1, Q1: explanation →In a class of students, $n(A)=20$, $n(B)=15$ and $n(A\cap B)=5$. Then $n(A\cup B)$ equals
Answer: 30
Model set 1, Q2: explanation →If $f(x)=2x+3$, then $f(f(1))$ is
Answer: 13
Model set 1, Q3: explanation →If $f(x)=x^2-1$ and $g(x)=x+2$, then $(f\circ g)(1)$ is
Answer: 8
Model set 1, Q4: explanation →If $2^x=32$ and $3^y=81$, then $x+y$ is
Answer: 9
Model set 1, Q5: explanation →The value of $8^{2/3}\times 9^{1/2}$ is
Answer: 12
Model set 1, Q6: explanation →The value of $\log_2 64-\log_3 27$ is
Answer: 3
Model set 1, Q7: explanation →If $\log x+\log(x-3)=1$ (base 10), then $x$ is
Answer: 5
Model set 1, Q8: explanation →The 5th term of the arithmetic progression $3,7,11,\dots$ is
Answer: 19
Model set 1, Q9: explanation →The sum of the first 10 terms of the AP $2,5,8,\dots$ is
Answer: 155
Model set 1, Q10: explanation →The sum of the first 5 terms of the GP $2,6,18,\dots$ is
Answer: 242
Model set 1, Q11: explanation →The sum to infinity of the series $8+4+2+1+\dots$ is
Answer: 16
Model set 1, Q12: explanation →The determinant of $\begin{pmatrix}2&3\1&4\end{pmatrix}$ is
Answer: 5
Model set 1, Q13: explanation →The matrix $\begin{pmatrix}k&4\1&2\end{pmatrix}$ is singular when $k$ equals
Answer: 2
Model set 1, Q14: explanation →The value of $^5P_2$ is
Answer: 20
Model set 1, Q15: explanation →The value of $^8C_3$ is
Answer: 56
Model set 1, Q16: explanation →The number of distinct arrangements of the letters of the word BOOK is
Answer: 12
Model set 1, Q17: explanation →The value of $\log_2 64 + \log_3 81$ is
Answer: 10
Model set 2, Q1: explanation →If $\log_x 125 = 3$, then $x$ equals
Answer: 5
Model set 2, Q2: explanation →The value of $\log_{10} 2 + \log_{10} 5$ is
Answer: 1
Model set 2, Q3: explanation →If $\log_3 (x-1) = 2$, then $x$ is
Answer: 10
Model set 2, Q4: explanation →If $\alpha$ and $\beta$ are the roots of $x^2-5x+6=0$, then $\alpha^2+\beta^2$ is
Answer: 13
Model set 2, Q39: explanation →The sum of the first 20 terms of the AP 3, 7, 11, ... is
Answer: 820
Model set 2, Q40: explanation →The sum to infinity of the series $8+4+2+1+\dots$ is
Answer: 16
Model set 2, Q41: explanation →The number of different arrangements of the letters of the word LEVEL is
Answer: 30
Model set 2, Q42: explanation →The value of $^8C_3$ is
Answer: 56
Model set 2, Q43: explanation →The coefficient of $x^2$ in the expansion of $(1+x)^6$ is
Answer: 15
Model set 2, Q44: explanation →The solution set of $|2x-3|<5$ is
Answer: $-1<x<4$
Model set 2, Q45: explanation →The median of 2, 4, 6, 8, 10, 12 is
Answer: 7
Model set 1, Q40: explanation →The standard deviation of the data 2, 4, 6, 8 is
Answer: $\sqrt5$
Model set 1, Q41: explanation →A card is drawn from a well-shuffled pack of 52 cards. The probability that it is a king or a queen is
Answer: $\tfrac{2}{13}$
Model set 1, Q42: explanation →Two fair coins are tossed. The probability of getting exactly one head is
Answer: $\tfrac12$
Model set 1, Q43: explanation →Two dice are thrown together. The probability that the sum is 8 is
Answer: $\frac{5}{36}$
Model set 2, Q15: explanation →A bag has 3 red and 5 blue balls. Two balls are drawn one after another without replacement. The probability that both are red is
Answer: $\frac{3}{28}$
Model set 2, Q16: explanation →If $A$ and $B$ are independent events with $P(A)=0.4$ and $P(B)=0.5$, then $P(A\cup B)$ is
Answer: 0.7
Model set 2, Q17: explanation →A fair coin is tossed three times. The probability of getting at least one head is
Answer: $\frac{7}{8}$
Model set 2, Q18: explanation →The mean of six numbers is 15. When one number is removed, the mean of the remaining five becomes 14. The number removed is
Answer: 20
Model set 2, Q34: explanation →The median of the data 3, 7, 5, 13, 9, 11 is
Answer: 8
Model set 2, Q35: explanation →A data set has mean 50 and standard deviation 10. Its coefficient of variation is
Answer: 20%
Model set 2, Q36: explanation →The slope of the line joining $(1,2)$ and $(3,8)$ is
Answer: 3
Model set 1, Q33: explanation →The equation of the line with slope 2 and passing through $(0,-3)$ is
Answer: $y=2x-3$
Model set 1, Q34: explanation →The distance between $(1,2)$ and $(4,6)$ is
Answer: 5
Model set 1, Q35: explanation →The line $4x+ky=5$ is parallel to $2x+3y=6$ when $k$ equals
Answer: 6
Model set 1, Q36: explanation →The distance between the points $(1,2)$ and $(4,6)$ is
Answer: 5
Model set 2, Q19: explanation →The equation of the line through $(2,3)$ with slope 2 is
Answer: $2x-y-1=0$
Model set 2, Q20: explanation →The radius of the circle $x^2+y^2-6x+8y=0$ is
Answer: 5
Model set 2, Q21: explanation →The area of the triangle with vertices $(0,0)$, $(4,0)$ and $(0,6)$ is
Answer: 12 square units
Model set 2, Q22: explanation →The perpendicular distance of the point $(3,4)$ from the line $3x+4y-5=0$ is
Answer: 4
Model set 2, Q23: explanation →The slope of the line $3x-6y+5=0$ is
Answer: $\frac12$
Model set 2, Q24: explanation →The value of $\tan60^\circ\cdot\cot30^\circ$ is
Answer: 3
Model set 1, Q37: explanation →If $\sin\theta=\tfrac35$ and $\theta$ is acute, then $\tan\theta$ is
Answer: $\tfrac34$
Model set 1, Q38: explanation →The value of $\sin75^\circ\cos15^\circ+\cos75^\circ\sin15^\circ$ is
Answer: 1
Model set 1, Q39: explanation →The value of $\sin30^\circ\cos60^\circ+\cos30^\circ\sin60^\circ$ is
Answer: 1
Model set 2, Q25: explanation →If $\sin\theta=\frac35$ and $\theta$ is acute, then $\tan\theta$ is
Answer: $\frac34$
Model set 2, Q26: explanation →If $\cos A=\frac45$ and $A$ is acute, then $\sin2A$ is
Answer: $\frac{24}{25}$
Model set 2, Q27: explanation →The value of $\cos75^\circ\cos15^\circ$ is
Answer: $\frac14$
Model set 2, Q28: explanation →The period of the function $\sin3x$ is
Answer: $\frac{2\pi}{3}$
Model set 2, Q29: explanation →$\displaystyle\lim_{x\to2}\dfrac{x^2-4}{x-2}$ is
Answer: 4
Model set 1, Q29: explanation →$\displaystyle\lim_{x\to0}\dfrac{\sin3x}{x}$ is
Answer: 3
Model set 1, Q30: explanation →The derivative of $x^3-2x^2+5$ with respect to $x$ is
Answer: $3x^2-4x$
Model set 1, Q31: explanation →The derivative of $e^{2x}$ is
Answer: $2e^{2x}$
Model set 1, Q32: explanation →The derivative of $x^2e^x$ with respect to $x$ is
Answer: $e^x(x^2+2x)$
Model set 2, Q30: explanation →The value of $\lim_{x\to0}\frac{\sin5x}{3x}$ is
Answer: $\frac53$
Model set 2, Q32: explanation →The local maximum value of $f(x)=x^3-3x$ is
Answer: 2
Model set 2, Q33: explanation →If $\vec a=(2,3)$ and $\vec b=(1,-1)$, then $\vec a\cdot\vec b$ is
Answer: -1
Model set 1, Q49: explanation →The vectors $\vec a=(1,2)$ and $\vec b=(3,k)$ are perpendicular when $k$ equals
Answer: $-\tfrac32$
Model set 1, Q50: explanation →If $\vec a=2\hat i+\hat j-\hat k$ and $\vec b=\hat i+3\hat j+\hat k$, then $\vec a\cdot\vec b$ is
Answer: 4
Model set 2, Q37: explanation →The vectors $2\hat i+p\hat j$ and $3\hat i-6\hat j$ are perpendicular when $p$ equals
Answer: 1
Model set 2, Q38: explanation →The determinant of the matrix $\begin{bmatrix}1&2\3&4\end{bmatrix}$ is
Answer:
Model set 2, Q5: explanation →If $A=\begin{bmatrix}2&1\0&3\end{bmatrix}$ and $B=\begin{bmatrix}1&0\4&2\end{bmatrix}$, the element in the second row and first column of $AB$ is
Answer: 12
Model set 2, Q6: explanation →If $\begin{vmatrix}x&2\3&4\end{vmatrix}=2$, then $x$ is
Answer: 2
Model set 2, Q7: explanation →The matrix $\begin{bmatrix}k&2\4&8\end{bmatrix}$ is singular when $k$ equals
Answer: 1
Model set 2, Q8: explanation →The volume of a cylinder of radius 7 cm and height 10 cm is (take $\pi=\frac{22}{7}$)
Answer: 1540 cm$^3$
Model set 2, Q11: explanation →A cone has base radius 5 cm and slant height 13 cm. Its volume is
Answer: $100\pi$ cm$^3$
Model set 2, Q12: explanation →The surface area of a sphere is 616 cm$^2$. Its radius is (take $\pi=\frac{22}{7}$)
Answer: 7 cm
Model set 2, Q13: explanation →The diagonal of a rectangle is 13 cm and one side is 12 cm. Its area is
Answer: 60 cm$^2$
Model set 2, Q14: explanation →A rectangle has perimeter 36 cm and length 10 cm. Its area is
Answer: 80 cm$^2$
Model set 1, Q26: explanation →The volume of a cylinder of radius 7 cm and height 10 cm (take $\pi=22/7$) is
Answer: 1540 cm$^3$
Model set 1, Q27: explanation →The total surface area of a cube is 150 cm$^2$. Its volume is
Answer: 125 cm$^3$
Model set 1, Q28: explanation →The value of $\int_0^2(3x^2+2x),dx$ is
Answer: 12
Model set 2, Q31: explanation →A price of Rs 800 is increased by 25% and the new price is then decreased by 20%. The final price is
Answer: Rs 800
Model set 1, Q18: explanation →The LCM of 12, 18 and 24 is
Answer: 72
Model set 1, Q19: explanation →Rs 1200 is divided in the ratio 3:5. The larger share is
Answer: Rs 750
Model set 1, Q20: explanation →A can finish a job in 12 days and B can finish it in 6 days. Working together they finish it in
Answer: 4 days
Model set 1, Q21: explanation →The simple interest on Rs 5000 at 8% per annum for 3 years is
Answer: Rs 1200
Model set 1, Q22: explanation →The compound interest on Rs 10000 at 10% per annum for 2 years is
Answer: Rs 2100
Model set 1, Q23: explanation →An article bought for Rs 400 is sold for Rs 500. The profit percent is
Answer: 25%
Model set 1, Q24: explanation →A shopkeeper marks an article 40% above its cost price and allows a 10% discount. His profit percent is
Answer: 26%
Model set 2, Q46: explanation →Four of five numbers are 8, 10, 12 and 14, and the average of all five is 12. The fifth number is
Answer: 16
Model set 1, Q25: explanation →Find the next term: 2, 6, 12, 20, 30, ?
Answer: 42
Model set 1, Q44: explanation →What comes next in the series 2, 6, 12, 20, 30, ... ?
Answer: 42
Model set 2, Q47: explanation →If CAT is coded as DBU, then DOG is coded as
Answer: EPH
Model set 1, Q45: explanation →In a certain code, CAT is written as ECV. How is DOG written in that code?
Answer: FQI
Model set 2, Q49: explanation →The angle between the hour hand and the minute hand at 3:30 is
Answer: $75^\circ$
Model set 1, Q46: explanation →What is the angle between the hour hand and the minute hand of a clock at 4:30?
Answer: $45^\circ$
Model set 2, Q48: explanation →Ram ranks 7th from the top in a class of 30 students. His rank from the bottom is
Answer: 24th
Model set 1, Q47: explanation →Ram is 7th from the top and 12th from the bottom in a class. How many students are in the class?
Answer: 18
Model set 2, Q50: explanation →Doctor is to hospital as teacher is to
Answer: school
Model set 1, Q48: explanation →The compound interest on Rs 10,000 for 2 years at 10% per annum, compounded annually, is
Answer: Rs 2,100
Model set 2, Q9: explanation →The difference between compound interest and simple interest on Rs 4,000 for 2 years at 10% per annum is
Answer: Rs 40
Model set 2, Q10: explanation →